From 1a2899e85da43c89c96bd1ba457ea3236dd598ac Mon Sep 17 00:00:00 2001 From: TimWeaving Date: Wed, 5 Oct 2022 00:10:35 +0100 Subject: [PATCH 01/11] Erroneous comma causing tuple in CCSD opeartor --- symmer/chemistry/build_molecule.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/symmer/chemistry/build_molecule.py b/symmer/chemistry/build_molecule.py index 70bd94d3..d27f6830 100644 --- a/symmer/chemistry/build_molecule.py +++ b/symmer/chemistry/build_molecule.py @@ -219,7 +219,7 @@ def data_dictionary(self): if self.pyscf_obj.run_ccsd: mol_data['calculated_properties']['CCSD'] = { 'energy':self.ccsd_energy, 'converged':bool(self.pyscf_obj.pyscf_ccsd.converged)} - mol_data['auxiliary_operators']['UCCSD_operator'] = safe_PauliwordOp_to_dict(self.UCC_q), + mol_data['auxiliary_operators']['UCCSD_operator'] = safe_PauliwordOp_to_dict(self.UCC_q) if self.pyscf_obj.run_fci: mol_data['calculated_properties']['FCI'] = { 'energy':self.fci_energy, 'converged':bool(self.pyscf_obj.pyscf_fci.converged)} From 83bd69901b702b6ded5c1bf34a91cb1c0ff133a6 Mon Sep 17 00:00:00 2001 From: TimWeaving Date: Wed, 5 Oct 2022 16:49:01 +0100 Subject: [PATCH 02/11] Adding Hamiltonians for which we may calculate the FCI energy --- tests/hamiltonian_data/B+_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/B+_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/BH2+_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/BH2+_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/BH_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/BH_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/B_STO-3G_DOUBLET_BK.json | 1 + tests/hamiltonian_data/B_STO-3G_DOUBLET_JW.json | 1 + tests/hamiltonian_data/BeH+_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/BeH+_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/BeH2_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/BeH2_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/Be_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/Be_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/CH+_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/CH+_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/CH2_STO-3G_TRIPLET_BK.json | 1 + tests/hamiltonian_data/CH2_STO-3G_TRIPLET_JW.json | 1 + tests/hamiltonian_data/CH3OH_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/CH3OH_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/CH4_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/CH4_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/CO2_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/CO2_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/CO_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/CO_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/C_STO-3G_TRIPLET_BK.json | 1 + tests/hamiltonian_data/C_STO-3G_TRIPLET_JW.json | 1 + tests/hamiltonian_data/F2_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/F2_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/H2O_STO-3G_SINGLET_BK.json | 2 +- tests/hamiltonian_data/H2O_STO-3G_SINGLET_JW.json | 2 +- tests/hamiltonian_data/H2S_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/H2S_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/H2_3-21G_SINGLET_BK.json | 1 + tests/hamiltonian_data/H2_3-21G_SINGLET_JW.json | 1 + tests/hamiltonian_data/H2_6-311G_SINGLET_BK.json | 1 + tests/hamiltonian_data/H2_6-311G_SINGLET_JW.json | 1 + tests/hamiltonian_data/H2_6-31G_SINGLET_BK.json | 1 + tests/hamiltonian_data/H2_6-31G_SINGLET_JW.json | 1 + tests/hamiltonian_data/H3+_3-21G_SINGLET_BK.json | 1 + tests/hamiltonian_data/H3+_3-21G_SINGLET_JW.json | 1 + tests/hamiltonian_data/H3+_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/H3+_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/H3O+_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/H3O+_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/H6_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/H6_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/HCN_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/HCN_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/HCl_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/HCl_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/HF_3-21G_SINGLET_BK.json | 1 + tests/hamiltonian_data/HF_3-21G_SINGLET_JW.json | 1 + tests/hamiltonian_data/HF_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/HF_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/HOOH_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/HOOH_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/HeH+_3-21G_SINGLET_BK.json | 1 + tests/hamiltonian_data/HeH+_3-21G_SINGLET_JW.json | 1 + tests/hamiltonian_data/HeH+_6-311G_SINGLET_BK.json | 1 + tests/hamiltonian_data/HeH+_6-311G_SINGLET_JW.json | 1 + tests/hamiltonian_data/LiH_3-21G_SINGLET_BK.json | 1 + tests/hamiltonian_data/LiH_3-21G_SINGLET_JW.json | 1 + tests/hamiltonian_data/LiH_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/LiH_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/LiOH_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/LiOH_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/Li_STO-3G_DOUBLET_BK.json | 1 + tests/hamiltonian_data/Li_STO-3G_DOUBLET_JW.json | 1 + tests/hamiltonian_data/MgH2_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/MgH2_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/Mg_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/Mg_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/N2_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/N2_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/NH2-_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/NH2-_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/NH3_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/NH3_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/NH4+_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/NH4+_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/NH_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/NH_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/N_STO-3G_QUARTET_BK.json | 1 + tests/hamiltonian_data/N_STO-3G_QUARTET_JW.json | 1 + tests/hamiltonian_data/NaH_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/NaH_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/NeH+_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/NeH+_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/O2_STO-3G_TRIPLET_BK.json | 1 + tests/hamiltonian_data/O2_STO-3G_TRIPLET_JW.json | 1 + tests/hamiltonian_data/OH-_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/OH-_STO-3G_SINGLET_JW.json | 1 + tests/hamiltonian_data/O_STO-3G_TRIPLET_JW.json | 1 + tests/hamiltonian_data/SiH4_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/SiH4_STO-3G_SINGLET_JW.json | 1 + 97 files changed, 97 insertions(+), 2 deletions(-) create mode 100644 tests/hamiltonian_data/B+_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/B+_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/BH2+_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/BH2+_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/BH_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/BH_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/B_STO-3G_DOUBLET_BK.json create mode 100644 tests/hamiltonian_data/B_STO-3G_DOUBLET_JW.json create mode 100644 tests/hamiltonian_data/BeH+_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/BeH+_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/BeH2_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/BeH2_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/Be_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/Be_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/CH+_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/CH+_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/CH2_STO-3G_TRIPLET_BK.json create mode 100644 tests/hamiltonian_data/CH2_STO-3G_TRIPLET_JW.json create mode 100644 tests/hamiltonian_data/CH3OH_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/CH3OH_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/CH4_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/CH4_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/CO2_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/CO2_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/CO_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/CO_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/C_STO-3G_TRIPLET_BK.json create mode 100644 tests/hamiltonian_data/C_STO-3G_TRIPLET_JW.json create mode 100644 tests/hamiltonian_data/F2_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/F2_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/H2S_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/H2S_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/H2_3-21G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/H2_3-21G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/H2_6-311G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/H2_6-311G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/H2_6-31G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/H2_6-31G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/H3+_3-21G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/H3+_3-21G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/H3+_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/H3+_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/H3O+_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/H3O+_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/H6_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/H6_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/HCN_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/HCN_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/HCl_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/HCl_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/HF_3-21G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/HF_3-21G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/HF_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/HF_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/HOOH_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/HOOH_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/HeH+_3-21G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/HeH+_3-21G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/HeH+_6-311G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/HeH+_6-311G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/LiH_3-21G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/LiH_3-21G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/LiH_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/LiH_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/LiOH_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/LiOH_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/Li_STO-3G_DOUBLET_BK.json create mode 100644 tests/hamiltonian_data/Li_STO-3G_DOUBLET_JW.json create mode 100644 tests/hamiltonian_data/MgH2_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/MgH2_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/Mg_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/Mg_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/N2_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/N2_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/NH2-_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/NH2-_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/NH3_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/NH3_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/NH4+_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/NH4+_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/NH_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/NH_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/N_STO-3G_QUARTET_BK.json create mode 100644 tests/hamiltonian_data/N_STO-3G_QUARTET_JW.json create mode 100644 tests/hamiltonian_data/NaH_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/NaH_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/NeH+_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/NeH+_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/O2_STO-3G_TRIPLET_BK.json create mode 100644 tests/hamiltonian_data/O2_STO-3G_TRIPLET_JW.json create mode 100644 tests/hamiltonian_data/OH-_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/OH-_STO-3G_SINGLET_JW.json create mode 100644 tests/hamiltonian_data/O_STO-3G_TRIPLET_JW.json create mode 100644 tests/hamiltonian_data/SiH4_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/SiH4_STO-3G_SINGLET_JW.json diff --git a/tests/hamiltonian_data/B+_STO-3G_SINGLET_BK.json b/tests/hamiltonian_data/B+_STO-3G_SINGLET_BK.json new file mode 100644 index 00000000..47a25fb7 --- /dev/null +++ b/tests/hamiltonian_data/B+_STO-3G_SINGLET_BK.json @@ -0,0 +1 @@ +{"hamiltonian": {"IIIIIIIIII": [-15.807523675303841, 0.0], "IIIIIIIIIZ": [0.14669318599473274, 0.0], "IIIIIIIIZI": [0.05012744644374434, 0.0], "IIIIIIIIZZ": [0.05012744644374434, 0.0], "IIIIIIZIII": [0.05012744644374427, 0.0], "IIIIIIZIZI": [0.12297096255301768, 0.0], "IIIIIIZIZZ": [0.1308783703669227, 0.0], "IIIIIZIIII": [0.14669318599473274, 0.0], "IIIIZIIIII": [0.050127446443744325, 0.0], "IIIIZIIIZI": [0.12297096255301768, 0.0], "IIIIZIIIZZ": [0.1308783703669227, 0.0], "IIIIZIZIII": [0.12297096255301768, 0.0], "IIIIZZIIII": [0.050127446443744304, 0.0], "IIIIZZIIZI": [0.1308783703669227, 0.0], "IIIIZZIIZZ": [0.12297096255301768, 0.0], "IIIIZZZIII": [0.1308783703669227, 0.0], "IIIZIZIZII": [0.14669318599473277, 0.0], "IIIZIZZZII": [0.05012744644374439, 0.0], "IIIZIZZZZI": [0.1308783703669227, 0.0], "IIIZIZZZZZ": [0.12297096255301768, 0.0], "IIIZZIZZII": [0.12297096255301768, 0.0], "IIIZZZZZII": [0.1308783703669227, 0.0], "IIZIIIIIII": [0.19716678433985307, 0.0], "IIZIIIIIZI": [0.10518811955315438, 0.0], "IIZIIIIIZZ": [0.13338097933982077, 0.0], "IIZIIIZIII": [0.10518811955315438, 0.0], "IIZIZIIIII": [0.10518811955315438, 0.0], "IIZIZZIIII": [0.13338097933982077, 0.0], "IIZZIZZZII": [0.13338097933982077, 0.0], "IZIIIIIIII": [0.7243233991555813, 0.0], "IZIZIIIIII": [0.13147116349681592, 0.0], "IZZIIZZZII": [0.10518811955315438, 0.0], "IZZZIIIIII": [0.19716678433985307, 0.0], "IZZZIIIIZI": [0.13338097933982077, 0.0], "IZZZIIIIZZ": [0.10518811955315438, 0.0], "IZZZIIZIII": [0.13338097933982077, 0.0], "IZZZZIIIII": [0.13338097933982077, 0.0], "IZZZZZIIII": [0.10518811955315438, 0.0], "ZIIIIIIIII": [3.977170261095485, 0.0], "ZIIIIIIIZI": [0.18016881768664628, 0.0], "ZIIIIIIIZZ": [0.18552226547593303, 0.0], "ZIIIIIZIII": [0.18016881768664628, 0.0], "ZIIIZIIIII": [0.18016881768664628, 0.0], "ZIIIZZIIII": [0.18552226547593303, 0.0], "ZIIZIZZZII": [0.18552226547593303, 0.0], "ZIZIIIIIII": [0.171157168061407, 0.0], "ZIZZIIIIII": [0.171157168061407, 0.0], "ZZIIIIIIII": [3.9771702610954853, 0.0], "ZZIIIIIIZI": [0.18552226547593303, 0.0], "ZZIIIIIIZZ": [0.18016881768664628, 0.0], "ZZIIIIZIII": [0.18552226547593303, 0.0], "ZZIIZIIIII": [0.18552226547593303, 0.0], "ZZIIZZIIII": 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"auxiliary_operators": {"number_operator": {"IIIIIIIIIIIIIIIIIIIIIIIIIIII": [14.0, 0.0], "IIIIIIIIIIIIIIIIIIIIIIIIIIIZ": [-0.5, 0.0], "IIIIIIIIIIIIIIIIIIIIIIIIIIZI": [-0.5, 0.0], "IIIIIIIIIIIIIIIIIIIIIIIIIZII": [-0.5, 0.0], "IIIIIIIIIIIIIIIIIIIIIIIIZIII": [-0.5, 0.0], "IIIIIIIIIIIIIIIIIIIIIIIZIIII": [-0.5, 0.0], "IIIIIIIIIIIIIIIIIIIIIIZIIIII": [-0.5, 0.0], "IIIIIIIIIIIIIIIIIIIIIZIIIIII": [-0.5, 0.0], "IIIIIIIIIIIIIIIIIIIIZIIIIIII": [-0.5, 0.0], "IIIIIIIIIIIIIIIIIIIZIIIIIIII": [-0.5, 0.0], "IIIIIIIIIIIIIIIIIIZIIIIIIIII": [-0.5, 0.0], "IIIIIIIIIIIIIIIIIZIIIIIIIIII": [-0.5, 0.0], "IIIIIIIIIIIIIIIIZIIIIIIIIIII": [-0.5, 0.0], "IIIIIIIIIIIIIIIZIIIIIIIIIIII": [-0.5, 0.0], "IIIIIIIIIIIIIIZIIIIIIIIIIIII": [-0.5, 0.0], "IIIIIIIIIIIIIZIIIIIIIIIIIIII": [-0.5, 0.0], "IIIIIIIIIIIIZIIIIIIIIIIIIIII": [-0.5, 0.0], "IIIIIIIIIIIZIIIIIIIIIIIIIIII": [-0.5, 0.0], "IIIIIIIIIIZIIIIIIIIIIIIIIIII": [-0.5, 0.0], "IIIIIIIIIZIIIIIIIIIIIIIIIIII": [-0.5, 0.0], "IIIIIIIIZIIIIIIIIIIIIIIIIIII": [-0.5, 0.0], 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a/tests/hamiltonian_data/H2O_STO-3G_SINGLET_JW.json +++ b/tests/hamiltonian_data/H2O_STO-3G_SINGLET_JW.json @@ -1 +1 @@ -{"hamiltonian": {"IIIIIIIIIIIIII": [-46.401782018380025, 0.0], "IIIIIIIIIIIIIZ": [0.8051803307518478, 0.0], "IIIIIIIIIIIIZI": [0.8051803307518477, 0.0], "IIIIIIIIIIIIZZ": [0.15514056784924918, 0.0], "IIIIIIIIIIIZII": [0.7771029421107303, 0.0], "IIIIIIIIIIIZIZ": [0.11274988198163242, 0.0], "IIIIIIIIIIIZZI": [0.14165690464413314, 0.0], "IIIIIIIIIIZIII": [0.77710294211073, 0.0], "IIIIIIIIIIZIIZ": [0.14165690464413314, 0.0], "IIIIIIIIIIZIZI": [0.11274988198163242, 0.0], "IIIIIIIIIIZZII": [0.14926528873813869, 0.0], "IIIIIIIIIZIIII": [1.3716297306352876, 0.0], "IIIIIIIIIZIIIZ": [0.15037501861507868, 0.0], "IIIIIIIIIZIIZI": [0.15646385538479896, 0.0], "IIIIIIIIIZIZII": [0.1375298838313267, 0.0], "IIIIIIIIIZZIII": [0.1472214079008568, 0.0], "IIIIIIIIZIIIII": [1.3716297306352874, 0.0], "IIIIIIIIZIIIIZ": [0.15646385538479896, 0.0], "IIIIIIIIZIIIZI": [0.15037501861507868, 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"YYXYIIII": [-0.009870730747874312, 0.0], "YYYXIIII": [-0.009870730747874312, 0.0]}}}} \ No newline at end of file diff --git a/tests/hamiltonian_data/H3+_3-21G_SINGLET_BK.json b/tests/hamiltonian_data/H3+_3-21G_SINGLET_BK.json new file mode 100644 index 00000000..1855863d --- /dev/null +++ b/tests/hamiltonian_data/H3+_3-21G_SINGLET_BK.json @@ -0,0 +1 @@ +{"hamiltonian": {"IIIIIIIIIIII": [4.290226608934874, 0.0], "IIIIIIIIIIZI": [-1.1942054401843218, 0.0], "IIIIIIIIIZII": [0.1609947657779403, 0.0], "IIIIIIIIIZIZ": [0.16099478975019163, 0.0], "IIIIIIIIIZZZ": [-1.1942054401843216, 0.0], "IIIIIIIIZIII": [-1.1942052308313158, 0.0], "IIIIIIIIZIZI": [0.10610128092726438, 0.0], "IIIIIIIIZIZZ": [0.10610128092726438, 0.0], "IIIIIIIIZZII": [-1.194205230831316, 0.0], "IIIIIIIIZZZI": [0.12439912631869418, 0.0], "IIIIIIIIZZZZ": [0.12439912631869418, 0.0], "IIIIIIZIIIII": [-0.8752206048033608, 0.0], "IIIIIIZIIIZI": [0.09383832052876237, 0.0], "IIIIIIZIIZZZ": [0.11431139200293808, 0.0], 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a/tests/hamiltonian_data/H3+_STO-3G_SINGLET_BK.json b/tests/hamiltonian_data/H3+_STO-3G_SINGLET_BK.json new file mode 100644 index 00000000..347bb61a --- /dev/null +++ b/tests/hamiltonian_data/H3+_STO-3G_SINGLET_BK.json @@ -0,0 +1 @@ +{"hamiltonian": {"IIIIII": [-0.30720113713407277, 0.0], "IIIIIZ": [0.16361886988259644, 0.0], "IIIIZI": [-0.11363254995095774, 0.0], "IIIIZZ": [-0.1136325499509578, 0.0], "IIZIII": [-0.11363228842158359, 0.0], "IIZIZI": [0.10689334239427405, 0.0], "IIZIZZ": [0.12580183483003404, 0.0], "IZIIII": [0.14671371888181672, 0.0], "IZIZII": [0.16361885937628165, 0.0], "IZZZII": [-0.11363228842158359, 0.0], "IZZZZI": [0.12580183483003404, 0.0], "IZZZZZ": [0.10689334239427405, 0.0], "ZIIIII": [0.21328402861631457, 0.0], "ZIIIZI": [0.10666965888151218, 0.0], "ZIIIZZ": [0.14267657274828394, 0.0], "ZIZIII": [0.10666963571099208, 0.0], "ZIZZII": [0.10666963571099208, 0.0], "ZZIIII": [0.21328402861631454, 0.0], "ZZIIZI": [0.14267657274828394, 0.0], "ZZIIZZ": 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a/tests/hamiltonian_data/H3+_STO-3G_SINGLET_JW.json b/tests/hamiltonian_data/H3+_STO-3G_SINGLET_JW.json new file mode 100644 index 00000000..4ee067c4 --- /dev/null +++ b/tests/hamiltonian_data/H3+_STO-3G_SINGLET_JW.json @@ -0,0 +1 @@ +{"hamiltonian": {"IIIIII": [-0.30720113713407277, 0.0], "IIIIIZ": [-0.1136325499509578, 0.0], "IIIIZI": [-0.11363254995095774, 0.0], "IIIIZZ": [0.16361886988259644, 0.0], "IIIZII": [-0.11363228842158359, 0.0], "IIIZIZ": [0.10689334239427405, 0.0], "IIIZZI": [0.12580183483003404, 0.0], "IIZIII": [-0.11363228842158359, 0.0], "IIZIIZ": [0.12580183483003404, 0.0], "IIZIZI": [0.10689334239427405, 0.0], "IIZZII": [0.16361885937628165, 0.0], "IZIIII": [0.21328402861631454, 0.0], "IZIIIZ": [0.10666965888151218, 0.0], "IZIIZI": [0.14267657274828394, 0.0], "IZIZII": [0.10666963571099208, 0.0], "IZZIII": [0.14267654879130076, 0.0], "ZIIIII": [0.21328402861631457, 0.0], "ZIIIIZ": [0.14267657274828394, 0.0], "ZIIIZI": [0.10666965888151218, 0.0], "ZIIZII": 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a/tests/hamiltonian_data/H3O+_STO-3G_SINGLET_BK.json b/tests/hamiltonian_data/H3O+_STO-3G_SINGLET_BK.json new file mode 100644 index 00000000..94d87087 --- /dev/null +++ b/tests/hamiltonian_data/H3O+_STO-3G_SINGLET_BK.json @@ -0,0 +1 @@ +{"hamiltonian": {"IIIIIIIIIIIIIIII": [-46.301481505165754, 0.0], "IIIIIIIIIIIIIIZI": [0.7453541282002341, 0.0], "IIIIIIIIIIIIIZII": [0.1449271455247259, 0.0], "IIIIIIIIIIIIZIII": [0.745354154356115, 0.0], "IIIIIIIIIIIIZIZI": [0.1085907388677419, 0.0], "IIIIIIIIIIIIZZII": [0.745354154356115, 0.0], "IIIIIIIIIIIIZZZI": [0.12070285681940508, 0.0], "IIIIIIIIIIZIIIII": [0.7028820811408169, 0.0], "IIIIIIIIIIZIIIZI": [0.09165274737657826, 0.0], "IIIIIIIIIIZIZIII": [0.09165274399968643, 0.0], "IIIIIIIIIIZIZZII": [0.12153385642013587, 0.0], "IIIIIIIIIZIIIIII": [0.21890666494837438, 0.0], "IIIIIIIIIZIZIIII": [0.11825664782463967, 0.0], "IIIIIIIIIZZZIIII": [0.7028820811408165, 0.0], "IIIIIIIIIZZZIIZI": [0.12153381961690163, 0.0], "IIIIIIIIIZZZZIII": 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a/tests/hamiltonian_data/H3O+_STO-3G_SINGLET_JW.json b/tests/hamiltonian_data/H3O+_STO-3G_SINGLET_JW.json new file mode 100644 index 00000000..f5459e2d --- /dev/null +++ b/tests/hamiltonian_data/H3O+_STO-3G_SINGLET_JW.json @@ -0,0 +1 @@ +{"hamiltonian": {"IIIIIIIIIIIIIIII": [-46.301481505165754, 0.0], "IIIIIIIIIIIIIIIZ": [0.7453541282002346, 0.0], "IIIIIIIIIIIIIIZI": [0.7453541282002347, 0.0], "IIIIIIIIIIIIIIZZ": [0.14492719534189596, 0.0], "IIIIIIIIIIIIIZII": [0.7453541543561137, 0.0], "IIIIIIIIIIIIIZIZ": [0.10859073886774186, 0.0], "IIIIIIIIIIIIIZZI": [0.12070285681940499, 0.0], "IIIIIIIIIIIIZIII": [0.7453541543561137, 0.0], "IIIIIIIIIIIIZIIZ": [0.12070285681940499, 0.0], "IIIIIIIIIIIIZIZI": [0.10859073886774186, 0.0], "IIIIIIIIIIIIZZII": [0.1449271455247257, 0.0], "IIIIIIIIIIIZIIII": [0.7028820811408163, 0.0], "IIIIIIIIIIIZIIIZ": [0.09165274737657826, 0.0], "IIIIIIIIIIIZIIZI": [0.12153381961690163, 0.0], "IIIIIIIIIIIZIZII": [0.0916527439996864, 0.0], "IIIIIIIIIIIZZIII": 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a/tests/hamiltonian_data/H6_STO-3G_SINGLET_BK.json b/tests/hamiltonian_data/H6_STO-3G_SINGLET_BK.json new file mode 100644 index 00000000..f7c3b66b --- /dev/null +++ b/tests/hamiltonian_data/H6_STO-3G_SINGLET_BK.json @@ -0,0 +1 @@ +{"hamiltonian": {"IIIIIIIIIIII": [-0.3248415360627373, 0.0], "IIIIIIIIIIZI": [-0.4237106124861669, 0.0], "IIIIIIIIIZII": [0.10316270055900197, 0.0], "IIIIIIIIIZIZ": [0.12942641103985628, 0.0], "IIIIIIIIIZZZ": [-0.4237106124861669, 0.0], "IIIIIIIIZIII": [-0.22680071594501788, 0.0], "IIIIIIIIZIZI": [0.06193918817632962, 0.0], "IIIIIIIIZIZZ": [0.06193918817632962, 0.0], "IIIIIIIIZZII": [-0.2268007159450178, 0.0], "IIIIIIIIZZZI": [0.10060326683992969, 0.0], "IIIIIIIIZZZZ": [0.10060326683992969, 0.0], "IIIIIIZIIIII": [-0.05933687844833767, 0.0], "IIIIIIZIIIZI": [0.07382453615797878, 0.0], "IIIIIIZIIZZZ": [0.10083534567677195, 0.0], "IIIIIIZIZIII": [0.06035299576905459, 0.0], "IIIIIIZIZZII": [0.09259855954185467, 0.0], "IIIIIZIIIIII": [0.09258637032257894, 0.0], 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a/tests/hamiltonian_data/LiH_STO-3G_SINGLET_JW.json b/tests/hamiltonian_data/LiH_STO-3G_SINGLET_JW.json new file mode 100644 index 00000000..2c7f2578 --- /dev/null +++ b/tests/hamiltonian_data/LiH_STO-3G_SINGLET_JW.json @@ -0,0 +1 @@ +{"hamiltonian": {"IIIIIIIIIIII": [-4.119009482891598, 0.0], "IIIIIIIIIIIZ": [-0.392186933376828, 0.0], "IIIIIIIIIIZI": [-0.3921869333768279, 0.0], "IIIIIIIIIIZZ": [0.1138445824533915, 0.0], "IIIIIIIIIZII": [-0.22962032354369827, 0.0], "IIIIIIIIIZIZ": [0.06229300998987446, 0.0], "IIIIIIIIIZZI": [0.06719573233650958, 0.0], "IIIIIIIIZIII": [-0.22962032354369832, 0.0], "IIIIIIIIZIIZ": [0.06719573233650958, 0.0], "IIIIIIIIZIZI": [0.06229300998987446, 0.0], "IIIIIIIIZZII": [0.07823637778985212, 0.0], "IIIIIIIZIIII": [-0.22962032354369838, 0.0], "IIIIIIIZIIIZ": [0.06229300998987446, 0.0], "IIIIIIIZIIZI": [0.06719573233650958, 0.0], "IIIIIIIZIZII": [0.06558452315458402, 0.0], "IIIIIIIZZIII": [0.06980180803300673, 0.0], "IIIIIIZIIIII": [-0.2296203235436983, 0.0], 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a/tests/hamiltonian_data/MgH2_STO-3G_SINGLET_BK.json b/tests/hamiltonian_data/MgH2_STO-3G_SINGLET_BK.json new file mode 100644 index 00000000..ec3f90ca --- /dev/null +++ b/tests/hamiltonian_data/MgH2_STO-3G_SINGLET_BK.json @@ -0,0 +1 @@ +{"hamiltonian": {"IIIIIIIIIIIIIIIIIIIIII": [-125.81785179913923, 0.0], "IIIIIIIIIIIIIIIIIIIIIZ": [0.11076729325312634, 0.0], "IIIIIIIIIIIIIIIIIIIIZI": [0.5877665759339789, 0.0], "IIIIIIIIIIIIIIIIIIIIZZ": [0.5877665759339789, 0.0], "IIIIIIIIIIIIIIIIIIZIII": [0.8717529709876088, 0.0], "IIIIIIIIIIIIIIIIIIZIZI": [0.09409560737610717, 0.0], "IIIIIIIIIIIIIIIIIIZIZZ": [0.0994233864645665, 0.0], "IIIIIIIIIIIIIIIIIZIIII": [0.11623148687962584, 0.0], "IIIIIIIIIIIIIIIIIZIZII": [0.11623148687962584, 0.0], "IIIIIIIIIIIIIIIIIZZZII": [0.8717529709876093, 0.0], "IIIIIIIIIIIIIIIIIZZZZI": [0.0994233864645665, 0.0], "IIIIIIIIIIIIIIIIIZZZZZ": [0.09409560737610717, 0.0], "IIIIIIIIIIIIIIIIZIIIII": [0.8717529709876078, 0.0], "IIIIIIIIIIIIIIIIZIIIZI": [0.09409560737610714, 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b/tests/hamiltonian_data/N_STO-3G_QUARTET_BK.json new file mode 100644 index 00000000..5ed52ac8 --- /dev/null +++ b/tests/hamiltonian_data/N_STO-3G_QUARTET_BK.json @@ -0,0 +1 @@ +{"hamiltonian": {"IIIIIIIIII": [-34.771814212671714, 0.0], "IIIIIIIIIZ": [0.19070113424452018, 0.0], "IIIIIIIIZI": [0.8156233992820403, 0.0], "IIIIIIIIZZ": [0.8156233992820404, 0.0], "IIIIIIZIII": [0.8156233992820404, 0.0], "IIIIIIZIZI": [0.15986224539028465, 0.0], "IIIIIIZIZZ": [0.17014187500836314, 0.0], "IIIIIZIIII": [0.19070113424452018, 0.0], "IIIIZIIIII": [0.8156233992820404, 0.0], "IIIIZIIIZI": [0.15986224539028465, 0.0], "IIIIZIIIZZ": [0.17014187500836314, 0.0], "IIIIZIZIII": [0.15986224539028465, 0.0], "IIIIZZIIII": [0.8156233992820405, 0.0], "IIIIZZIIZI": [0.17014187500836314, 0.0], "IIIIZZIIZZ": [0.15986224539028465, 0.0], "IIIIZZZIII": [0.17014187500836314, 0.0], "IIIZIZIZII": [0.19070113424452018, 0.0], "IIIZIZZZII": [0.8156233992820404, 0.0], "IIIZIZZZZI": [0.17014187500836314, 0.0], 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{"qubit_encoding": "jordan_wigner", "unit": "angstrom", "geometry": "2\n \nNe\t0\t0\t0.3182\nH\t0\t0\t-3.1818", "basis": "sto-3g", "charge": 1, "spin": 0, "hf_array": [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0], "hf_method": "pyscf.scf.hf_symm.SymAdaptedRHF", "n_particles": 10, "n_qubits": 12, "convergence_threshold": 1e-06, "point_group": {"groupname": "Coov", "topgroup": "Coov"}, "calculated_properties": {"HF": {"energy": -126.60458691468915, "converged": true}, "MP2": {"energy": -126.6045878530174, "converged": true}, "CCSD": {"energy": -126.60458716382549, "converged": true}, "FCI": {"energy": -126.60458716382408, "converged": true}}, "auxiliary_operators": {"number_operator": {"IIIIIIIIIIII": [6.0, 0.0], "IIIIIIIIIIIZ": [-0.5, 0.0], "IIIIIIIIIIZI": [-0.5, 0.0], "IIIIIIIIIZII": [-0.5, 0.0], "IIIIIIIIZIII": [-0.5, 0.0], "IIIIIIIZIIII": [-0.5, 0.0], "IIIIIIZIIIII": [-0.5, 0.0], "IIIIIZIIIIII": [-0.5, 0.0], "IIIIZIIIIIII": [-0.5, 0.0], "IIIZIIIIIIII": [-0.5, 0.0], "IIZIIIIIIIII": [-0.5, 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file diff --git a/tests/hamiltonian_data/O_STO-3G_TRIPLET_JW.json b/tests/hamiltonian_data/O_STO-3G_TRIPLET_JW.json new file mode 100644 index 00000000..b3450193 --- /dev/null +++ b/tests/hamiltonian_data/O_STO-3G_TRIPLET_JW.json @@ -0,0 +1 @@ +{"hamiltonian": {"IIIIIIIIII": [-47.02315198523468, 0.0], "IIIIIIIIIZ": [1.3339095688459233, 0.0], "IIIIIIIIZI": [1.333909568845924, 0.0], "IIIIIIIIZZ": [0.2200397733437609, 0.0], "IIIIIIIZII": [1.3339095688459233, 0.0], "IIIIIIIZIZ": [0.1844564395049732, 0.0], "IIIIIIIZZI": [0.19631755078456914, 0.0], "IIIIIIZIII": [1.3339095688459242, 0.0], "IIIIIIZIIZ": [0.19631755078456914, 0.0], "IIIIIIZIZI": [0.1844564395049732, 0.0], "IIIIIIZZII": [0.2200397733437609, 0.0], "IIIIIZIIII": [1.3339095688459237, 0.0], "IIIIIZIIIZ": [0.1844564395049732, 0.0], "IIIIIZIIZI": [0.19631755078456914, 0.0], "IIIIIZIZII": [0.1844564395049732, 0.0], "IIIIIZZIII": [0.19631755078456914, 0.0], "IIIIZIIIII": [1.3339095688459233, 0.0], "IIIIZIIIIZ": [0.19631755078456914, 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"YYIIIIIIIIIIIIIIIIYXIIIIII": [-7.152738966855197e-06, 0.0]}}}} \ No newline at end of file From c2935414db22ee112bc65b5426f0dc6543fcd0fd Mon Sep 17 00:00:00 2001 From: TimWeaving Date: Mon, 10 Oct 2022 15:46:51 +0100 Subject: [PATCH 03/11] Optimal clique cover for small symmetry bases - avoids iterated tapering. Raises warning when the greedy method is used (above 10 symmetry terms). --- symmer/symplectic/stabilizer_op.py | 12 ++++++++++-- 1 file changed, 10 insertions(+), 2 deletions(-) diff --git a/symmer/symplectic/stabilizer_op.py b/symmer/symplectic/stabilizer_op.py index 3a105937..42d4d89b 100644 --- a/symmer/symplectic/stabilizer_op.py +++ b/symmer/symplectic/stabilizer_op.py @@ -1,6 +1,7 @@ import numpy as np from typing import Dict, List, Tuple, Union from functools import reduce +import warnings from cached_property import cached_property from symmer.utils import _rref_binary, _cref_binary from symmer.symplectic import PauliwordOp, symplectic_to_string @@ -62,7 +63,7 @@ def from_dictionary(cls, @classmethod def symmetry_basis(cls, PwordOp: PauliwordOp, - commuting_override:bool=False + commuting_override:bool=False, ) -> "StabilizerOp": """ Identify a symmetry basis for the supplied Pauli operator with symplectic representation M = [ X | Z ]. We perform columnwise @@ -91,7 +92,14 @@ def symmetry_basis(cls, return S else: # if any of the stabilizers are not mutually commuting, take the largest commuting subset - S_commuting = S.clique_cover()[0] + if S.n_terms < 10: + # expensive clique cover finding optimal commuting subset + S_commuting = S.largest_clique(edge_relation='C') + else: + # greedy graph-colouring approach when symmetry basis is large + S_commuting = S.clique_cover(edge_relation='C')[0] + warnings.warn('Greedy method may identify non-optimal commuting symmetry terms; might be able to taper again.') + return cls(S_commuting.symp_matrix, np.ones(S_commuting.n_terms)) def _check_stab(self) -> None: From 2d71104e9d771e9e9ff058c602f503c5f6d2e532 Mon Sep 17 00:00:00 2001 From: TimWeaving Date: Mon, 10 Oct 2022 17:16:37 +0100 Subject: [PATCH 04/11] Slightly more efficient Pauli multiplication (makes sure larger operator is on the left so fewer terms to iterate over). --- .../CS-VQE for Electronic Structure.ipynb | 103 +- notebooks/CS_VQE usage.ipynb | 80 +- notebooks/Unitary Partitioning Example.ipynb | 1553 ++++++++++++++++- poetry.lock | 23 +- pyproject.toml | 1 + 5 files changed, 1594 insertions(+), 166 deletions(-) diff --git a/notebooks/CS-VQE for Electronic Structure.ipynb b/notebooks/CS-VQE for Electronic Structure.ipynb index f0187f5a..3a51b67a 100644 --- a/notebooks/CS-VQE for Electronic Structure.ipynb +++ b/notebooks/CS-VQE for Electronic Structure.ipynb @@ -738,7 +738,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "id": "5be573ec", "metadata": {}, "outputs": [ @@ -792,7 +792,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "id": "1be9c499", "metadata": {}, "outputs": [ @@ -845,7 +845,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 6, "id": "def1b88b", "metadata": {}, "outputs": [ @@ -905,7 +905,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 58, "id": "d3512213", "metadata": {}, "outputs": [], @@ -929,7 +929,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 59, "id": "bf909985", "metadata": {}, "outputs": [ @@ -974,7 +974,7 @@ " 0.286+0.000j ZZZZZ}" ] }, - "execution_count": 10, + "execution_count": 59, "metadata": {}, "output_type": "execute_result" } @@ -993,13 +993,13 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 60, "id": "c609c3fd", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] @@ -1052,7 +1052,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 61, "id": "043e1a50", "metadata": {}, "outputs": [ @@ -1069,11 +1069,11 @@ "\n", "The clique operator A(r) is:\n", "\n", - " 0.000 ZXIII +\n", + "-0.000 ZXIII +\n", "-1.000 IZZZZ\n", "\n", - "The optimal paramters are nu=[ 1 1 1 -1], r=[ 0.00000001 -1. ],\n", - "which yields a noncontextual energy of n(nu,r) = -14.35188047620201\n" + "The optimal paramters are nu=[ 1 1 1 -1], r=[-0.00000006 -1. ],\n", + "which yields a noncontextual energy of n(nu,r) = -14.351880476202005\n" ] } ], @@ -1107,7 +1107,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 62, "id": "68cde7f5", "metadata": {}, "outputs": [ @@ -1117,11 +1117,6 @@ "text": [ "We may project into the contextual subspace stabilized by A(r) and ['ZIZZZ'] via a sequence of rotations:\n", "\n", - "P_0 = 1-0j ZYZZZ\n", - "P_1 = 1+0j IYZZZ\n", - "P_2 = 1+0j YIZZZ\n", - "P_3 = 1+0j IYIII\n", - "P_4 = 1+0j YIIII\n", "\n", "and tracing over qubit positions [1 0] yields the 3-qubit Hamiltonian:\n", "\n", @@ -1157,16 +1152,62 @@ "print(f'We may project into the contextual subspace stabilized by A(r) '+\n", " f'and {list(S.to_dictionary.keys())} via a sequence of rotations:\\n')\n", "\n", - "for index, (P_k, angle) in enumerate(\n", - " cs_vqe.unitary_partitioning_rotations+cs_vqe.stabilizers.stabilizer_rotations\n", - " ):\n", - " P_k.sigfig=0\n", - " print(f'P_{index} = {P_k}')\n", + "#for index, (P_k, angle) in enumerate(\n", + "# cs_vqe.unitary_partitioning_rotations+cs_vqe.stabilizers.stabilizer_rotations\n", + "# ):\n", + "# P_k.sigfig=0\n", + "# print(f'P_{index} = {P_k}')\n", " \n", "print(f'\\nand tracing over qubit positions {cs_vqe.stab_qubit_indices} yields the {H_cs.n_qubits}-qubit Hamiltonian:\\n')\n", "print(H_cs)" ] }, + { + "cell_type": "code", + "execution_count": 63, + "id": "5313b96e", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[( 1.000+0.000j IYZZZ, None),\n", + " ( 1.000+0.000j YIZZZ, None),\n", + " ( 1.000+0.000j IYIII, None),\n", + " ( 1.000+0.000j YIIII, None)]" + ] + }, + "execution_count": 63, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cs_vqe.stabilizers.stabilizer_rotations" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "id": "f5e3b115", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + " 0.000+0.000j IIIII +\n", + "-0.000-1.000j ZYZZZ" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cs_vqe.unitary_partitioning_rotations" + ] + }, { "cell_type": "markdown", "id": "1e1c0c4b", @@ -1177,7 +1218,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 65, "id": "724f1ae9", "metadata": {}, "outputs": [ @@ -1185,7 +1226,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Converged VQE energy = -14.403322006108894 with FCI error 0.0003331019587768935\n" + "Converged VQE energy = -14.403328571352972 with FCI error 0.000326536714698733\n" ] } ], @@ -1208,13 +1249,13 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 66, "id": "e0b1c8bd", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ "
" ] @@ -1238,14 +1279,6 @@ "axis.legend()\n", "plt.show()" ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "be0a8c7b", - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { diff --git a/notebooks/CS_VQE usage.ipynb b/notebooks/CS_VQE usage.ipynb index 7f0b6fdb..4cca9382 100644 --- a/notebooks/CS_VQE usage.ipynb +++ b/notebooks/CS_VQE usage.ipynb @@ -20,7 +20,7 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 1, "id": "291ee440", "metadata": {}, "outputs": [ @@ -75,7 +75,7 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 5, "id": "90045aaf", "metadata": {}, "outputs": [], @@ -96,7 +96,7 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 6, "id": "9fb61dde", "metadata": {}, "outputs": [ @@ -150,7 +150,7 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 7, "id": "06b536f1", "metadata": {}, "outputs": [ @@ -193,7 +193,7 @@ }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 8, "id": "1565f781", "metadata": {}, "outputs": [ @@ -242,7 +242,7 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 9, "id": "c9c9dcac", "metadata": {}, "outputs": [ @@ -251,8 +251,8 @@ "output_type": "stream", "text": [ "The ground state of the noncontextual Hamiltonian is -2.4748417658131507\n", - "The energy obtained from minimization of the classical objective function is -2.474841765813\n", - "The error is -1.5054624213917123e-13\n" + "The energy obtained from minimization of the classical objective function is -2.4748417658131445\n", + "The error is -6.217248937900877e-15\n" ] } ], @@ -273,7 +273,7 @@ }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 10, "id": "1edcf802", "metadata": {}, "outputs": [ @@ -305,7 +305,7 @@ }, { "cell_type": "code", - "execution_count": 48, + "execution_count": 13, "id": "2356a2e8", "metadata": {}, "outputs": [ @@ -327,7 +327,7 @@ "-0.000-0.858j IXII" ] }, - "execution_count": 48, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } @@ -349,7 +349,7 @@ }, { "cell_type": "code", - "execution_count": 49, + "execution_count": 14, "id": "fcc51e61", "metadata": {}, "outputs": [ @@ -366,7 +366,7 @@ " 1.000+0.000j XYXI" ] }, - "execution_count": 49, + "execution_count": 14, "metadata": {}, "output_type": "execute_result" } @@ -392,7 +392,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 15, "id": "e327bbb8", "metadata": {}, "outputs": [ @@ -474,7 +474,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 16, "id": "193035b4", "metadata": {}, "outputs": [], @@ -485,7 +485,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 17, "id": "eeb32d3f", "metadata": {}, "outputs": [ @@ -506,8 +506,8 @@ " 0.253 YXYI +\n", "-0.709 XZXI\n", "\n", - "We obtain the contextual energy error -2.4748417658131325\n", - "with error 0.34438670763913004\n", + "We obtain the contextual energy error -2.474841765813145\n", + "with error 0.3443867076391176\n", "qubit count of new CS-VQE H = 0\n", "\n", "*********************************************\n", @@ -522,8 +522,8 @@ " 0.253 YXYI +\n", "-0.709 XZXI\n", "\n", - "We obtain the contextual energy error -2.649488658497315\n", - "with error 0.1697398149549474\n", + "We obtain the contextual energy error -2.649488656354124\n", + "with error 0.1697398170981388\n", "qubit count of new CS-VQE H = 1\n", "\n", "*********************************************\n", @@ -538,8 +538,8 @@ " 0.253 YXYI +\n", "-0.709 XZXI\n", "\n", - "We obtain the contextual energy error -2.5108157940205658\n", - "with error 0.3084126794316968\n", + "We obtain the contextual energy error -2.510815789194936\n", + "with error 0.3084126842573265\n", "qubit count of new CS-VQE H = 1\n", "\n", "*********************************************\n", @@ -554,8 +554,8 @@ " 0.253 YXYI +\n", "-0.709 XZXI\n", "\n", - "We obtain the contextual energy error -2.4748417658131325\n", - "with error 0.34438670763913004\n", + "We obtain the contextual energy error -2.474841765813145\n", + "with error 0.3443867076391176\n", "qubit count of new CS-VQE H = 1\n", "\n", "*********************************************\n", @@ -581,8 +581,8 @@ " 0.253 YXYI +\n", "-0.709 XZXI\n", "\n", - "We obtain the contextual energy error -2.7065925666192165\n", - "with error 0.11263590683304603\n", + "We obtain the contextual energy error -2.706592559510841\n", + "with error 0.1126359139414217\n", "qubit count of new CS-VQE H = 2\n", "\n", "*********************************************\n", @@ -596,8 +596,8 @@ " 0.253 YXYI +\n", "-0.709 XZXI\n", "\n", - "We obtain the contextual energy error -2.6494886584973156\n", - "with error 0.16973981495494694\n", + "We obtain the contextual energy error -2.6494886563541225\n", + "with error 0.16973981709814012\n", "qubit count of new CS-VQE H = 2\n", "\n", "*********************************************\n", @@ -611,8 +611,8 @@ " 0.253 YXYI +\n", "-0.709 XZXI\n", "\n", - "We obtain the contextual energy error -2.5108157940205658\n", - "with error 0.3084126794316968\n", + "We obtain the contextual energy error -2.5108157891949374\n", + "with error 0.30841268425732515\n", "qubit count of new CS-VQE H = 2\n", "\n", "*********************************************\n", @@ -659,8 +659,8 @@ " 0.253 YXYI +\n", "-0.709 XZXI\n", "\n", - "We obtain the contextual energy error -2.706592566619216\n", - "with error 0.11263590683304647\n", + "We obtain the contextual energy error -2.706592559510839\n", + "with error 0.11263591394142347\n", "qubit count of new CS-VQE H = 3\n", "\n", "*********************************************\n", @@ -669,8 +669,8 @@ "Enforcing the symmetry generators\n", "-1 IIIZ\n", "\n", - "We obtain the contextual energy error -2.8192284734522657\n", - "with error -3.1086244689504383e-15\n", + "We obtain the contextual energy error -2.819228473452263\n", + "with error -4.440892098500626e-16\n", "qubit count of new CS-VQE H = 3\n", "\n", "*********************************************\n", @@ -709,7 +709,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "/Users/lex/anaconda3/envs/symred/lib/python3.9/site-packages/symmer/projection/cs_vqe.py:310: UserWarning: No stabilizers were specifed so the operator was returned\n", + "/home/tweaving/anaconda3/lib/python3.8/site-packages/symmer/projection/cs_vqe.py:310: UserWarning: No stabilizers were specifed so the operator was returned\n", " warnings.warn('No stabilizers were specifed so the operator was returned')\n" ] } @@ -775,7 +775,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 18, "id": "623e63cb", "metadata": {}, "outputs": [ @@ -783,7 +783,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Enforcing -1.000+0.000j IIIZ we obtain an energy error of -3.1086244689504383e-15.\n", + "Enforcing -1.000+0.000j IIIZ we obtain an energy error of -4.440892098500626e-16.\n", "qubit count of reduced CS-VQE H: 3\n" ] } @@ -807,7 +807,7 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 19, "id": "ef9fcabd", "metadata": {}, "outputs": [ @@ -819,7 +819,7 @@ "-1.000+0.000j YIYI\n", "and A(r)\n", "\n", - " we obtain an energy error of 0.34438670763913004.\n", + " we obtain an energy error of 0.3443867076391176.\n", "qubit count of reduced CS-VQE H: 1\n" ] } @@ -866,7 +866,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "vscode": { "interpreter": { diff --git a/notebooks/Unitary Partitioning Example.ipynb b/notebooks/Unitary Partitioning Example.ipynb index b10a1f7c..c6c3c41e 100644 --- a/notebooks/Unitary Partitioning Example.ipynb +++ b/notebooks/Unitary Partitioning Example.ipynb @@ -32,17 +32,17 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 2, "id": "ad9a0546", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "11" + "201" ] }, - "execution_count": 39, + "execution_count": 2, "metadata": {}, "output_type": "execute_result" } @@ -53,7 +53,7 @@ "\n", "\n", "### randomly generate anticommuting operator\n", - "nq = 5\n", + "nq = 100\n", "test_op = AntiCommutingOp.from_PauliwordOp(random_anitcomm_2n_1_PauliwordOp(nq))\n", "test_op.coeff_vec = (test_op.coeff_vec.real).astype(complex)\n", "test_op.n_terms" @@ -61,27 +61,217 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 3, "id": "a2223686", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "-0.162+0.000j YYXZY +\n", - "-0.292+0.000j ZYYYI +\n", - "-0.233+0.000j IXIII +\n", - " 0.179+0.000j YZYZX +\n", - " 1.328+0.000j IZYIZ +\n", - "-1.635+0.000j ZZIYY +\n", - "-0.292+0.000j YZXII +\n", - "-0.671+0.000j XZIZX +\n", - " 0.029+0.000j ZZIIX +\n", - " 2.092+0.000j XYZXY +\n", - "-0.875+0.000j XZXYI" + " 0.228+0.000j ZXYYIXXYZIZXYXIIZYZYYXXZXZYIYZIIYYIIIIYXZIIXIZIIXYYYXYIZZIYZXYXIXZYYXYXXZZIYYIXIYYZXXZXZYIZYIYXIZZYY +\n", + 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"execution_count": 9, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -154,7 +344,228 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 4, + "id": "96972485", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + " 0.228+0.000j ZXYYIXXYZIZXYXIIZYZYYXXZXZYIYZIIYYIIIIYXZIIXIZIIXYYYXYIZZIYZXYXIXZYYXYXXZZIYYIXIYYZXXZXZYIZYIYXIZZYY +\n", + "-0.567+0.000j XIXXIIXXZZIXZIZYZZZXYIIXIYZXIYZXXZZZYZXXIXYYZIYYYXYZYXXIZXYIXIIXXIXIZXIIZXZIZIYYZIZZXIYZXZXYXZYZYIZY +\n", + " 0.713+0.000j XIXIXXXZIXXXIIZZZXZYXZYZIYZXIYXIYZZIZIZZYYZYZIXXIYZYXYZZYZYIIYZYZIXXXZZIZYXZZZIZXXZYIIIYZZIXZYXZYYII +\n", + " 0.157+0.000j YZYZYXZZIZXZIYXZIIIXZYXYIIXIIIXZIZXYXXZZIXIIYYZIXIYXXIXYYXXIYZXYXXZXYZZXXZXYXZXYZIXZIXIZYXIIZIXXIIZZ +\n", + " 0.161+0.000j IZXZXZIXIIXIIXIZZIYYXZYIZZYYXXZZXIIYYIYZYIIXIYYYXZZZXIZZYZZYZXIYYXIIZXXZIXZIYYYZXYYYIYZZIYZIIZZXXXZZ +\n", + "-0.432+0.000j 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reduced too\n", "# rotations_LCU = PauliwordOp of LCU unitary that does this\n", @@ -173,7 +584,246 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 6, + "id": "eaa5abc1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + " 1.000+0.000j XIXIXXXZIXXXIIZZZXZYXZYZIYZXIYXIYZZIZIZZYYZYZIXXIYZYXYZZYZYIIYZYZIXXXZZIZYXZZZIZXXZYIIIYZZIXZYXZYYII" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Ps_LCU" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "93c4ee50", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0.724+0.000j IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII +\n", + "-0.000-0.011j IZZIZZIZYXYXIXIZYZZXXXXZZYZYXZYXYYIIZXZXZXZZXXYIIZYIZXZIXXIIXIYIXXIIYYXXXYIIZYZYXIXZYXYYZXZIIYXZYXZZ +\n", + "-0.000-0.055j 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XYXXZXIYIYZXXZIIYIZYIYYYXZXIXIYYZYIZZZYYXZXIIIXIXXZXZYZXIIZXIZIYYIYYYXXZIXZZZXYIYYXZYZYYIIZZIYXXXYIZ +\n", + "-0.000-0.056j XXYYXZIIIIXIZIXIYIXZIXZYIXZXZIXZIYXXXIXXXIIYIIYZYYXYIIXIXZYZIYIXYZXXXYZXYZXXZYIZZZXYIXYXXIIYYZYIIIIX +\n", + " 0.000+0.069j YXXXYZYZZYZIYZYIZZZYXYYIIZZIXZXYYYYIYIIYZZZIYYXXXYYXZXYZZXZXXZYXYYIYXYYXXZXXYYYXZYIZXXYIYYYIXZYXIXZZ +\n", + " 0.000+0.048j YYXXYZYIIYXYZYZIXXYIYIIZIZXIZYXIXZYYYIIIYYYXIZXZYXXZIYZXXXXZYZYXIYZXYYZIIYXIXYYZIZYYXXZXZYIZYXYYYYZY +\n", + "-0.000-0.026j YXYXXIYZYZZZZZZZZYXXZXXIZXYYYXZXZXYYXXZXXZXYXYZZYYZIYYXIXXIYYYXIIYYIXXZIYIXIYZZXXZZXZIXZIZZZYZZXIZIX +\n", + "-0.000-0.008j XXYXYXYZZZYIIYZYYZIXXYYZXIYIIXZYYZYYIZXIZIIXZZZXXIZXZZZYYIYIYYIYYYXXYIIZYXYZYXZXXZYYXXYXIZIZIIXZXIZY +\n", + " 0.000+0.057j YXYXYYXXIIXYIXIYXIZYZYYXYZIZYZZYIYXZYIYYZXZZYXZZYXIIIYYYZXYYYIYIZXZZXIXXZZIXIYZIYXZYYXZZYXXZZIXIIYZY\n" + ] + } + ], + "source": [ + "print(rotations_LCU)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, "id": "f959495c", "metadata": {}, "outputs": [ @@ -183,7 +833,7 @@ "True" ] }, - "execution_count": 32, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -195,51 +845,156 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 10, "id": "73931950", "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "143 ms ± 5.81 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" + ] + } + ], + "source": [ + "# check reduction\n", + "%timeit rotations_LCU * normed_clique_LCU * rotations_LCU.dagger" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "id": "03600643", + "metadata": {}, + "outputs": [], + "source": [ + "def modified_mult(A, B):\n", + " if A.n_terms > B.n_terms:\n", + " return (B.conjugate() * A.conjugate()).conjugate()\n", + " else:\n", + " return A * B" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "id": "b2daace9", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "141 ms ± 7.41 ms per loop (mean ± std. dev. of 7 runs, 10 loops each)\n" + ] + } + ], + "source": [ + "%timeit modified_mult(rotations_LCU, modified_mult(normed_clique_LCU, rotations_LCU.conjugate))" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "id": "3d0cca75", + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - " 1.000+0.000j IXIII" + "True" ] }, - "execution_count": 33, + "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "# check reduction\n", - "rotations_LCU * normed_clique_LCU * rotations_LCU.conjugate" + "modified_mult(rotations_LCU, modified_mult(normed_clique_LCU, rotations_LCU.conjugate)) == rotations_LCU * normed_clique_LCU * rotations_LCU.conjugate" ] }, { "cell_type": "code", - "execution_count": 34, + "execution_count": null, + "id": "a29d525a", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, "id": "68651f8b", "metadata": {}, + "outputs": [], + "source": [ + "# other method to perform conjugation\n", + "%timeit conjugate_Pop_with_R(normed_clique_LCU, rotations_LCU)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "09036fe9", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 45, + "id": "9e89a71a", + "metadata": {}, "outputs": [ { "data": { "text/plain": [ - " 1.000+0.000j IXIII" + "201" ] }, - "execution_count": 34, + "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "# other method to perform conjugation\n", - "conjugate_Pop_with_R(normed_clique_LCU, rotations_LCU)" + "rotations_LCU.n_terms" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "e7c40a34", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "200" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(rotations_SeqRot)" ] }, { "cell_type": "code", - "execution_count": 18, + "execution_count": null, + "id": "3b9ca643", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 46, "id": "96984559", "metadata": {}, "outputs": [ @@ -247,16 +1002,16 @@ "name": "stdout", "output_type": "stream", "text": [ - "normaliziation factor: 3.2116805082177207\n" + "normaliziation factor: 14.796559890619632\n" ] }, { "data": { "text/plain": [ - " 3.212+0.000j IXIII" + " 14.797+0.000j YIXZYIZYXIYIXXXIZXXZXXXIZYIXZIXYYIXXZZZXIYIIIZXZYXYIZZYIZIIYIIXZZIZYXIYZXZXZIXYIYZXXXIIZYYIYIXYZYYYZ" ] }, - "execution_count": 18, + "execution_count": 46, "metadata": {}, "output_type": "execute_result" } @@ -270,11 +1025,30 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 47, "id": "401e52ba", "metadata": {}, - "outputs": [], - "source": [] + "outputs": [ + { + "ename": "KeyboardInterrupt", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m/tmp/ipykernel_183227/3642266276.py\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mconjugate_Pop_with_R\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnormed_clique_LCU\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrotations_LCU\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/symmer/symplectic/anticommuting_op.py\u001b[0m in \u001b[0;36mconjugate_Pop_with_R\u001b[0;34m(Pop, R)\u001b[0m\n\u001b[1;32m 324\u001b[0m \u001b[0;31m# rot_H += overall_coeff_PiPaPj\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 325\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 326\u001b[0;31m phaseless_prod, coeff_vec = mul_symplectic(phaseless_prod_PiPa, PiPa_coeff_vec,\n\u001b[0m\u001b[1;32m 327\u001b[0m Pj_vec, overall_coeff)\n\u001b[1;32m 328\u001b[0m \u001b[0msym_vec_list\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mphaseless_prod\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/symmer/utils.py\u001b[0m in \u001b[0;36mmul_symplectic\u001b[0;34m(symp_vec1, coeff1, symp_vec2, coeff2)\u001b[0m\n\u001b[1;32m 340\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 341\u001b[0m \u001b[0mY_count1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbitwise_and\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_block1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mZ_block1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 342\u001b[0;31m \u001b[0mY_count2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbitwise_and\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_block2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mZ_block2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 343\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 344\u001b[0m \u001b[0;31m# phaseless multiplication is binary addition in symplectic representation\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m<__array_function__ internals>\u001b[0m in \u001b[0;36msum\u001b[0;34m(*args, **kwargs)\u001b[0m\n", + "\u001b[0;32m~/.local/lib/python3.8/site-packages/numpy/core/fromnumeric.py\u001b[0m in \u001b[0;36msum\u001b[0;34m(a, axis, dtype, out, keepdims, initial, where)\u001b[0m\n\u001b[1;32m 2257\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mres\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2258\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2259\u001b[0;31m return _wrapreduction(a, np.add, 'sum', axis, dtype, out, keepdims=keepdims,\n\u001b[0m\u001b[1;32m 2260\u001b[0m initial=initial, where=where)\n\u001b[1;32m 2261\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/.local/lib/python3.8/site-packages/numpy/core/fromnumeric.py\u001b[0m in \u001b[0;36m_wrapreduction\u001b[0;34m(obj, ufunc, method, axis, dtype, out, **kwargs)\u001b[0m\n\u001b[1;32m 67\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 68\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 69\u001b[0;31m \u001b[0;32mdef\u001b[0m \u001b[0m_wrapreduction\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mufunc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 70\u001b[0m passkwargs = {k: v for k, v in kwargs.items()\n\u001b[1;32m 71\u001b[0m if v is not np._NoValue}\n", + "\u001b[0;31mKeyboardInterrupt\u001b[0m: " + ] + } + ], + "source": [ + "conjugate_Pop_with_R(normed_clique_LCU, rotations_LCU)" + ] }, { "cell_type": "markdown", @@ -286,7 +1060,7 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 8, "id": "58a09e4c", "metadata": {}, "outputs": [], @@ -302,7 +1076,25 @@ }, { "cell_type": "code", - 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-346,17 +1138,19 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 40, "id": "d88aeb3f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - " 3.212+0.000j IXIII" + " 14.034+0.000j IIIZYYYIXZXYYYYXYXIIYZYYYIYXXIZZXXIIZYYIYXYYXZIZIYXXZXYIIIXZXIYXYIYXZYXYYYXZXIYIYIIIYXXZZZIZXZYXYIZX +\n", + " 0.000+0.000j ZYXXZZYXYXIIIZZZYZIIXZZZXYIYXYXYIXIXYIXIIIXYXIXYXXZXYYZIYYIXYXYXIYXXYXXXIZZYYYZXIZYXXIZXYXZIZIIZYYZX +\n", + " 0.000+0.000j YZXXXZIIZXIZXYYIIZIZIYZXIIXXXIZYZZZYIYYIXYYIYZIIZZZIXYIXZXZXXXYXZZIZIYXIZIZXXIIZXIYZXZYYIXYYXZXXXYXX" ] }, - "execution_count": 23, + "execution_count": 40, "metadata": {}, "output_type": "execute_result" } @@ -368,11 +1162,423 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 41, "id": "05f9d442", "metadata": {}, - "outputs": [], - "source": [] + "outputs": [ + { + "data": { + "text/plain": [ + "[( 1.000-0.000j 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PauliwordOp.random(test_op.n_qubits, n_terms)\n", @@ -422,7 +1628,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 14, "id": "60fe7e71", "metadata": {}, "outputs": [ @@ -430,8 +1636,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "max possible P terms on defined qubits: 1024\n", - "max terms SeqRot: 61440\n" + "max possible P terms on defined qubits: 1606938044258990275541962092341162602522202993782792835301376\n", + "max terms SeqRot: 321387608851798055108392418468232520504440598756558567060275200\n" ] } ], @@ -443,19 +1649,77 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 15, "id": "c0af0050", "metadata": {}, "outputs": [ { - "data": { - "text/plain": [ - "755" - ] - }, - "execution_count": 27, - "metadata": {}, - "output_type": "execute_result" + "name": "stderr", + "output_type": "stream", + "text": [ + "ERROR:root:Internal Python error in the inspect module.\n", + "Below is the traceback from this internal error.\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Traceback (most recent call last):\n", + " File \"/home/tweaving/.local/lib/python3.8/site-packages/IPython/core/interactiveshell.py\", line 3444, in run_code\n", + " exec(code_obj, self.user_global_ns, self.user_ns)\n", + " File \"/tmp/ipykernel_183227/1624288337.py\", line 1, in \n", + " op.perform_rotations(rotations_SeqRot).n_terms\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/site-packages/symmer/symplectic/base.py\", line 623, in perform_rotations\n", + " op_copy = op_copy._rotate_by_single_Pword(pauli_rotation, angle).cleanup()\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/site-packages/symmer/symplectic/base.py\", line 282, in cleanup\n", + " *symplectic_cleanup(\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/site-packages/symmer/utils.py\", line 137, in symplectic_cleanup\n", + " reduced_symp_matrix = sorted_terms[mask_unique_terms]\n", + "KeyboardInterrupt\n", + "\n", + "During handling of the above exception, another exception occurred:\n", + "\n", + "Traceback (most recent call last):\n", + " File \"/home/tweaving/.local/lib/python3.8/site-packages/IPython/core/interactiveshell.py\", line 2064, in showtraceback\n", + " stb = value._render_traceback_()\n", + "AttributeError: 'KeyboardInterrupt' object has no attribute '_render_traceback_'\n", + "\n", + "During handling of the above exception, another exception occurred:\n", + "\n", + "Traceback (most recent call last):\n", + " File \"/home/tweaving/.local/lib/python3.8/site-packages/IPython/core/ultratb.py\", line 1101, in get_records\n", + " return _fixed_getinnerframes(etb, number_of_lines_of_context, tb_offset)\n", + " File \"/home/tweaving/.local/lib/python3.8/site-packages/IPython/core/ultratb.py\", line 248, in wrapped\n", + " return f(*args, **kwargs)\n", + " File \"/home/tweaving/.local/lib/python3.8/site-packages/IPython/core/ultratb.py\", line 281, in _fixed_getinnerframes\n", + " records = fix_frame_records_filenames(inspect.getinnerframes(etb, context))\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/inspect.py\", line 1515, in getinnerframes\n", + " frameinfo = (tb.tb_frame,) + getframeinfo(tb, context)\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/inspect.py\", line 1473, in getframeinfo\n", + " filename = getsourcefile(frame) or getfile(frame)\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/inspect.py\", line 708, in getsourcefile\n", + " if getattr(getmodule(object, filename), '__loader__', None) is not None:\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/inspect.py\", line 754, in getmodule\n", + " os.path.realpath(f)] = module.__name__\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/posixpath.py\", line 391, in realpath\n", + " path, ok = _joinrealpath(filename[:0], filename, {})\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/posixpath.py\", line 424, in _joinrealpath\n", + " newpath = join(path, name)\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/posixpath.py\", line 82, in join\n", + " for b in map(os.fspath, p):\n", + "KeyboardInterrupt\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n", + "KeyboardInterrupt\n", + "\n" + ] } ], "source": [ @@ -464,7 +1728,146 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 19, + "id": "5ea62abb", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "155\n", + "232\n", + "350\n", + "526\n", + "785\n", + "1149\n", + "1733\n", + "2555\n", + "3806\n", + "5834\n", + "8723\n", + "12612\n", + "19190\n", + "28993\n", + "43020\n", + "66114\n", + "97685\n", + "145910\n", + "210403\n", + "317273\n", + "467762\n", + "707897\n", + "1071419\n", + "1592002\n", + "2391669\n", + "3641773\n", + "5413622\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "ERROR:root:Internal Python error in the inspect module.\n", + "Below is the traceback from this internal error.\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Traceback (most recent call last):\n", + " File \"/home/tweaving/.local/lib/python3.8/site-packages/IPython/core/interactiveshell.py\", line 3444, in run_code\n", + " exec(code_obj, self.user_global_ns, self.user_ns)\n", + " File \"/tmp/ipykernel_183227/4133640676.py\", line 2, in \n", + " print(op.perform_rotations(rotations_SeqRot[:i]).n_terms)\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/site-packages/symmer/symplectic/base.py\", line 623, in perform_rotations\n", + " op_copy = op_copy._rotate_by_single_Pword(pauli_rotation, angle).cleanup()\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/site-packages/symmer/symplectic/base.py\", line 606, in _rotate_by_single_Pword\n", + " anticom_part = (anticom_self.multiply_by_constant(np.cos(angle)) +\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/site-packages/symmer/symplectic/base.py\", line 317, in __add__\n", + " return PauliwordOp(P_symp_mat_new, P_new_coeffs).cleanup()\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/site-packages/symmer/symplectic/base.py\", line 282, in cleanup\n", + " *symplectic_cleanup(\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/site-packages/symmer/utils.py\", line 144, in symplectic_cleanup\n", + " reduced_symp_matrix = reduced_symp_matrix[mask_nonzero]\n", + "KeyboardInterrupt\n", + "\n", + "During handling of the above exception, another exception occurred:\n", + "\n", + "Traceback (most recent call last):\n", + " File \"/home/tweaving/.local/lib/python3.8/site-packages/IPython/core/interactiveshell.py\", line 2064, in showtraceback\n", + " stb = value._render_traceback_()\n", + "AttributeError: 'KeyboardInterrupt' object has no attribute '_render_traceback_'\n", + "\n", + "During handling of the above exception, another exception occurred:\n", + "\n", + "Traceback (most recent call last):\n", + " File \"/home/tweaving/.local/lib/python3.8/site-packages/IPython/core/ultratb.py\", line 1101, in get_records\n", + " return _fixed_getinnerframes(etb, number_of_lines_of_context, tb_offset)\n", + " File \"/home/tweaving/.local/lib/python3.8/site-packages/IPython/core/ultratb.py\", line 248, in wrapped\n", + " return f(*args, **kwargs)\n", + " File \"/home/tweaving/.local/lib/python3.8/site-packages/IPython/core/ultratb.py\", line 281, in _fixed_getinnerframes\n", + " records = fix_frame_records_filenames(inspect.getinnerframes(etb, context))\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/inspect.py\", line 1515, in getinnerframes\n", + " frameinfo = (tb.tb_frame,) + getframeinfo(tb, context)\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/inspect.py\", line 1473, in getframeinfo\n", + " filename = getsourcefile(frame) or getfile(frame)\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/inspect.py\", line 708, in getsourcefile\n", + " if getattr(getmodule(object, filename), '__loader__', None) is not None:\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/inspect.py\", line 754, in getmodule\n", + " os.path.realpath(f)] = module.__name__\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/posixpath.py\", line 391, in realpath\n", + " path, ok = _joinrealpath(filename[:0], filename, {})\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/posixpath.py\", line 425, in _joinrealpath\n", + " if not islink(newpath):\n", + " File \"/home/tweaving/anaconda3/lib/python3.8/posixpath.py\", line 167, in islink\n", + " st = os.lstat(path)\n", + "KeyboardInterrupt\n" + ] + }, + { + "ename": "TypeError", + "evalue": "object of type 'NoneType' has no len()", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)", + " \u001b[0;31m[... skipping hidden 1 frame]\u001b[0m\n", + "\u001b[0;32m/tmp/ipykernel_183227/4133640676.py\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m50\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mop\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mperform_rotations\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrotations_SeqRot\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mn_terms\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/symmer/symplectic/base.py\u001b[0m in \u001b[0;36mperform_rotations\u001b[0;34m(self, rotations)\u001b[0m\n\u001b[1;32m 622\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mpauli_rotation\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mangle\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrotations\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 623\u001b[0;31m \u001b[0mop_copy\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mop_copy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_rotate_by_single_Pword\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpauli_rotation\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mangle\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcleanup\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 624\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mop_copy\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/symmer/symplectic/base.py\u001b[0m in \u001b[0;36m_rotate_by_single_Pword\u001b[0;34m(self, Pword, angle)\u001b[0m\n\u001b[1;32m 605\u001b[0m \u001b[0;31m# if angle is specified, performs non-Clifford rotation\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 606\u001b[0;31m anticom_part = (anticom_self.multiply_by_constant(np.cos(angle)) + \n\u001b[0m\u001b[1;32m 607\u001b[0m (anticom_self*Pword_copy).multiply_by_constant(-1j*np.sin(angle)))\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/symmer/symplectic/base.py\u001b[0m in \u001b[0;36m__add__\u001b[0;34m(self, PwordOp)\u001b[0m\n\u001b[1;32m 316\u001b[0m \u001b[0;31m# cleanup run to remove duplicate rows (Pauliwords)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 317\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mPauliwordOp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mP_symp_mat_new\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mP_new_coeffs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcleanup\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 318\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/symmer/symplectic/base.py\u001b[0m in \u001b[0;36mcleanup\u001b[0;34m(self, zero_threshold)\u001b[0m\n\u001b[1;32m 281\u001b[0m return PauliwordOp(\n\u001b[0;32m--> 282\u001b[0;31m *symplectic_cleanup(\n\u001b[0m\u001b[1;32m 283\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msymp_matrix\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcoeff_vec\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mzero_threshold\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mzero_threshold\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/symmer/utils.py\u001b[0m in \u001b[0;36msymplectic_cleanup\u001b[0;34m(symp_matrix, coeff_vec, zero_threshold)\u001b[0m\n\u001b[1;32m 143\u001b[0m \u001b[0mmask_nonzero\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mabs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mreduced_coeff_vec\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m>\u001b[0m\u001b[0mzero_threshold\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 144\u001b[0;31m \u001b[0mreduced_symp_matrix\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mreduced_symp_matrix\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mmask_nonzero\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 145\u001b[0m \u001b[0mreduced_coeff_vec\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mreduced_coeff_vec\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mmask_nonzero\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mKeyboardInterrupt\u001b[0m: ", + "\nDuring handling of the above exception, another exception occurred:\n", + "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m~/.local/lib/python3.8/site-packages/IPython/core/interactiveshell.py\u001b[0m in \u001b[0;36mshowtraceback\u001b[0;34m(self, exc_tuple, filename, tb_offset, exception_only, running_compiled_code)\u001b[0m\n\u001b[1;32m 2063\u001b[0m \u001b[0;31m# in the engines. This should return a list of strings.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2064\u001b[0;31m \u001b[0mstb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_render_traceback_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2065\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0mException\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mAttributeError\u001b[0m: 'KeyboardInterrupt' object has no attribute '_render_traceback_'", + "\nDuring handling of the above exception, another exception occurred:\n", + "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", + " \u001b[0;31m[... skipping hidden 1 frame]\u001b[0m\n", + "\u001b[0;32m~/.local/lib/python3.8/site-packages/IPython/core/interactiveshell.py\u001b[0m in \u001b[0;36mshowtraceback\u001b[0;34m(self, exc_tuple, filename, tb_offset, exception_only, running_compiled_code)\u001b[0m\n\u001b[1;32m 2064\u001b[0m \u001b[0mstb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_render_traceback_\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 2065\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0mException\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2066\u001b[0;31m stb = self.InteractiveTB.structured_traceback(etype,\n\u001b[0m\u001b[1;32m 2067\u001b[0m value, tb, tb_offset=tb_offset)\n\u001b[1;32m 2068\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/.local/lib/python3.8/site-packages/IPython/core/ultratb.py\u001b[0m in \u001b[0;36mstructured_traceback\u001b[0;34m(self, etype, value, tb, tb_offset, number_of_lines_of_context)\u001b[0m\n\u001b[1;32m 1365\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1366\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtb\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1367\u001b[0;31m return FormattedTB.structured_traceback(\n\u001b[0m\u001b[1;32m 1368\u001b[0m self, etype, value, tb, tb_offset, number_of_lines_of_context)\n\u001b[1;32m 1369\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/.local/lib/python3.8/site-packages/IPython/core/ultratb.py\u001b[0m in \u001b[0;36mstructured_traceback\u001b[0;34m(self, etype, value, tb, tb_offset, number_of_lines_of_context)\u001b[0m\n\u001b[1;32m 1265\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mmode\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mverbose_modes\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1266\u001b[0m \u001b[0;31m# Verbose modes need a full traceback\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1267\u001b[0;31m return VerboseTB.structured_traceback(\n\u001b[0m\u001b[1;32m 1268\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0metype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtb_offset\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnumber_of_lines_of_context\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1269\u001b[0m )\n", + "\u001b[0;32m~/.local/lib/python3.8/site-packages/IPython/core/ultratb.py\u001b[0m in \u001b[0;36mstructured_traceback\u001b[0;34m(self, etype, evalue, etb, tb_offset, number_of_lines_of_context)\u001b[0m\n\u001b[1;32m 1122\u001b[0m \u001b[0;34m\"\"\"Return a nice text document describing the traceback.\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1123\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1124\u001b[0;31m formatted_exception = self.format_exception_as_a_whole(etype, evalue, etb, number_of_lines_of_context,\n\u001b[0m\u001b[1;32m 1125\u001b[0m tb_offset)\n\u001b[1;32m 1126\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/.local/lib/python3.8/site-packages/IPython/core/ultratb.py\u001b[0m in \u001b[0;36mformat_exception_as_a_whole\u001b[0;34m(self, etype, evalue, etb, number_of_lines_of_context, tb_offset)\u001b[0m\n\u001b[1;32m 1080\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1081\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1082\u001b[0;31m \u001b[0mlast_unique\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrecursion_repeat\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfind_recursion\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0morig_etype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mevalue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrecords\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 1083\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1084\u001b[0m \u001b[0mframes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat_records\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrecords\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlast_unique\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrecursion_repeat\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/.local/lib/python3.8/site-packages/IPython/core/ultratb.py\u001b[0m in \u001b[0;36mfind_recursion\u001b[0;34m(etype, value, records)\u001b[0m\n\u001b[1;32m 380\u001b[0m \u001b[0;31m# first frame (from in to out) that looks different.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 381\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mis_recursion_error\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0metype\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrecords\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 382\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrecords\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 383\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 384\u001b[0m \u001b[0;31m# Select filename, lineno, func_name to track frames with\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mTypeError\u001b[0m: object of type 'NoneType' has no len()" + ] + } + ], + "source": [ + "for i in range(1, 50):\n", + " print(op.perform_rotations(rotations_SeqRot[:i]).n_terms)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, "id": "a276b341", "metadata": {}, "outputs": [ @@ -472,8 +1875,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "max terms on qubits: 1024\n", - "max terms LCU: 3630\n" + "max terms on qubits: 1606938044258990275541962092341162602522202993782792835301376\n", + "max terms LCU: 4040100\n" ] } ], @@ -485,17 +1888,17 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 12, "id": "8cfcdec3", "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "570" + "1004316" ] }, - "execution_count": 29, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" } @@ -511,7 +1914,9 @@ "id": "d650d8a8", "metadata": {}, "outputs": [], - "source": [] + "source": [ + "rot" + ] }, { "cell_type": "markdown", @@ -553,7 +1958,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" } }, "nbformat": 4, diff --git a/poetry.lock b/poetry.lock index 83c77d1b..5bb06956 100644 --- a/poetry.lock +++ b/poetry.lock @@ -324,18 +324,18 @@ protobuf = ">=3.12.0" [[package]] name = "h5py" -version = "3.2.1" +version = "3.1.0" description = "Read and write HDF5 files from Python" category = "main" optional = false -python-versions = ">=3.7" +python-versions = ">=3.6" [package.dependencies] cached-property = {version = "*", markers = "python_version < \"3.8\""} numpy = [ - {version = ">=1.14.5", markers = "python_version == \"3.7\""}, - {version = ">=1.17.5", markers = "python_version == \"3.8\""}, {version = ">=1.19.3", markers = "python_version >= \"3.9\""}, + {version = ">=1.17.5", markers = "python_version == \"3.8\""}, + {version = ">=1.14.5", markers = "python_version == \"3.7\""}, ] [[package]] @@ -1145,7 +1145,7 @@ testing = ["pytest (>=6)", "pytest-checkdocs (>=2.4)", "pytest-flake8", "pytest- [metadata] lock-version = "1.1" python-versions = "^3.7" -content-hash = "df8645f5ef90a260c1fe43689eee585b3e8aed6edce7b3303d7b751b6e4086e5" +content-hash = "b3b2f0348ef42fa2fc38568c422fcf89616fae9f00c98f9614079582866ed250" [metadata.files] atomicwrites = [ @@ -1374,18 +1374,7 @@ grpcio = [ {file = "grpcio-1.46.1.tar.gz", hash = "sha256:4835b0f5fedbee3a3d6eea48f4e65dffd30b52c078690fa97ddc9fcea1e3b35d"}, ] grpcio-status = [] -h5py = [ - {file = "h5py-3.2.1-cp37-cp37m-macosx_10_9_x86_64.whl", hash = "sha256:6766104ed13ff40b3b7bfd49f13fced5274103ee9af53667e7a97c5236b14741"}, - {file = "h5py-3.2.1-cp37-cp37m-manylinux1_x86_64.whl", hash = "sha256:4160cb0d35a83c6fb9f1cad65e826dfaeb044e001549ea78003573fb6bee4042"}, - {file = "h5py-3.2.1-cp37-cp37m-win_amd64.whl", hash = "sha256:fdabe99139a9c5e1a416b7ed38c89505f8501b376d54496e1bb737cb33df61cf"}, - {file = "h5py-3.2.1-cp38-cp38-macosx_10_9_x86_64.whl", hash = "sha256:d8467fa56356ad2efad2b5986326e71d4d74505de6f6c7bb46dbba09b37459ac"}, - {file = "h5py-3.2.1-cp38-cp38-manylinux1_x86_64.whl", hash = "sha256:a6632ac11167bbad1a8fc5c82508b97ab8c12bdfe4b659254b6f7f63d3c76744"}, - {file = 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b/pyproject.toml @@ -17,6 +17,7 @@ black = "^22.1.0" flake8 = "^4.0.1" py3Dmol = "^1.8.0" pyzx = "^0.7.0" +h5py = "<=3.1" [tool.poetry.dev-dependencies] From 0e348b0f1de1f448891b2f9a3d0f175be2afb8ef Mon Sep 17 00:00:00 2001 From: TimWeaving Date: Mon, 10 Oct 2022 17:16:55 +0100 Subject: [PATCH 05/11] Multiplication update --- symmer/projection/base.py | 10 +-- symmer/projection/cs_vqe.py | 42 +++++++---- symmer/symplectic/anticommuting_op.py | 2 +- symmer/symplectic/base.py | 101 ++++++++------------------ symmer/symplectic/majorana_op.py | 10 +-- symmer/symplectic/observable_op.py | 2 +- 6 files changed, 68 insertions(+), 99 deletions(-) diff --git a/symmer/projection/base.py b/symmer/projection/base.py index a4933f4b..17c82302 100644 --- a/symmer/projection/base.py +++ b/symmer/projection/base.py @@ -75,8 +75,7 @@ def _perform_projection(self, def perform_projection(self, operator: PauliwordOp, ref_state: Union[List[int], np.array]=None, - sector: Union[List[int], np.array]=None, - insert_rotations:List[Tuple[str, float]]=[] + sector: Union[List[int], np.array]=None ) -> PauliwordOp: """ Input a PauliwordOp and returns the reduced operator corresponding with the specified stabilizers and eigenvalues. @@ -95,12 +94,9 @@ def perform_projection(self, self.stab_qubit_indices = np.where(self.rotated_stabilizers.symp_matrix)[1] % operator.n_qubits self.free_qubit_indices = np.setdiff1d(np.arange(operator.n_qubits),self.stab_qubit_indices) - # insert any supplementary rotations coming from the child class to be applied first - stab_rotations = insert_rotations + self.stabilizers.stabilizer_rotations - # perform the full list of rotations on the input operator... - if stab_rotations != []: - op_rotated = operator.perform_rotations(stab_rotations) + if len(self.stabilizers.stabilizer_rotations) > 0: + op_rotated = operator.perform_rotations(self.stabilizers.stabilizer_rotations) else: op_rotated = operator diff --git a/symmer/projection/cs_vqe.py b/symmer/projection/cs_vqe.py index 21cebad9..71892925 100644 --- a/symmer/projection/cs_vqe.py +++ b/symmer/projection/cs_vqe.py @@ -49,7 +49,7 @@ def __init__(self, self.clique_normalizaion, self.normalized_clique) = self.clique_operator.unitary_partitioning(up_method=unitary_partitioning_method, s_index=None) - self.C0.coeff_vec[0] = round(self.C0.coeff_vec[0].real) + #self.C0.coeff_vec[0] = round(self.C0.coeff_vec[0].real) def basis_score(self, basis: StabilizerOp, @@ -255,7 +255,23 @@ def convex_problem(nu): self.noncontextual_energy = self.noncontextual_objective_function( nu = self.symmetry_generators.coeff_vec, r=None ) - + + def perform_unitary_paritioning(self, + operator: PauliwordOp + ) -> PauliwordOp: + if self.unitary_partitioning_method=='LCU': + RHRdag = (self.unitary_partitioning_rotations * operator + * self.unitary_partitioning_rotations.dagger).cleanup() + elif self.unitary_partitioning_method=='seq_rot': + RHRdag = operator.perform_rotations(self.unitary_partitioning_rotations) + else: + raise ValueError('Unrecognised unitary partitioning rotation method, must be one of LCU or seq_rot.') + return RHRdag + + @cached_property + def UP_rotated_operator(self): + return self.perform_unitary_paritioning(self.operator) + def project_onto_subspace(self, stabilizers: StabilizerOp = None, enforce_clique_operator = False, @@ -267,8 +283,14 @@ def project_onto_subspace(self, # define the operator to be projected (aux_operator faciliates ansatze to be projected) if aux_operator is not None: operator_to_project = aux_operator.copy() + if enforce_clique_operator: + # if the clique operator is to be enforced, perform unitary partitioning: + operator_to_project = self.perform_unitary_paritioning(operator_to_project) else: - operator_to_project = self.operator.copy() + if enforce_clique_operator: + operator_to_project = self.UP_rotated_operator + else: + operator_to_project = self.operator.copy() if stabilizers is not None: if self.n_cliques > 0: @@ -297,15 +319,11 @@ def project_onto_subspace(self, # in accordance with the noncontextual ground state self.update_eigenvalues(fix_stabilizers) - # if the clique operator is to be enforced, perform unitary partitioning: - insert_rotations=[] if enforce_clique_operator and self.n_cliques > 0: # if any stabilizers in the list contain more than one term then apply unitary partitioning fix_stabilizers += self.C0 - insert_rotations = self.unitary_partitioning_rotations elif enforce_clique_operator and self.n_cliques > 0: fix_stabilizers = StabilizerOp(self.C0.symp_matrix, self.C0.coeff_vec) - insert_rotations = self.unitary_partitioning_rotations else: warnings.warn('No stabilizers were specifed so the operator was returned') return operator_to_project @@ -313,16 +331,8 @@ def project_onto_subspace(self, # instantiate the parent S3_projection class with the stabilizers we are enforcing super().__init__(fix_stabilizers) - if isinstance(insert_rotations, PauliwordOp) and self.unitary_partitioning_method=='LCU': - # apply LCU to operator - # TODO: need to make this cleaner! - operator_to_project = (self.unitary_partitioning_rotations * operator_to_project - * self.unitary_partitioning_rotations.conjugate).cleanup() - insert_rotations = [] - return self.perform_projection( - operator=operator_to_project, - insert_rotations=insert_rotations + operator=operator_to_project ) class CS_VQE_LW(S3_projection): diff --git a/symmer/symplectic/anticommuting_op.py b/symmer/symplectic/anticommuting_op.py index c05d1fb4..a99a400f 100644 --- a/symmer/symplectic/anticommuting_op.py +++ b/symmer/symplectic/anticommuting_op.py @@ -282,7 +282,7 @@ def conjugate_Pop_with_R(Pop:PauliwordOp, """ if Pop.n_terms == 1: - rot_H = (R * Pop * R.conjugate).cleanup() + rot_H = (R * Pop * R.dagger).cleanup() else: # anticommutes == 1 and commutes == 0 commutation_check = (~Pop.commutes_termwise(R)).astype(int) diff --git a/symmer/symplectic/base.py b/symmer/symplectic/base.py index c0027984..f1e90143 100644 --- a/symmer/symplectic/base.py +++ b/symmer/symplectic/base.py @@ -366,22 +366,12 @@ def _mul_symplectic(self, coeff_vec = phase_mod * self.coeff_vec * coeff return phaseless_prod, coeff_vec - def __mul__(self, - mul_obj: Union["PauliwordOp", "QuantumState", complex], + def _multiply_by_operator(self, + PwordOp: Union["PauliwordOp", "QuantumState", complex], zero_threshold: float = 1e-15 ) -> "PauliwordOp": """ Right-multiplication of this PauliwordOp by another PauliwordOp or QuantumState ket. """ - if isinstance(mul_obj, Number): - return self.multiply_by_constant(mul_obj) - - if isinstance(mul_obj, QuantumState): - # allows one to apply PauliwordOps to QuantumStates - # (corresponds with multipcation of the underlying state_op) - assert(mul_obj.vec_type == 'ket'), 'cannot multiply a bra from the left' - PwordOp = mul_obj.state_op - else: - PwordOp = mul_obj assert (self.n_qubits == PwordOp.n_qubits), 'PauliwordOps defined for different number of qubits' if PwordOp.n_terms == 1: @@ -403,6 +393,32 @@ def __mul__(self, np.vstack(symp_stack), np.hstack(coeff_stack), zero_threshold=zero_threshold ) ) + return pauli_mult_out + + def __mul__(self, + mul_obj: Union["PauliwordOp", "QuantumState", complex], + zero_threshold: float = 1e-15 + ) -> "PauliwordOp": + """ Right-multiplication of this PauliwordOp by another PauliwordOp or QuantumState ket. + """ + if isinstance(mul_obj, Number): + return self.multiply_by_constant(mul_obj) + + if isinstance(mul_obj, QuantumState): + # allows one to apply PauliwordOps to QuantumStates + # (corresponds with multipcation of the underlying state_op) + assert(mul_obj.vec_type == 'ket'), 'cannot multiply a bra from the left' + PwordOp = mul_obj.state_op + else: + PwordOp = mul_obj + + # more efficient to multiply the larger operator from the right + if self.n_terms < PwordOp.n_terms: + pauli_mult_out = PwordOp.dagger._multiply_by_operator( + self.dagger, zero_threshold=zero_threshold).dagger + else: + pauli_mult_out = self._multiply_by_operator( + PwordOp, zero_threshold=zero_threshold) if isinstance(mul_obj, QuantumState): coeff_vec = pauli_mult_out.coeff_vec*(1j**pauli_mult_out.Y_count) @@ -410,6 +426,7 @@ def __mul__(self, return QuantumState(pauli_mult_out.X_block.astype(int), coeff_vec).cleanup() else: return pauli_mult_out + def __imul__(self, PwordOp: "PauliwordOp" @@ -720,7 +737,7 @@ def clique_cover(self, return cliques @cached_property - def conjugate(self) -> "PauliwordOp": + def dagger(self) -> "PauliwordOp": """ Returns: Pword_conj (PauliwordOp): The Hermitian conjugated operator @@ -807,60 +824,6 @@ def to_sparse_matrix(self) -> csr_matrix: ) return sparse_matrix - def conjugate_op(self, R: 'PauliwordOp') -> 'PauliwordOp': - """ - For a defined linear combination of pauli operators : R = ∑_{𝑖} ci Pi ... (note each P self-adjoint!) - - perform the adjoint rotation R self R† = R [∑_{a} ca Pa] R† - - Args: - R (PauliwordOp): operator to rotate self by - Returns: - rot_H (PauliwordOp): rotated operator - - ### Notes - R = ∑_{𝑖} ci Pi - R^{†} = ∑_{j} cj^{*} Pj - note i and j here run over the same indices! - apply R H R^{†} where H is self (current Pauli defined in class object) - - ### derivation: - - = (∑_{𝑖} ci Pi ) * (∑_{a} ca Pa ) * ∑_{j} cj^{*} Pj - - = ∑_{a}∑_{i}∑_{j} (ci ca cj^{*}) Pi Pa Pj - - # can write as case for when i==j and i!=j - - = ∑_{a}∑_{i=j} (ci ca ci^{*}) Pi Pa Pi + ∑_{a}∑_{i}∑_{j!=i} (ci ca cj^{*}) Pi Pa Pj - - # let C by the termwise commutator matrix between H and R - = ∑_{a}∑_{i=j} (-1)^{C_{ia}} (ci ca ci^{*}) Pa + ∑_{a}∑_{i}∑_{j!=i} (ci ca cj^{*}) Pi Pa Pj - - # next write final term over upper triange (as i and j run over same indices) - ## so add common terms for i and j and make j>i - - = ∑_{a}∑_{i=j} (-1)^{C_{ia}} (ci ca ci^{*}) Pa - + ∑_{a}∑_{i}∑_{j>i} (ci ca cj^{*}) Pi Pa Pj + (cj ca ci^{*}) Pj Pa Pi - - # then need to know commutation relation betwen terms in R - ## given by adjaceny matrix of R... here A - - - = ∑_{a}∑_{i=j} (-1)^{C_{ia}} (ci ca ci^{*}) Pa - + ∑_{a}∑_{i}∑_{j>i} (ci ca cj^{*}) Pi Pa Pj + (-1)^{C_{ia}+A_{ij}+C_{ja}}(cj ca ci^{*}) Pi Pa Pj - - - = ∑_{a}∑_{i=j} (-1)^{C_{ia}} (ci ca ci^{*}) Pa - + ∑_{a}∑_{i}∑_{j>i} (ci ca cj^{*} + (-1)^{C_{ia}+A_{ij}+C_{ja}}(cj ca ci^{*})) Pi Pa Pj - - - """ - - # see from symmer.symplectic.anticommuting_op import conjugate_Pop_with_R - raise NotImplementedError('not done yet. Full function at: from symmer.symplectic.anticommuting_op.conjugate_Pop_with_R') - - def random_anitcomm_2n_1_PauliwordOp(n_qubits, complex_coeff=True, apply_clifford=True): """ Generate a anticommuting PauliOperator of size 2n+1 on n qubits (max possible size) with normally distributed coefficients. Generates in structured way then uses Clifford rotation (default) @@ -1115,7 +1078,7 @@ def sectors_present(self, symmetry): """ symmetry_copy = symmetry.copy() symmetry_copy.coeff_vec = np.ones(symmetry.n_terms) - sector = np.array([self.conjugate*S*self for S in symmetry_copy]) + sector = np.array([self.dagger*S*self for S in symmetry_copy]) return sector @cached_property @@ -1128,7 +1091,7 @@ def normalize(self): return QuantumState(self.state_matrix, coeff_vector, vec_type=self.vec_type) @cached_property - def conjugate(self) -> "QuantumState": + def dagger(self) -> "QuantumState": """ Returns: conj_state (QuantumState): The Hermitian conjugated state i.e. bra -> ket, ket -> bra diff --git a/symmer/symplectic/majorana_op.py b/symmer/symplectic/majorana_op.py index 911629c8..cb052b59 100644 --- a/symmer/symplectic/majorana_op.py +++ b/symmer/symplectic/majorana_op.py @@ -202,7 +202,7 @@ def commutes(self, return self.commutator(M_OP).n_terms == 0 @property - def conjugate(self) -> "MajoranaOp": + def dagger(self) -> "MajoranaOp": """ Similar idea to hermitian conjugate operation on Fermionic operators (reverse order then dagger) As operators are self dagger, just reverse order! @@ -504,8 +504,8 @@ def _recursively_rotate(self, maj_basis): # rotate Z onto different term maj_rot_op = MajoranaOp([[], rot_op_inds], [np.cos(np.pi / 4), 1j * np.sin(np.pi / 4)]) - rot_basis_out = (maj_rot_op * maj_basis * maj_rot_op.conjugate).cleanup() - rot_piv = (maj_rot_op * pivot_maj * maj_rot_op.conjugate).cleanup() + rot_basis_out = (maj_rot_op * maj_basis * maj_rot_op.dagger).cleanup() + rot_piv = (maj_rot_op * pivot_maj * maj_rot_op.dagger).cleanup() self.maj_rotations.append(maj_rot_op) elif rot_op[pivot_point_even] == rot_op[pivot_point_odd] == 0: @@ -525,11 +525,11 @@ def _recursively_rotate(self, maj_basis): rot2_sym[1] = rot_op2 maj_rot_op2 = MajoranaOp(rot2_sym, [np.cos(np.pi / 4), 1j * np.sin(np.pi / 4)]) - rot_basis_out2 = maj_rot_op2 * rot_basis_out * maj_rot_op2.conjugate # .cleanup() + rot_basis_out2 = maj_rot_op2 * rot_basis_out * maj_rot_op2.dagger # .cleanup() self.maj_rotations.append(maj_rot_op2) - rotated_term = (maj_rot_op2 * rot_piv * maj_rot_op2.conjugate).cleanup() + rotated_term = (maj_rot_op2 * rot_piv * maj_rot_op2.dagger).cleanup() self.rotated_basis.append(rotated_term) diff --git a/symmer/symplectic/observable_op.py b/symmer/symplectic/observable_op.py index b635c87b..3ce54a88 100644 --- a/symmer/symplectic/observable_op.py +++ b/symmer/symplectic/observable_op.py @@ -208,7 +208,7 @@ def _ansatz_expectation_statevector(self, return (psi @ self.to_sparse_matrix @ psi.T)[0,0].real else: psi = ansatz_op.exponentiate() * QuantumState([ref_state]) - return (psi.conjugate * self * psi).real + return (psi.dagger * self * psi).real @cached_property def QWC_decomposition(self): From 39fc1192463aaeec2a5adc942abdfa69d06996a0 Mon Sep 17 00:00:00 2001 From: TimWeaving Date: Mon, 10 Oct 2022 17:50:46 +0100 Subject: [PATCH 06/11] Fixing dependency issues --- pyproject.toml | 1 - symmer/chemistry/build_molecule.py | 4 ++-- symmer/symplectic/ansatz_op.py | 9 ++------- symmer/utils.py | 19 ------------------- 4 files changed, 4 insertions(+), 29 deletions(-) diff --git a/pyproject.toml b/pyproject.toml index ee55f96e..d380f8c2 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -16,7 +16,6 @@ isort = "^5.10.1" black = "^22.1.0" flake8 = "^4.0.1" py3Dmol = "^1.8.0" -pyzx = "^0.7.0" h5py = "<=3.1" [tool.poetry.dev-dependencies] diff --git a/symmer/chemistry/build_molecule.py b/symmer/chemistry/build_molecule.py index d27f6830..ba09ef36 100644 --- a/symmer/chemistry/build_molecule.py +++ b/symmer/chemistry/build_molecule.py @@ -1,4 +1,4 @@ -from functools import cached_property +from cached_property import cached_property from symmer.symplectic import PauliwordOp, QuantumState from symmer.utils import QubitOperator_to_dict, safe_PauliwordOp_to_dict from symmer.chemistry import ( @@ -72,7 +72,7 @@ def __init__(self, self.H_q = fermion_to_qubit_operator(self.H, self.qubit_mapping_str, N_qubits=self.n_qubits) self.T_q = fermion_to_qubit_operator(self.T, self.qubit_mapping_str, N_qubits=self.n_qubits) - self.UCC_q = self.T_q - self.T_q.conjugate + self.UCC_q = self.T_q - self.T_q.dagger self.UCC_q.coeff_vec = self.UCC_q.coeff_vec.imag self.SOR_q = self.second_order_response() diff --git a/symmer/symplectic/ansatz_op.py b/symmer/symplectic/ansatz_op.py index c60be656..7869d4a7 100644 --- a/symmer/symplectic/ansatz_op.py +++ b/symmer/symplectic/ansatz_op.py @@ -3,7 +3,6 @@ from functools import reduce from cached_property import cached_property from symmer.symplectic import PauliwordOp -from symmer.utils import ZX_calculus_reduction from qiskit.circuit import QuantumCircuit, ParameterVector class AnsatzOp(PauliwordOp): @@ -61,8 +60,7 @@ def to_QuantumCircuit(self, ref_state: np.array = None, basis_change_indices: Dict[str, List[int]] = {'X_indices':[],'Y_indices':[]}, trotter_number: int = 1, - bind_params: bool = True, - ZX_reduction = False + bind_params: bool = True ) -> str: """ Convert the operator to a QASM circuit string for input @@ -119,8 +117,5 @@ def circuit_from_step(angle, H_indices, S_indices, CNOT_indices, RZ_index): qc.s(qiskit_ordering(i)) for i in basis_change_indices['X_indices']: qc.h(qiskit_ordering(i)) - - if ZX_reduction: - qc = ZX_calculus_reduction(qc) - + return qc \ No newline at end of file diff --git a/symmer/utils.py b/symmer/utils.py index 8197ec8a..61bc56b3 100644 --- a/symmer/utils.py +++ b/symmer/utils.py @@ -2,7 +2,6 @@ import scipy as sp from typing import Tuple, Dict from qiskit import QuantumCircuit -import pyzx as zx import openfermion as of def symplectic_to_string(symp_vec) -> str: @@ -170,24 +169,6 @@ def lp_norm(vector: np.array, p:int=2) -> float: """ return np.power(np.sum(np.power(np.abs(vector), p)), 1/p) -def ZX_calculus_reduction(qc: QuantumCircuit) -> QuantumCircuit: - """ Simplify the circuit via ZX calculus using PyZX... - Only works on parametrized circuits! - - Returns: - simplified_qc (QuantumCircuit): the reduced circuit via ZX calculus - """ - # to perform ZX-calculus optimization - qc_qasm = qc.qasm() - qc_pyzx = zx.Circuit.from_qasm(qc_qasm) - g = qc_pyzx.to_graph() - zx.full_reduce(g) # simplifies the Graph in-place - g.normalize() - c_opt = zx.extract_circuit(g.copy()) - simplified_qc = QuantumCircuit.from_qasm_str(c_opt.to_qasm()) - - return simplified_qc - def _rref_binary(matrix: np.array) -> np.array: """ Row-reduced echelon form over the binary field (GF2) - rows are not reordered here for efficiency (not required in some use cases, e.g. symmetry identification) From 8a6ddf0aae85a51d2f122dce9979d3c4c09b7d85 Mon Sep 17 00:00:00 2001 From: TimWeaving Date: Mon, 10 Oct 2022 17:51:16 +0100 Subject: [PATCH 07/11] Fixed notebook problems arising from the change conjugate -> dagger --- .../CS-VQE for Electronic Structure.ipynb | 1036 +++++++++-------- notebooks/CS_VQE usage.ipynb | 89 +- .../H3+ ground state failure example.ipynb | 38 +- notebooks/QuantumState usage.ipynb | 116 +- notebooks/QubitTapering usage.ipynb | 252 ++-- .../Tapering the Heisenberg Hamiltonian.ipynb | 123 +- 6 files changed, 820 insertions(+), 834 deletions(-) diff --git a/notebooks/CS-VQE for Electronic Structure.ipynb b/notebooks/CS-VQE for Electronic Structure.ipynb index 3a51b67a..3a40e1c5 100644 --- a/notebooks/CS-VQE for Electronic Structure.ipynb +++ b/notebooks/CS-VQE for Electronic Structure.ipynb @@ -38,10 +38,10 @@ "CCSD converged? True\n", "FCI converged? True\n", "\n", - "HF energy: -14.351880476202012\n", - "MP2 energy: -14.376238850841505\n", - "CCSD energy: -14.40365075175316\n", - "FCI energy: -14.403655108067671\n", + "HF energy: -14.351880476202023\n", + "MP2 energy: -14.376238850841515\n", + "CCSD energy: -14.403650751752787\n", + "FCI energy: -14.40365510806768\n", "\n", "\n", "Number of qubits: 10\n" @@ -87,456 +87,456 @@ "name": "stdout", "output_type": "stream", "text": [ - "-7.857500653536853 [0^ 0] +\n", - "1.1376669191197273 [0^ 0^ 0 0] +\n", - "-0.12666505470671072 [0^ 0^ 0 2] +\n", - "-0.1266650547067108 [0^ 0^ 2 0] +\n", - "0.022148953868166094 [0^ 0^ 2 2] +\n", - "0.007799539287510106 [0^ 0^ 4 4] +\n", - "0.007799539287510106 [0^ 0^ 6 6] +\n", - "0.007799539287510106 [0^ 0^ 8 8] +\n", - "1.1376669191197273 [0^ 1^ 1 0] +\n", - "-0.12666505470671072 [0^ 1^ 1 2] +\n", - "-0.1266650547067108 [0^ 1^ 3 0] +\n", - "0.022148953868166094 [0^ 1^ 3 2] +\n", - "0.007799539287510106 [0^ 1^ 5 4] +\n", - "0.007799539287510106 [0^ 1^ 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"0.010281285614826115 [7^ 1^ 7 3] +\n", + "-0.0044699708754874475 [7^ 2^ 0 7] +\n", + "0.20479845197244193 [7^ 2^ 2 7] +\n", + "0.010281285614826111 [7^ 2^ 6 1] +\n", + "0.04340448973076089 [7^ 2^ 6 3] +\n", + "-0.0044699708754874475 [7^ 3^ 1 7] +\n", + "0.20479845197244193 [7^ 3^ 3 7] +\n", + "0.010281285614826111 [7^ 3^ 7 1] +\n", + "0.04340448973076089 [7^ 3^ 7 3] +\n", + "0.20068014132216427 [7^ 4^ 4 7] +\n", + "0.012124689610585583 [7^ 4^ 6 5] +\n", + "0.20068014132216427 [7^ 5^ 5 7] +\n", + "0.012124689610585583 [7^ 5^ 7 5] +\n", + "0.007799539287510122 [7^ 6^ 0 1] +\n", + "0.010281285614826115 [7^ 6^ 0 3] +\n", + "0.010281285614826111 [7^ 6^ 2 1] +\n", + "0.04340448973076089 [7^ 6^ 2 3] +\n", + "0.012124689610585583 [7^ 6^ 4 5] +\n", + "0.22492952054333537 [7^ 6^ 6 7] +\n", + "0.012124689610585583 [7^ 6^ 8 9] +\n", + "-1.6341574655066096 [7^ 7] +\n", + "0.007799539287510122 [7^ 7^ 1 1] +\n", + "0.010281285614826115 [7^ 7^ 1 3] +\n", + "0.010281285614826111 [7^ 7^ 3 1] +\n", + "0.04340448973076089 [7^ 7^ 3 3] +\n", + "0.012124689610585583 [7^ 7^ 5 5] +\n", + "0.22492952054333537 [7^ 7^ 7 7] +\n", + "0.012124689610585583 [7^ 7^ 9 9] +\n", + "0.012124689610585583 [7^ 8^ 6 9] +\n", + "0.20068014132216427 [7^ 8^ 8 7] +\n", + "0.012124689610585583 [7^ 9^ 7 9] +\n", + "0.20068014132216427 [7^ 9^ 9 7] +\n", + "0.284614418228139 [8^ 0^ 0 8] +\n", + "-0.0044699708754874475 [8^ 0^ 2 8] +\n", + "0.007799539287510122 [8^ 0^ 8 0] +\n", + "0.010281285614826115 [8^ 0^ 8 2] +\n", + "0.284614418228139 [8^ 1^ 1 8] +\n", + "-0.0044699708754874475 [8^ 1^ 3 8] +\n", + "0.007799539287510122 [8^ 1^ 9 0] +\n", + "0.010281285614826115 [8^ 1^ 9 2] +\n", + "-0.0044699708754874475 [8^ 2^ 0 8] +\n", + "0.20479845197244193 [8^ 2^ 2 8] +\n", + "0.010281285614826111 [8^ 2^ 8 0] +\n", + "0.04340448973076089 [8^ 2^ 8 2] +\n", + "-0.0044699708754874475 [8^ 3^ 1 8] +\n", + "0.20479845197244193 [8^ 3^ 3 8] +\n", + "0.010281285614826111 [8^ 3^ 9 0] +\n", + "0.04340448973076089 [8^ 3^ 9 2] +\n", + "0.20068014132216427 [8^ 4^ 4 8] +\n", + "0.012124689610585583 [8^ 4^ 8 4] +\n", + "0.20068014132216427 [8^ 5^ 5 8] +\n", + "0.012124689610585583 [8^ 5^ 9 4] +\n", + "0.20068014132216427 [8^ 6^ 6 8] +\n", + "0.012124689610585583 [8^ 6^ 8 6] +\n", + "0.20068014132216427 [8^ 7^ 7 8] +\n", + "0.012124689610585583 [8^ 7^ 9 6] +\n", + "-1.6341574655066096 [8^ 8] +\n", + "0.007799539287510122 [8^ 8^ 0 0] +\n", + "0.010281285614826115 [8^ 8^ 0 2] +\n", + "0.010281285614826111 [8^ 8^ 2 0] +\n", + "0.04340448973076089 [8^ 8^ 2 2] +\n", + "0.012124689610585583 [8^ 8^ 4 4] +\n", + "0.012124689610585583 [8^ 8^ 6 6] +\n", + "0.22492952054333537 [8^ 8^ 8 8] +\n", + "0.007799539287510122 [8^ 9^ 1 0] +\n", + "0.010281285614826115 [8^ 9^ 1 2] +\n", + "0.010281285614826111 [8^ 9^ 3 0] +\n", + "0.04340448973076089 [8^ 9^ 3 2] +\n", + "0.012124689610585583 [8^ 9^ 5 4] +\n", + "0.012124689610585583 [8^ 9^ 7 6] +\n", + "0.22492952054333537 [8^ 9^ 9 8] +\n", + "0.284614418228139 [9^ 0^ 0 9] +\n", + "-0.0044699708754874475 [9^ 0^ 2 9] +\n", + "0.007799539287510122 [9^ 0^ 8 1] +\n", + "0.010281285614826115 [9^ 0^ 8 3] +\n", + "0.284614418228139 [9^ 1^ 1 9] +\n", + "-0.0044699708754874475 [9^ 1^ 3 9] +\n", + "0.007799539287510122 [9^ 1^ 9 1] +\n", + "0.010281285614826115 [9^ 1^ 9 3] +\n", + "-0.0044699708754874475 [9^ 2^ 0 9] +\n", + "0.20479845197244193 [9^ 2^ 2 9] +\n", + "0.010281285614826111 [9^ 2^ 8 1] +\n", + "0.04340448973076089 [9^ 2^ 8 3] +\n", + "-0.0044699708754874475 [9^ 3^ 1 9] +\n", + "0.20479845197244193 [9^ 3^ 3 9] +\n", + "0.010281285614826111 [9^ 3^ 9 1] +\n", + "0.04340448973076089 [9^ 3^ 9 3] +\n", + "0.20068014132216427 [9^ 4^ 4 9] +\n", + "0.012124689610585583 [9^ 4^ 8 5] +\n", + "0.20068014132216427 [9^ 5^ 5 9] +\n", + "0.012124689610585583 [9^ 5^ 9 5] +\n", + "0.20068014132216427 [9^ 6^ 6 9] +\n", + "0.012124689610585583 [9^ 6^ 8 7] +\n", + "0.20068014132216427 [9^ 7^ 7 9] +\n", + "0.012124689610585583 [9^ 7^ 9 7] +\n", + "0.007799539287510122 [9^ 8^ 0 1] +\n", + "0.010281285614826115 [9^ 8^ 0 3] +\n", + "0.010281285614826111 [9^ 8^ 2 1] +\n", + "0.04340448973076089 [9^ 8^ 2 3] +\n", + "0.012124689610585583 [9^ 8^ 4 5] +\n", + "0.012124689610585583 [9^ 8^ 6 7] +\n", + "0.22492952054333537 [9^ 8^ 8 9] +\n", + "-1.6341574655066096 [9^ 9] +\n", + "0.007799539287510122 [9^ 9^ 1 1] +\n", + "0.010281285614826115 [9^ 9^ 1 3] +\n", + "0.010281285614826111 [9^ 9^ 3 1] +\n", + "0.04340448973076089 [9^ 9^ 3 3] +\n", + "0.012124689610585583 [9^ 9^ 5 5] +\n", + "0.012124689610585583 [9^ 9^ 7 7] +\n", + "0.22492952054333537 [9^ 9^ 9 9]\n" ] } ], @@ -746,7 +746,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Ground state energy = -14.403655108067726, with FCI error 5.5067062021407764e-14.\n", + "Ground state energy = -14.403655108067708, with FCI error 2.842170943040401e-14.\n", "\n", "The ground state is:\n", "\n", @@ -853,28 +853,28 @@ "name": "stdout", "output_type": "stream", "text": [ - "The ground state energy of the Hamiltonian is -14.403655108067726\n", - "and for the 5-qubit tapered Hamiltonian it is -14.403655108067646;\n", - "the energy error is 7.993605777301127e-14.\n", + "The ground state energy of the Hamiltonian is -14.403655108067708\n", + "and for the 5-qubit tapered Hamiltonian it is -14.40365510806768;\n", + "the energy error is 2.842170943040401e-14.\n", "\n", "The tapered ground state is:\n", "\n", - " 0.186+0.000j |00001> +\n", - " 0.186+0.000j |00010> +\n", - " 0.001+0.000j |00011> +\n", - " 0.186+0.000j |00100> +\n", - " 0.001+0.000j |00101> +\n", - " 0.001+0.000j |00110> +\n", - " 0.003+0.000j |01001> +\n", - " 0.003+0.000j |01010> +\n", - " 0.003+0.000j |01100> +\n", - "-0.003+0.000j |10001> +\n", - "-0.003+0.000j |10010> +\n", - "-0.003+0.000j |10100> +\n", - " 0.946+0.000j |11000> +\n", - " 0.001+0.000j |11001> +\n", - " 0.001+0.000j |11010> +\n", - " 0.001+0.000j |11100>\n" + "-0.186+0.000j |00001> +\n", + "-0.186+0.000j |00010> +\n", + "-0.001+0.000j |00011> +\n", + "-0.186+0.000j |00100> +\n", + "-0.001+0.000j |00101> +\n", + "-0.001+0.000j |00110> +\n", + "-0.003+0.000j |01001> +\n", + "-0.003+0.000j |01010> +\n", + "-0.003+0.000j |01100> +\n", + " 0.003+0.000j |10001> +\n", + " 0.003+0.000j |10010> +\n", + " 0.003+0.000j |10100> +\n", + "-0.946+0.000j |11000> +\n", + "-0.001+0.000j |11001> +\n", + "-0.001+0.000j |11010> +\n", + "-0.001+0.000j |11100>\n" ] } ], @@ -905,7 +905,7 @@ }, { "cell_type": "code", - "execution_count": 58, + "execution_count": 7, "id": "d3512213", "metadata": {}, "outputs": [], @@ -929,7 +929,7 @@ }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 8, "id": "bf909985", "metadata": {}, "outputs": [ @@ -944,37 +944,37 @@ " 0.389+0.000j IIZIZ +\n", " 0.389+0.000j IIZZI +\n", " 0.263+0.000j IIZZZ +\n", - " -0.047+0.000j ZIIII +\n", - " 0.183+0.000j ZIIIZ +\n", - " 0.183+0.000j ZIIZI +\n", - " 0.281+0.000j ZIIZZ +\n", - " 0.183+0.000j ZIZII +\n", - " 0.281+0.000j ZIZIZ +\n", - " 0.281+0.000j ZIZZI +\n", - " 2.243-0.000j ZIZZZ,\n", - " 'clique_0': 0.060+0.000j IXIII +\n", - " -0.060+0.000j IXZZZ +\n", - " -0.038+0.000j ZXIII +\n", - " -0.010+0.000j ZXIIZ +\n", - " -0.010+0.000j ZXIZI +\n", - " 0.010+0.000j ZXIZZ +\n", - " -0.010+0.000j ZXZII +\n", - " 0.010+0.000j ZXZIZ +\n", - " 0.010+0.000j ZXZZI +\n", - " 0.038+0.000j ZXZZZ,\n", - " 'clique_1': -0.047+0.000j IZIII +\n", + " -0.047+0.000j IZIII +\n", " 0.183+0.000j IZIIZ +\n", " 0.183+0.000j IZIZI +\n", " 0.281+0.000j IZIZZ +\n", " 0.183+0.000j IZZII +\n", " 0.281+0.000j IZZIZ +\n", " 0.281+0.000j IZZZI +\n", - " 2.243-0.000j IZZZZ +\n", + " 2.243-0.000j IZZZZ,\n", + " 'clique_0': -0.060+0.000j XIIII +\n", + " 0.060+0.000j XIZZZ +\n", + " 0.038-0.000j XZIII +\n", + " 0.010+0.000j XZIIZ +\n", + " 0.010+0.000j XZIZI +\n", + " -0.010+0.000j XZIZZ +\n", + " 0.010+0.000j XZZII +\n", + " -0.010+0.000j XZZIZ +\n", + " -0.010+0.000j XZZZI +\n", + " -0.038+0.000j XZZZZ,\n", + " 'clique_1': -0.047+0.000j ZIIII +\n", + " 0.183+0.000j ZIIIZ +\n", + " 0.183+0.000j ZIIZI +\n", + " 0.281+0.000j ZIIZZ +\n", + " 0.183+0.000j ZIZII +\n", + " 0.281+0.000j ZIZIZ +\n", + " 0.281+0.000j ZIZZI +\n", + " 2.243-0.000j ZIZZZ +\n", " 0.670+0.000j ZZIII +\n", " 0.286+0.000j ZZZZZ}" ] }, - "execution_count": 59, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -993,15 +993,15 @@ }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 10, "id": "c609c3fd", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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\n", "text/plain": [ - "
" + "
" ] }, "metadata": {}, @@ -1052,7 +1052,7 @@ }, { "cell_type": "code", - "execution_count": 61, + "execution_count": 13, "id": "043e1a50", "metadata": {}, "outputs": [ @@ -1065,15 +1065,15 @@ " 1 IIIIZ \n", " 1 IIIZI \n", " 1 IIZII \n", - "-1 ZIIII\n", + "-1 IZIII\n", "\n", "The clique operator A(r) is:\n", "\n", - "-0.000 ZXIII +\n", - "-1.000 IZZZZ\n", + " 0.000 XZIII +\n", + "-1.000 ZIZZZ\n", "\n", - "The optimal paramters are nu=[ 1 1 1 -1], r=[-0.00000006 -1. ],\n", - "which yields a noncontextual energy of n(nu,r) = -14.351880476202005\n" + "The optimal paramters are nu=[ 1 1 1 -1], r=[ 8.66934371e-08 -1.00000000e+00],\n", + "which yields a noncontextual energy of n(nu,r) = -14.351880476202018\n" ] } ], @@ -1107,7 +1107,7 @@ }, { "cell_type": "code", - "execution_count": 62, + "execution_count": 19, "id": "68cde7f5", "metadata": {}, "outputs": [ @@ -1115,7 +1115,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "We may project into the contextual subspace stabilized by A(r) and ['ZIZZZ'] via a sequence of rotations:\n", + "We may project into the contextual subspace stabilized by A(r) and ['IZZZZ'] via a sequence of rotations:\n", "\n", "\n", "and tracing over qubit positions [1 0] yields the 3-qubit Hamiltonian:\n", @@ -1146,7 +1146,7 @@ "source": [ "from symmer.symplectic import StabilizerOp\n", "\n", - "S = StabilizerOp.from_list(['ZIZZZ'])\n", + "S = StabilizerOp.from_list(['IZZZZ'])\n", "H_cs = cs_vqe.project_onto_subspace(stabilizers=S, enforce_clique_operator=True)\n", "\n", "print(f'We may project into the contextual subspace stabilized by A(r) '+\n", @@ -1164,7 +1164,7 @@ }, { "cell_type": "code", - "execution_count": 63, + "execution_count": 20, "id": "5313b96e", "metadata": {}, "outputs": [ @@ -1177,7 +1177,7 @@ " ( 1.000+0.000j YIIII, None)]" ] }, - "execution_count": 63, + "execution_count": 20, "metadata": {}, "output_type": "execute_result" } @@ -1188,7 +1188,7 @@ }, { "cell_type": "code", - "execution_count": 64, + "execution_count": 21, "id": "f5e3b115", "metadata": {}, "outputs": [ @@ -1196,10 +1196,10 @@ "data": { "text/plain": [ " 0.000+0.000j IIIII +\n", - "-0.000-1.000j ZYZZZ" + " 0.000+1.000j YZZZZ" ] }, - "execution_count": 64, + "execution_count": 21, "metadata": {}, "output_type": "execute_result" } @@ -1218,7 +1218,7 @@ }, { "cell_type": "code", - "execution_count": 65, + "execution_count": 22, "id": "724f1ae9", "metadata": {}, "outputs": [ @@ -1226,7 +1226,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Converged VQE energy = -14.403328571352972 with FCI error 0.000326536714698733\n" + "Converged VQE energy = -14.403297522148037 with FCI error 0.00035758591964274444\n" ] } ], @@ -1249,20 +1249,18 @@ }, { "cell_type": "code", - "execution_count": 66, + "execution_count": 23, "id": "e0b1c8bd", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", + "image/png": 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\n", "text/plain": [ - "
" + "
" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -1279,6 +1277,14 @@ "axis.legend()\n", "plt.show()" ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ab77ce22", + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -1297,7 +1303,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.7.13" }, "vscode": { "interpreter": { diff --git a/notebooks/CS_VQE usage.ipynb b/notebooks/CS_VQE usage.ipynb index 4cca9382..5b8fea55 100644 --- a/notebooks/CS_VQE usage.ipynb +++ b/notebooks/CS_VQE usage.ipynb @@ -75,7 +75,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 2, "id": "90045aaf", "metadata": {}, "outputs": [], @@ -96,7 +96,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 3, "id": "9fb61dde", "metadata": {}, "outputs": [ @@ -150,7 +150,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 4, "id": "06b536f1", "metadata": {}, "outputs": [ @@ -193,7 +193,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 5, "id": "1565f781", "metadata": {}, "outputs": [ @@ -242,7 +242,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 6, "id": "c9c9dcac", "metadata": {}, "outputs": [ @@ -251,8 +251,8 @@ "output_type": "stream", "text": [ "The ground state of the noncontextual Hamiltonian is -2.4748417658131507\n", - "The energy obtained from minimization of the classical objective function is -2.4748417658131445\n", - "The error is -6.217248937900877e-15\n" + "The energy obtained from minimization of the classical objective function is -2.4748417658130966\n", + "The error is -5.417888360170764e-14\n" ] } ], @@ -273,7 +273,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 7, "id": "1edcf802", "metadata": {}, "outputs": [ @@ -305,7 +305,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 8, "id": "2356a2e8", "metadata": {}, "outputs": [ @@ -327,7 +327,7 @@ "-0.000-0.858j IXII" ] }, - "execution_count": 13, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -349,7 +349,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 9, "id": "fcc51e61", "metadata": {}, "outputs": [ @@ -361,14 +361,15 @@ ] }, { - "data": { - "text/plain": [ - " 1.000+0.000j XYXI" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" + "ename": "AttributeError", + "evalue": "'PauliwordOp' object has no attribute 'conjugate'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m/tmp/ipykernel_12602/3220794072.py\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0mcs_vqe\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0munitary_partitioning_method\u001b[0m\u001b[0;34m==\u001b[0m\u001b[0;34m'LCU'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'result of applying LCU rotations to A(r)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0mrotated_Ar\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcs_vqe\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0munitary_partitioning_rotations\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mcs_vqe\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclique_operator\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mcs_vqe\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0munitary_partitioning_rotations\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconjugate\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 7\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0mrotated_Ar\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mAttributeError\u001b[0m: 'PauliwordOp' object has no attribute 'conjugate'" + ] } ], "source": [ @@ -392,7 +393,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 10, "id": "e327bbb8", "metadata": {}, "outputs": [ @@ -474,7 +475,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 11, "id": "193035b4", "metadata": {}, "outputs": [], @@ -485,7 +486,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 12, "id": "eeb32d3f", "metadata": {}, "outputs": [ @@ -506,8 +507,8 @@ " 0.253 YXYI +\n", "-0.709 XZXI\n", "\n", - "We obtain the contextual energy error -2.474841765813145\n", - "with error 0.3443867076391176\n", + "We obtain the contextual energy error -2.4748417658130966\n", + "with error 0.344386707639166\n", "qubit count of new CS-VQE H = 0\n", "\n", "*********************************************\n", @@ -522,8 +523,8 @@ " 0.253 YXYI +\n", "-0.709 XZXI\n", "\n", - "We obtain the contextual energy error -2.649488656354124\n", - "with error 0.1697398170981388\n", + "We obtain the contextual energy error -2.6494886626647505\n", + "with error 0.1697398107875121\n", "qubit count of new CS-VQE H = 1\n", "\n", "*********************************************\n", @@ -538,8 +539,8 @@ " 0.253 YXYI +\n", "-0.709 XZXI\n", "\n", - "We obtain the contextual energy error -2.510815789194936\n", - "with error 0.3084126842573265\n", + "We obtain the contextual energy error -2.5108157812971803\n", + "with error 0.30841269215508227\n", "qubit count of new CS-VQE H = 1\n", "\n", "*********************************************\n", @@ -554,8 +555,8 @@ " 0.253 YXYI +\n", "-0.709 XZXI\n", "\n", - "We obtain the contextual energy error -2.474841765813145\n", - "with error 0.3443867076391176\n", + "We obtain the contextual energy error -2.4748417658130966\n", + "with error 0.344386707639166\n", "qubit count of new CS-VQE H = 1\n", "\n", "*********************************************\n", @@ -581,8 +582,8 @@ " 0.253 YXYI +\n", "-0.709 XZXI\n", "\n", - "We obtain the contextual energy error -2.706592559510841\n", - "with error 0.1126359139414217\n", + "We obtain the contextual energy error -2.7065925580437877\n", + "with error 0.11263591540847484\n", "qubit count of new CS-VQE H = 2\n", "\n", "*********************************************\n", @@ -596,8 +597,8 @@ " 0.253 YXYI +\n", "-0.709 XZXI\n", "\n", - "We obtain the contextual energy error -2.6494886563541225\n", - "with error 0.16973981709814012\n", + "We obtain the contextual energy error -2.6494886626647514\n", + "with error 0.1697398107875112\n", "qubit count of new CS-VQE H = 2\n", "\n", "*********************************************\n", @@ -611,8 +612,8 @@ " 0.253 YXYI +\n", "-0.709 XZXI\n", "\n", - "We obtain the contextual energy error -2.5108157891949374\n", - "with error 0.30841268425732515\n", + "We obtain the contextual energy error -2.51081578129718\n", + "with error 0.3084126921550827\n", "qubit count of new CS-VQE H = 2\n", "\n", "*********************************************\n", @@ -659,8 +660,8 @@ " 0.253 YXYI +\n", "-0.709 XZXI\n", "\n", - "We obtain the contextual energy error -2.706592559510839\n", - "with error 0.11263591394142347\n", + "We obtain the contextual energy error -2.7065925580437873\n", + "with error 0.11263591540847528\n", "qubit count of new CS-VQE H = 3\n", "\n", "*********************************************\n", @@ -709,7 +710,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "/home/tweaving/anaconda3/lib/python3.8/site-packages/symmer/projection/cs_vqe.py:310: UserWarning: No stabilizers were specifed so the operator was returned\n", + "/home/tweaving/anaconda3/envs/symmer/lib/python3.7/site-packages/symmer/projection/cs_vqe.py:328: UserWarning: No stabilizers were specifed so the operator was returned\n", " warnings.warn('No stabilizers were specifed so the operator was returned')\n" ] } @@ -754,7 +755,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 13, "id": "6a8b998b", "metadata": {}, "outputs": [], @@ -775,7 +776,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 14, "id": "623e63cb", "metadata": {}, "outputs": [ @@ -807,7 +808,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 15, "id": "ef9fcabd", "metadata": {}, "outputs": [ @@ -819,7 +820,7 @@ "-1.000+0.000j YIYI\n", "and A(r)\n", "\n", - " we obtain an energy error of 0.3443867076391176.\n", + " we obtain an energy error of 0.344386707639166.\n", "qubit count of reduced CS-VQE H: 1\n" ] } @@ -866,7 +867,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.7.13" }, "vscode": { "interpreter": { diff --git a/notebooks/H3+ ground state failure example.ipynb b/notebooks/H3+ ground state failure example.ipynb index c05d7e1f..13b1fcb6 100644 --- a/notebooks/H3+ ground state failure example.ipynb +++ b/notebooks/H3+ ground state failure example.ipynb @@ -34,7 +34,7 @@ "HF energy: -1.2468600063384467\n", "MP2 energy: -1.2658602663569571\n", "CCSD energy: -1.2741446169583148\n", - "FCI energy: -1.274144467123987\n", + "FCI energy: -1.2741444671239888\n", "\n", "\n", "Number of qubits: 6\n" @@ -73,7 +73,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Least eigenvalue = -1.3507306438907685 | FCI error = -0.07658617676678148\n" + "Least eigenvalue = -1.3507306438907631 | FCI error = -0.07658617676677437\n" ] } ], @@ -95,7 +95,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "id": "15aef568", "metadata": {}, "outputs": [ @@ -103,12 +103,12 @@ "name": "stdout", "output_type": "stream", "text": [ - "Eigenvector with eigenvalue -1.3507306438907685:\n", + "Eigenvector with eigenvalue -1.3507306438907631:\n", "\n", - " 0.064+0.101j |001011> +\n", - " 0.077+0.122j |100011> +\n", - "-0.077-0.122j |101100> +\n", - "-0.521-0.820j |111000>\n" + " 0.062+0.102j |001011> +\n", + " 0.075+0.123j |100011> +\n", + "-0.075-0.123j |101100> +\n", + "-0.507-0.829j |111000>\n" ] } ], @@ -128,7 +128,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 4, "id": "5265519a", "metadata": {}, "outputs": [ @@ -136,13 +136,13 @@ "name": "stdout", "output_type": "stream", "text": [ - "Least eigenvalue = -1.274144467124002 | FCI error = -1.509903313490213e-14\n", + "Least eigenvalue = -1.2741444671239903 | FCI error = -1.5543122344752192e-15\n", "\n", - "Eigenvector with eigenvalue -1.274144467124002:\n", + "Eigenvector with eigenvalue -1.2741444671239903:\n", "\n", - " 0.059+0.073j |000011> +\n", - " 0.059+0.073j |001100> +\n", - "-0.625-0.769j |110000>\n" + " 0.082+0.045j |000011> +\n", + " 0.082+0.045j |001100> +\n", + "-0.867-0.479j |110000>\n" ] } ], @@ -176,6 +176,14 @@ "metadata": {}, "outputs": [], "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8b50467c", + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { @@ -194,7 +202,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.7.13" }, "vscode": { "interpreter": { diff --git a/notebooks/QuantumState usage.ipynb b/notebooks/QuantumState usage.ipynb index 762bf886..f64b4bf3 100644 --- a/notebooks/QuantumState usage.ipynb +++ b/notebooks/QuantumState usage.ipynb @@ -176,27 +176,27 @@ "name": "stdout", "output_type": "stream", "text": [ - " 0.263+0.182j |1101010011> +\n", - " 0.287+0.149j |1110011011> +\n", - " 0.047+0.315j |1001011111> +\n", - " 0.337+0.140j |0010011101> +\n", - " 0.210+0.130j |0011111100> +\n", - " 0.133+0.343j |1111110000> +\n", - " 0.188+0.049j |0111010101> +\n", - " 0.195+0.221j |1011000000> +\n", - " 0.276+0.189j |1011010000> +\n", - " 0.334+0.119j |1001001101>\n", + " 0.257+0.050j |1010010011> +\n", + " 0.152+0.293j |1110000001> +\n", + " 0.339+0.364j |0100001101> +\n", + " 0.201+0.013j |1110000111> +\n", + " 0.322+0.239j |0011100110> +\n", + " 0.047+0.252j |0100010100> +\n", + " 0.047+0.011j |1101001000> +\n", + " 0.107+0.314j |1000010010> +\n", + " 0.296+0.094j |0111001000> +\n", + " 0.253+0.191j |0010011101>\n", "\n", - " 0.164+0.343j |1010111101> +\n", - " 0.024+0.171j |1110110011> +\n", - " 0.126+0.193j |1000111010> +\n", - " 0.273+0.247j |0111100000> +\n", - " 0.180+0.323j |1010110100> +\n", - " 0.094+0.271j |0001101111> +\n", - " 0.317+0.170j |1111111001> +\n", - " 0.295+0.253j |0111100000> +\n", - " 0.141+0.101j |1111100100> +\n", - " 0.272+0.181j |1010011101>\n" + " 0.134+0.117j |1101101100> +\n", + " 0.263+0.270j |1111011100> +\n", + " 0.250+0.182j |1000011011> +\n", + " 0.173+0.064j |1000100100> +\n", + " 0.025+0.303j |0100001101> +\n", + " 0.343+0.332j |0110110011> +\n", + " 0.021+0.298j |1111111101> +\n", + " 0.229+0.004j |0111011101> +\n", + " 0.312+0.041j |0000101000> +\n", + " 0.220+0.296j |1000111001>\n" ] } ], @@ -214,7 +214,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 9, "id": "2c9aa59f", "metadata": {}, "outputs": [ @@ -222,27 +222,27 @@ "name": "stdout", "output_type": "stream", "text": [ - " 0.062+0.179j |0001101111> +\n", - " 0.223+0.093j |0010011101> +\n", - " 0.139+0.086j |0011111100> +\n", - " 0.125+0.032j |0111010101> +\n", - " 0.376+0.330j |0111100000> +\n", - " 0.083+0.128j |1000111010> +\n", - " 0.221+0.079j |1001001101> +\n", - " 0.031+0.209j |1001011111> +\n", - " 0.180+0.120j |1010011101> +\n", - " 0.119+0.214j |1010110100> +\n", - " 0.108+0.227j |1010111101> +\n", - " 0.129+0.146j |1011000000> +\n", - " 0.182+0.125j |1011010000> +\n", - " 0.174+0.120j |1101010011> +\n", - " 0.190+0.098j |1110011011> +\n", - " 0.016+0.113j |1110110011> +\n", - " 0.093+0.067j |1111100100> +\n", - " 0.088+0.227j |1111110000> +\n", - " 0.210+0.112j |1111111001>\n", + " 0.209+0.027j |0000101000> +\n", + " 0.169+0.128j |0010011101> +\n", + " 0.215+0.160j |0011100110> +\n", + " 0.243+0.446j |0100001101> +\n", + " 0.032+0.168j |0100010100> +\n", + " 0.229+0.222j |0110110011> +\n", + " 0.198+0.063j |0111001000> +\n", + " 0.153+0.003j |0111011101> +\n", + " 0.072+0.210j |1000010010> +\n", + " 0.167+0.121j |1000011011> +\n", + " 0.115+0.043j |1000100100> +\n", + " 0.147+0.198j |1000111001> +\n", + " 0.171+0.034j |1010010011> +\n", + " 0.032+0.007j |1101001000> +\n", + " 0.090+0.078j |1101101100> +\n", + " 0.102+0.196j |1110000001> +\n", + " 0.134+0.009j |1110000111> +\n", + " 0.176+0.180j |1111011100> +\n", + " 0.014+0.200j |1111111101>\n", "\n", - "Norm: (1.0000000000000002+0j)\n" + "Norm: (0.9999999999999998+0j)\n" ] } ], @@ -250,12 +250,12 @@ "psi = (psi_1 + psi_2).normalize\n", "print(psi)\n", "print()\n", - "print('Norm:', psi.conjugate * psi)" + "print('Norm:', psi.dagger * psi)" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 11, "id": "bc1e9705", "metadata": {}, "outputs": [ @@ -263,18 +263,18 @@ "name": "stdout", "output_type": "stream", "text": [ - " 5.125+0.000j ZIIYYYIYXX +\n", - "-0.120+0.000j YYXXYXYZXZ +\n", - " 1.356+0.000j YYXXYXYZXY +\n", - " 1.144+0.000j IIZYXXIXYY +\n", - " 0.250+0.000j XXIZYXYZXY +\n", - "-3.997+0.000j YXYYZZXIZY +\n", - " 0.874+0.000j ZXYYYZZYIZ +\n", - " 0.737+0.000j IIIYZXIXYZ +\n", - " 8.325+0.000j YXYXZIIXXX +\n", - "-0.195+0.000j YYXZZYYIIY\n", + " 1.876+0.000j YYIZYIXIYI +\n", + " 1.386+0.000j YZZYZIIYYY +\n", + "-0.155+0.000j ZIYZYIZXZY +\n", + "-4.208+0.000j XYIXZIZXZZ +\n", + "-0.297+0.000j IIIIYXZYZI +\n", + " 3.366+0.000j YYZZXIIXYY +\n", + " 0.238+0.000j XYIIXYIIZI +\n", + " 6.436+0.000j YIIYIYYIIX +\n", + "-0.722+0.000j YYIYIXIZIX +\n", + "-0.533+0.000j XZZYIYYZXZ\n", "\n", - "Expectation value = (-0.3411776054252657+1.3877787807814457e-17j)\n" + "Expectation value = (-0.12298367631617613+6.938893903907228e-18j)\n" ] } ], @@ -282,7 +282,7 @@ "op = random_herm_op(N, 10)\n", "print(op)\n", "print()\n", - "print('Expectation value =', psi.conjugate * op * psi)" + "print('Expectation value =', psi.dagger * op * psi)" ] }, { @@ -295,7 +295,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 13, "id": "bb741ebd", "metadata": {}, "outputs": [ @@ -317,7 +317,7 @@ "statevector[500] = np.sqrt(3/6)\n", "psi = QuantumState.from_array(statevector)\n", "print(psi)\n", - "print(psi.conjugate * psi)" + "print(psi.dagger * psi)" ] }, { @@ -345,7 +345,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.7.13" } }, "nbformat": 4, diff --git a/notebooks/QubitTapering usage.ipynb b/notebooks/QubitTapering usage.ipynb index e3c1b1d2..c751fd41 100644 --- a/notebooks/QubitTapering usage.ipynb +++ b/notebooks/QubitTapering usage.ipynb @@ -36,7 +36,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 11, "id": "67641e92", "metadata": {}, "outputs": [ @@ -54,10 +54,10 @@ "CCSD converged? True\n", "FCI converged? True\n", "\n", - "HF energy: -1.333349777097311\n", - "MP2 energy: -1.6161399127016054\n", - "CCSD energy: -1.8261847346725237\n", - "FCI energy: -1.8743019741837195\n", + "HF energy: -1.3333497770973124\n", + "MP2 energy: -1.6161399127016065\n", + "CCSD energy: -1.8261847366338029\n", + "FCI energy: -1.8643921454229408\n", "\n", "\n", "Number of qubits: 8\n" @@ -86,12 +86,12 @@ "multiplicity = 1\n", "charge = 0\n", "\n", - "molecule = MoleculeBuilder(geometry=geometry, charge=charge, basis=basis, spin=0, run_fci=True, print_info=True)" + "molecule = MoleculeBuilder(geometry=geometry, charge=charge, basis=basis, spin=0, symmetry=True, run_fci=True, print_info=True)" ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 12, "id": "305eef63", "metadata": {}, "outputs": [ @@ -216,7 +216,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 13, "id": "2cb87f24", "metadata": {}, "outputs": [ @@ -224,113 +224,113 @@ "data": { "text/plain": [ "{'IIIIIIII': (-1.0811399195666886+0j),\n", - " 'IIIIIIIZ': (0.013810914373994614+0j),\n", - " 'IIIIIIZI': (0.013810914373994537+0j),\n", - " 'IIIIIIZZ': (0.09424143717952177+0j),\n", - " 'IIIIIZII': (0.03758180217247291+0j),\n", - " 'IIIIIZIZ': (0.04955248667420177+0j),\n", - " 'IIIIIZZI': (0.07052407412802449+0j),\n", - " 'IIIIZIII': (0.037581802172472846+0j),\n", - " 'IIIIZIIZ': (0.07052407412802449+0j),\n", - " 'IIIIZIZI': (0.04955248667420177+0j),\n", - " 'IIIIZZII': (0.11637394770154717+0j),\n", - " 'IIIZIIII': (0.037581802172472895+0j),\n", - " 'IIIZIIIZ': (0.04186848978406614+0j),\n", - " 'IIIZIIZI': (0.10114884701928667+0j),\n", - " 'IIIZIZII': (0.05356550494495824+0j),\n", - " 'IIIZZIII': (0.053636244956641634+0j),\n", - " 'IIZIIIII': (0.03758180217247281+0j),\n", - " 'IIZIIIIZ': (0.10114884701928667+0j),\n", - " 'IIZIIIZI': (0.04186848978406614+0j),\n", - " 'IIZIIZII': (0.053636244956641634+0j),\n", - " 'IIZIZIII': (0.05356550494495824+0j),\n", - " 'IIZZIIII': (0.11637394770154719+0j),\n", - " 'IZIIIIII': (0.06458158745266908+0j),\n", - 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" 'XZZZXXZX': (-0.03455504445638335+0j),\n", - " 'XZZZXYZY': (-0.03455504445638335+0j),\n", - " 'YZZZYXZX': (-0.03455504445638335+0j),\n", - " 'YZZZYYZY': (-0.03455504445638335+0j),\n", - " 'XZXXZZZX': (0.033409848638420565+0j),\n", - " 'XZXYZZZY': (0.033409848638420565+0j),\n", - " 'YZYXZZZX': (0.033409848638420565+0j),\n", - " 'YZYYZZZY': (0.033409848638420565+0j),\n", - " 'XXIIIIYY': (-0.02356440205914443+0j),\n", - " 'XYIIIIYX': (0.02356440205914443+0j),\n", - " 'YXIIIIXY': (0.02356440205914443+0j),\n", - " 'YYIIIIXX': (-0.02356440205914443+0j),\n", - " 'XXIIYYII': (-0.05724862633431721+0j),\n", - " 'XYIIYXII': (0.05724862633431721+0j),\n", - " 'YXIIXYII': (0.05724862633431721+0j),\n", - " 'YYIIXXII': (-0.05724862633431721+0j),\n", - " 'XXYYIIII': (-0.018939856552919392+0j),\n", - " 'XYYXIIII': (0.018939856552919392+0j),\n", - " 'YXXYIIII': (0.018939856552919392+0j),\n", - " 'YYXXIIII': (-0.018939856552919392+0j)}" + " 'ZIIZIIII': (0.06882246148173882+0j),\n", + " 'ZIZIIIII': (0.04988260492881946+0j),\n", + " 'ZZIIIIII': (0.09088382270620028+0j),\n", + " 'IIIIXXYY': (-0.020971587453822636+0j),\n", + " 'IIIIXYYX': (0.020971587453822636+0j),\n", + " 'IIIIYXXY': (0.020971587453822636+0j),\n", + " 'IIIIYYXX': (-0.020971587453822636+0j),\n", + " 'IIXXIIYY': (-0.05928035723522046+0j),\n", + " 'IIXYIIYX': (0.05928035723522046+0j),\n", + " 'IIYXIIXY': (0.05928035723522046+0j),\n", + " 'IIYYIIXX': (-0.05928035723522046+0j),\n", + " 'IIXXYYII': (-7.074001168339472e-05+0j),\n", + " 'IIXYYXII': (7.074001168339472e-05+0j),\n", + " 'IIYXXYII': (7.074001168339472e-05+0j),\n", + " 'IIYYXXII': (-7.074001168339472e-05+0j),\n", + " 'IXIZZZZX': (-0.026686664801746283+0j),\n", + " 'IXZIZZZX': (0.006723183836674227+0j),\n", + " 'IXZZIZZX': (0.027645787727647718+0j),\n", + " 'IXZZZIZX': (-0.0069092567287355605+0j),\n", + " 'IXZZZZIX': (-0.012720876709062082+0j),\n", + " 'IXZZZZZX': (-0.014308578576769924+0j),\n", + " 'IYIZZZZY': (-0.026686664801746283+0j),\n", + " 'IYZIZZZY': (0.006723183836674227+0j),\n", + " 'IYZZIZZY': (0.027645787727647718+0j),\n", + " 'IYZZZIZY': (-0.0069092567287355605+0j),\n", + " 'IYZZZZIY': (-0.012720876709062082+0j),\n", + " 'IYZZZZZY': (-0.014308578576769924+0j),\n", + " 'ZXZZZZZX': (0.013667145245773627+0j),\n", + " 'ZYZZZZZY': (0.013667145245773627+0j),\n", + " 'IXZZXYYI': (0.03455504445638328+0j),\n", + " 'IXZZYYXI': (-0.03455504445638328+0j),\n", + " 'IYZZXXYI': (-0.03455504445638328+0j),\n", + " 'IYZZYXXI': (0.03455504445638328+0j),\n", + " 'IXXYZZYI': (-0.03340984863842051+0j),\n", + " 'IXYYZZXI': (0.03340984863842051+0j),\n", + " 'IYXXZZYI': (0.03340984863842051+0j),\n", + " 'IYYXZZXI': (-0.03340984863842051+0j),\n", + " 'XIZZZZXI': (0.013667145245773626+0j),\n", + " 'XZIZZZXI': (0.006723183836674227+0j),\n", + " 'XZZIZZXI': (-0.026686664801746283+0j),\n", + " 'XZZZIZXI': (-0.0069092567287355605+0j),\n", + " 'XZZZZIXI': (0.027645787727647718+0j),\n", + " 'XZZZZZXI': (-0.014308578576769926+0j),\n", + " 'XZZZZZXZ': (-0.012720876709062082+0j),\n", + " 'YIZZZZYI': (0.013667145245773626+0j),\n", + " 'YZIZZZYI': (0.006723183836674227+0j),\n", + " 'YZZIZZYI': (-0.026686664801746283+0j),\n", + " 'YZZZIZYI': (-0.0069092567287355605+0j),\n", + " 'YZZZZIYI': (0.027645787727647718+0j),\n", + " 'YZZZZZYI': (-0.014308578576769926+0j),\n", + " 'YZZZZZYZ': (-0.012720876709062082+0j),\n", + " 'XZZZXXZX': (-0.034555044456383285+0j),\n", + " 'XZZZXYZY': (-0.034555044456383285+0j),\n", + " 'YZZZYXZX': (-0.034555044456383285+0j),\n", + " 'YZZZYYZY': (-0.034555044456383285+0j),\n", + " 'XZXXZZZX': (0.03340984863842051+0j),\n", + " 'XZXYZZZY': (0.03340984863842051+0j),\n", + " 'YZYXZZZX': (0.03340984863842051+0j),\n", + " 'YZYYZZZY': (0.03340984863842051+0j),\n", + " 'XXIIIIYY': (-0.023564402059144368+0j),\n", + " 'XYIIIIYX': (0.023564402059144368+0j),\n", + " 'YXIIIIXY': (0.023564402059144368+0j),\n", + " 'YYIIIIXX': (-0.023564402059144368+0j),\n", + " 'XXIIYYII': (-0.05724862633431717+0j),\n", + " 'XYIIYXII': (0.05724862633431717+0j),\n", + " 'YXIIXYII': (0.05724862633431717+0j),\n", + " 'YYIIXXII': (-0.05724862633431717+0j),\n", + " 'XXYYIIII': (-0.018939856552919354+0j),\n", + " 'XYYXIIII': (0.018939856552919354+0j),\n", + " 'YXXYIIII': (0.018939856552919354+0j),\n", + " 'YYXXIIII': (-0.018939856552919354+0j)}" ] }, - "execution_count": 12, + "execution_count": 13, "metadata": {}, "output_type": "execute_result" } @@ -349,7 +349,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 14, "id": "d9ab5a88", "metadata": {}, "outputs": [ @@ -362,7 +362,7 @@ " 1 IZIZIZIZ" ] }, - "execution_count": 13, + "execution_count": 14, "metadata": {}, "output_type": "execute_result" } @@ -375,7 +375,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 15, "id": "651ece02", "metadata": {}, "outputs": [ @@ -435,7 +435,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 16, "id": "03b40998", "metadata": {}, "outputs": [ @@ -462,7 +462,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 17, "id": "7244101d", "metadata": {}, "outputs": [ @@ -489,7 +489,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 18, "id": "3d54b931", "metadata": {}, "outputs": [ @@ -580,7 +580,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 19, "id": "2bde8799", "metadata": {}, "outputs": [ @@ -588,9 +588,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "The ground state energy of the full system is -1.87430197418373,\n", - "whereas for the tapered system we find the energy is -1.8643921454229446.\n", - "The absolute error is 0.009909828760785278.\n" + "The ground state energy of the full system is -1.8743019741837155,\n", + "whereas for the tapered system we find the energy is -1.864392145422943.\n", + "The absolute error is 0.009909828760772399.\n" ] } ], @@ -613,7 +613,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 20, "id": "1daa0bed", "metadata": {}, "outputs": [ @@ -647,7 +647,7 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 21, "id": "a17ca852", "metadata": {}, "outputs": [ @@ -669,8 +669,8 @@ " 0.021+0.067j |10100101>\n", "\n", "Taking the dominant amplitude 0.135+0.439j |11100100> for sector selection...\n", - "we obtain the sector [-1 -1 1 1], in which the ground state energy is -1.8743019741837192.\n", - "The absolute error is 1.0658141036401503e-14.\n" + "we obtain the sector [-1 -1 1 1], in which the ground state energy is -1.8743019741837181.\n", + "The absolute error is -2.6645352591003757e-15.\n" ] } ], @@ -724,7 +724,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.7.13" } }, "nbformat": 4, diff --git a/notebooks/Tapering the Heisenberg Hamiltonian.ipynb b/notebooks/Tapering the Heisenberg Hamiltonian.ipynb index c51dd747..4497b0e3 100644 --- a/notebooks/Tapering the Heisenberg Hamiltonian.ipynb +++ b/notebooks/Tapering the Heisenberg Hamiltonian.ipynb @@ -15,7 +15,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 1, "id": "072ceab2", "metadata": {}, "outputs": [ @@ -25,26 +25,26 @@ "text": [ "The heisenberg Hamiltonian is\n", "\n", - "-0.481+0.000j IIZZ +\n", - "-0.481+0.000j IZZI +\n", - "-0.481+0.000j ZZII +\n", - "-0.210+0.000j IIYY +\n", - "-0.210+0.000j IYYI +\n", - "-0.210+0.000j YYII +\n", - "-0.083+0.000j IIXX +\n", - "-0.083+0.000j IXXI +\n", - "-0.083+0.000j XXII\n", + "-0.247+0.000j IIXX +\n", + "-0.247+0.000j IXXI +\n", + "-0.247+0.000j XXII +\n", + "-0.145+0.000j IIZZ +\n", + "-0.145+0.000j IZZI +\n", + "-0.145+0.000j ZZII +\n", + "-0.112+0.000j IIYY +\n", + "-0.112+0.000j IYYI +\n", + "-0.112+0.000j YYII\n", "\n", - "with ground state energy -1.5161210135558105 and corresponding eigenvector\n", + "with ground state energy -0.7529922520770905 and corresponding eigenvector\n", "\n", - " 0.683-0.000j |0000> +\n", - "-0.175+0.000j |0011> +\n", - "-0.027+0.000j |0101> +\n", - "-0.051+0.000j |0110> +\n", - "-0.051+0.000j |1001> +\n", - "-0.027+0.000j |1010> +\n", - "-0.175+0.000j |1100> +\n", - " 0.683+0.000j |1111>\n" + " 0.439-0.000j |0000> +\n", + " 0.366+0.000j |0011> +\n", + " 0.290+0.000j |0101> +\n", + " 0.298+0.000j |0110> +\n", + " 0.298+0.000j |1001> +\n", + " 0.290+0.000j |1010> +\n", + " 0.366+0.000j |1100> +\n", + " 0.439+0.000j |1111>\n" ] } ], @@ -88,35 +88,6 @@ "We may perform a VQE simulation over this space:" ] }, - { - "cell_type": "code", - "execution_count": 8, - "id": "ac63729c", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([[0, 0, 0, 0, 0, 0, 1, 1],\n", - " [0, 0, 0, 0, 0, 1, 1, 0],\n", - " [0, 0, 0, 0, 1, 1, 0, 0],\n", - " [0, 0, 1, 1, 0, 0, 1, 1],\n", - " [0, 1, 1, 0, 0, 1, 1, 0],\n", - " [1, 1, 0, 0, 1, 1, 0, 0],\n", - " [0, 0, 1, 1, 0, 0, 0, 0],\n", - " [0, 1, 1, 0, 0, 0, 0, 0],\n", - " [1, 1, 0, 0, 0, 0, 0, 0]])" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "H.symp_matrix.astype(int)" - ] - }, { "cell_type": "markdown", "id": "4ba9484e", @@ -127,7 +98,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 3, "id": "a1738822", "metadata": { "scrolled": true @@ -175,7 +146,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 4, "id": "d0560d49", "metadata": {}, "outputs": [ @@ -185,26 +156,26 @@ "text": [ "We rotate the Hamiltonian accordingly:\n", "\n", - "-0.481+0.000j IIZZ +\n", - "-0.083+0.000j IIXX +\n", - "-0.210+0.000j IIYY +\n", - " 0.481-0.000j IXZI +\n", - " 0.083-0.000j IXXX +\n", - " 0.481-0.000j XIZZ +\n", - " 0.210-0.000j XIZX +\n", - " 0.083-0.000j XXIX +\n", - "-0.210+0.000j XXYY\n", + "-0.145+0.000j IIZZ +\n", + "-0.247+0.000j IIXX +\n", + "-0.112+0.000j IIYY +\n", + " 0.145-0.000j IXZI +\n", + " 0.247-0.000j IXXX +\n", + " 0.145-0.000j XIZZ +\n", + " 0.112-0.000j XIZX +\n", + " 0.247-0.000j XXIX +\n", + "-0.112+0.000j XXYY\n", "\n", "and observe that qubit positions [1 0] consist only of Pauli I, X operators.\n", "\n", "These may therefore be removed to yield a 2-qubit reduced Hamiltonian:\n", "\n", - "-0.481+0.000j ZI +\n", - "-0.961+0.000j ZZ +\n", - " 0.083+0.000j IX +\n", - "-0.210+0.000j ZX +\n", - "-0.166+0.000j XX +\n", - "-0.419+0.000j YY\n" + "-0.145+0.000j ZI +\n", + "-0.291+0.000j ZZ +\n", + " 0.247+0.000j IX +\n", + "-0.112+0.000j ZX +\n", + "-0.494+0.000j XX +\n", + "-0.224+0.000j YY\n" ] } ], @@ -220,7 +191,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 5, "id": "f58a7949", "metadata": {}, "outputs": [ @@ -231,7 +202,7 @@ " 1 XXXX" ] }, - "execution_count": 12, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" } @@ -250,7 +221,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 6, "id": "db6d9dec", "metadata": {}, "outputs": [ @@ -258,16 +229,16 @@ "name": "stdout", "output_type": "stream", "text": [ - "The ground state energy of the Hamiltonian is -1.5161210135558105\n", - "and for the 2-qubit tapered Hamiltonian it is -1.516121013555812;\n", - "the energy error is 1.5543122344752192e-15.\n", + "The ground state energy of the Hamiltonian is -0.7529922520770905\n", + "and for the 2-qubit tapered Hamiltonian it is -0.7529922520770895;\n", + "the energy error is 9.992007221626409e-16.\n", "\n", "The tapered ground state is:\n", "\n", - "-0.965+0.000j |00> +\n", - "-0.073+0.000j |01> +\n", - "-0.039+0.000j |10> +\n", - " 0.247+0.000j |11>\n" + "-0.621+0.000j |00> +\n", + " 0.421+0.000j |01> +\n", + " 0.411+0.000j |10> +\n", + "-0.518+0.000j |11>\n" ] } ], @@ -315,7 +286,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.8" + "version": "3.7.13" }, "vscode": { "interpreter": { From 4f8d59547885c3d86f22a5c997a4476e56f0a6bd Mon Sep 17 00:00:00 2001 From: TimWeaving Date: Tue, 11 Oct 2022 20:37:53 +0100 Subject: [PATCH 08/11] Way that HF state was generated not scalable - now built manually from knowledge of qubit encoding. Same for spin parity operators. --- symmer/chemistry/build_molecule.py | 26 +++++------ symmer/chemistry/chem_utils.py | 74 ++++++++++++++++++++++++++++-- 2 files changed, 82 insertions(+), 18 deletions(-) diff --git a/symmer/chemistry/build_molecule.py b/symmer/chemistry/build_molecule.py index ba09ef36..54a926c9 100644 --- a/symmer/chemistry/build_molecule.py +++ b/symmer/chemistry/build_molecule.py @@ -2,9 +2,9 @@ from symmer.symplectic import PauliwordOp, QuantumState from symmer.utils import QubitOperator_to_dict, safe_PauliwordOp_to_dict from symmer.chemistry import ( - FermionicHamiltonian, FermioniCC, PySCFDriver, - fermion_to_qubit_operator, get_fermionic_number_operator, get_fermionic_up_down_parity_operators -) + FermionicHamiltonian, FermioniCC, PySCFDriver, build_bk_matrix, + fermion_to_qubit_operator, get_fermionic_number_operator, get_parity_operators_JW, get_parity_operators_BK + ) import numpy as np from openfermion import get_fermion_operator, jordan_wigner, FermionOperator, hermitian_conjugated from typing import Tuple, List @@ -56,10 +56,9 @@ def __init__(self, self.T_fermion.build_operator() self.n_qubits = self.H_fermion.n_qubits - hf_ferm_array = self.H_fermion.hf_fermionic_basis_state - HF_fermionic_op = FermionOperator(' '.join([f'{pos}^' for pos in hf_ferm_array.nonzero()[0]]), 1) - self.HF_fermionic_op_q = fermion_to_qubit_operator(HF_fermionic_op, self.qubit_mapping_str, N_qubits=self.n_qubits) - self.hf_array = (self.HF_fermionic_op_q * QuantumState([[0]*self.n_qubits])).state_matrix[0] + self.hf_array = self.H_fermion.hf_fermionic_basis_state + if self.qubit_mapping_str == 'bravyi_kitaev': + self.hf_array = (build_bk_matrix(self.n_qubits) @ self.hf_array.reshape(-1,1)).reshape(-1) % 2 if self.print_info: print() @@ -176,13 +175,12 @@ def number_operator(self): def up_down_parity_operators(self): """ Assumes alternating up/down spin orbitals """ - parity_up_op, parity_down_op = get_fermionic_up_down_parity_operators(self.n_qubits) - parity_up_pword = fermion_to_qubit_operator( - parity_up_op, self.qubit_mapping_str, N_qubits=self.n_qubits - ) - parity_down_pword = fermion_to_qubit_operator( - parity_down_op, self.qubit_mapping_str, N_qubits=self.n_qubits - ) + if self.qubit_mapping_str == 'jordan_wigner': + parity_up_pword, parity_down_pword = get_parity_operators_JW(self.n_qubits) + elif self.qubit_mapping_str == 'bravyi_kitaev': + parity_up_pword, parity_down_pword = get_parity_operators_BK(self.n_qubits) + else: + raise ValueError('Unrecognised qubit mapping, must be one of jordan_wigner or bravyi_kitaev') return parity_up_pword, parity_down_pword def data_dictionary(self): diff --git a/symmer/chemistry/chem_utils.py b/symmer/chemistry/chem_utils.py index b4273633..9cfdf1e6 100644 --- a/symmer/chemistry/chem_utils.py +++ b/symmer/chemistry/chem_utils.py @@ -7,7 +7,7 @@ import py3Dmol from pyscf.tools import cubegen from openfermion import FermionOperator, count_qubits -from openfermion.transforms import jordan_wigner, bravyi_kitaev, parity_code +from openfermion.transforms import jordan_wigner, bravyi_kitaev#, parity_code from symmer.symplectic.base import QuantumState from symmer.utils import QubitOperator_to_dict from symmer.symplectic import PauliwordOp @@ -210,6 +210,24 @@ def get_fermionic_up_down_parity_operators(N_qubits: int) -> Tuple[FermionOperat return parity_up, parity_down +def build_bk_matrix(n_qubits): + """ Implemented from https://onlinelibrary.wiley.com/doi/full/10.1002/qua.24969 + """ + assert n_qubits > 0 + B = np.array([[1]]) + + n_q_power2 = int(np.ceil(np.log2(n_qubits))) + for _ in range(n_q_power2): + zero = np.zeros_like(B) + zero_ones = zero.copy() + zero_ones[-1,:] =1 + + B = np.block([ + [ B, zero ], + [ zero_ones, B ] + ]) + + return B[:n_qubits, :n_qubits] def fermion_to_qubit_operator(Fermionic_operator: FermionOperator, qubit_mapping_str: str, @@ -226,9 +244,11 @@ def fermion_to_qubit_operator(Fermionic_operator: FermionOperator, Returns: qubit_operator (PauliwordOp): qubit operator of fermonic operator (under certain mapping) """ - fermonic_to_qubit_map = {'jordan_wigner': jordan_wigner, - 'bravyi_kitaev': bravyi_kitaev, - 'parity_code': parity_code} + fermonic_to_qubit_map = { + 'jordan_wigner': jordan_wigner, + 'bravyi_kitaev': bravyi_kitaev, + #'parity_code': parity_code + } if qubit_mapping_str.lower() not in fermonic_to_qubit_map.keys(): print(f'valid qubit mappings : {list(fermonic_to_qubit_map.keys())}') @@ -245,3 +265,49 @@ def fermion_to_qubit_operator(Fermionic_operator: FermionOperator, # want to return PauliWordOp (but results in circular import!) ## aka PauliWordOp base class imports utils and so import here causes problems. return PauliwordOp.from_dictionary(q_op_dict) + +def get_parity_operators_JW(n_qubits): + """ Assumes alternating up/down spin orbitals + """ + spin_up_parity_Z_block = np.arange(1, n_qubits+1) % 2 + spin_up_parity_op = PauliwordOp(np.hstack( + [np.zeros_like(spin_up_parity_Z_block), spin_up_parity_Z_block]), [1]) + + spin_down_parity_Z_block = np.arange(n_qubits) % 2 + spin_down_parity_op = PauliwordOp(np.hstack( + [np.zeros_like(spin_down_parity_Z_block), spin_down_parity_Z_block]), [1]) + + return spin_up_parity_op, spin_down_parity_op + +def get_parity_operators_BK(n_qubits): + """ Assumes alternating up/down spin orbitals + """ + spin_up_parity_Z_block = np.arange(1, n_qubits+1) % 2 + spin_up_parity_op = PauliwordOp(np.hstack( + [np.zeros_like(spin_up_parity_Z_block), spin_up_parity_Z_block]), [1]) + + parity_mat = build_bk_matrix(n_qubits) + temp_array = parity_mat.copy() + argmax_list = [] + counter = 0 + while counter Date: Tue, 11 Oct 2022 20:38:08 +0100 Subject: [PATCH 09/11] Adding NaCl molecule to hamiltonian_data --- tests/hamiltonian_data/NaCl_STO-3G_SINGLET_BK.json | 1 + tests/hamiltonian_data/NaCl_STO-3G_SINGLET_JW.json | 1 + 2 files changed, 2 insertions(+) create mode 100644 tests/hamiltonian_data/NaCl_STO-3G_SINGLET_BK.json create mode 100644 tests/hamiltonian_data/NaCl_STO-3G_SINGLET_JW.json diff --git a/tests/hamiltonian_data/NaCl_STO-3G_SINGLET_BK.json b/tests/hamiltonian_data/NaCl_STO-3G_SINGLET_BK.json new file mode 100644 index 00000000..b2fecac7 --- /dev/null +++ b/tests/hamiltonian_data/NaCl_STO-3G_SINGLET_BK.json @@ -0,0 +1 @@ +{"hamiltonian": {"IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII": [-373.10112076491157, 0.0], "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZI": [1.7113436247265557, 0.0], "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZII": [0.12033880274999831, 0.0], "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIZ": [0.11865361528336402, 0.0], "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZZ": [1.7113436247265557, 0.0], "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIII": [1.4612618110676645, 0.0], "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIZI": [0.0994484221059004, 0.0], "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIZZ": [0.0994484221059004, 0.0], "IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZII": [1.4612618110676645, 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initialization for QuantumState, with an additional normalization method (for measurement counts) --- symmer/symplectic/base.py | 37 ++++++++++++++++++++++++++++++++++++- 1 file changed, 36 insertions(+), 1 deletion(-) diff --git a/symmer/symplectic/base.py b/symmer/symplectic/base.py index f1e90143..1f5840df 100644 --- a/symmer/symplectic/base.py +++ b/symmer/symplectic/base.py @@ -970,6 +970,16 @@ def __add__(self, """ new_state = self.state_op + Qstate.state_op return QuantumState(new_state.X_block, new_state.coeff_vec) + + def __radd__(self, + add_obj: Union[int, "QuantumState"] + ) -> "QuantumState": + """ Allows use of sum() over a list of PauliwordOps + """ + if add_obj == 0: + return self + else: + return self + add_obj def __sub__(self, Qstate: "QuantumState" @@ -1083,12 +1093,25 @@ def sectors_present(self, symmetry): @cached_property def normalize(self): - """ + """ Normalize a state by dividing through its norm. + Returns: self (QuantumState) """ coeff_vector = self.state_op.coeff_vec/norm(self.state_op.coeff_vec) return QuantumState(self.state_matrix, coeff_vector, vec_type=self.vec_type) + + @cached_property + def normalize_counts(self): + """ Normalize a state by dividing through by the sum of coefficients and taking its square + root. This normalization is faithful to the probability distribution one might obtain from + quantum circuit sampling. A subtle difference, but important! + + Returns: + self (QuantumState) + """ + coeff_vector = np.sqrt(self.state_op.coeff_vec/np.sum(self.state_op.coeff_vec)) + return QuantumState(self.state_matrix, coeff_vector, vec_type=self.vec_type) @cached_property def dagger(self) -> "QuantumState": @@ -1167,6 +1190,18 @@ def sample_state(self, n_samples: int, return_normalized: bool=False) -> "Quantu else: return samples_as_coeff_state + @classmethod + def from_dictionary(cls, + state_dict: Dict[str, complex] + ) -> "QuantumState": + """ Initialize a QuantumState from a dictionary of the form {'1101':a, '0110':b, '1010':c, ...}. This is useful for + converting the measurement output of a quantum circuit to a QuantumState object for further manipulation/bootstrapping. + """ + bin_strings, coeff_vector = zip(*state_dict.items()) + coeff_vector = np.array(coeff_vector) + state_matrix = np.array([[int(i) for i in bstr] for bstr in bin_strings]) + return cls(state_matrix, coeff_vector) + @classmethod def from_array(cls, statevector: np.array, From 8a130f490fe1ecda7f4ec1dee0d6a854d499e358 Mon Sep 17 00:00:00 2001 From: TimWeaving Date: Mon, 17 Oct 2022 10:02:46 +0100 Subject: [PATCH 11/11] to_dictionary methpd for QuantumState class --- symmer/symplectic/base.py | 14 +++++++++++++- 1 file changed, 13 insertions(+), 1 deletion(-) diff --git a/symmer/symplectic/base.py b/symmer/symplectic/base.py index 1f5840df..d02b58ba 100644 --- a/symmer/symplectic/base.py +++ b/symmer/symplectic/base.py @@ -1094,7 +1094,7 @@ def sectors_present(self, symmetry): @cached_property def normalize(self): """ Normalize a state by dividing through its norm. - + Returns: self (QuantumState) """ @@ -1190,6 +1190,18 @@ def sample_state(self, n_samples: int, return_normalized: bool=False) -> "Quantu else: return samples_as_coeff_state + @cached_property + def to_dictionary(self) -> Dict[str, complex]: + """ Return the QuantumState as a dictionary + """ + state_dict = dict( + zip( + [''.join([str(i) for i in row]) for row in self.state_matrix], + self.state_op.coeff_vec + ) + ) + return state_dict + @classmethod def from_dictionary(cls, state_dict: Dict[str, complex]