Apply "tapering off qubits" technique of sections VII and VIII in https://arxiv.org/pdf/1701.08213.pdf

[ndattani]

H2/STO-3G should become a 1-qubit problem, and the data in Table I of the paper can be reproduced. But we can explore far larger systems that are closer to what classical quantum chemists are interested in.

[amccaskey]

This has been implemented for Jordan Wigner in https://github.com/ORNL-QCI/xacc-vqe/blob/master/task/tasks/DiagonalizeTask.cpp

However, I am still having issues with Bravyi-Kitaev. My strategy has been to enumerate all bit strings with NELEC ones set - these form the basis for my Hamiltonian subspace that I will diagonalize. As stated this works for JW, however for BK I build up the occupation -> bravyi-kitaev basis transformation (Eq 50 of tapering qubits) and apply it to all NELEC eigenstates to produce corresponding BK eigenstates. I then build up the Hamiltonian matrix elements in this basis and diagonalize.

This works for problems that have NQubits as a power of 2. It does not work for problems that have NQubits not a power of 2 (for example H2 6-31++G, NQubits=12). Seeley, Love paper says in these cases to take the submatrix of the next largest BK transformation matrix 2^m > M and pull out the submatrix that corresponds to the number of orbitals you have. So clearly something wrong is happening there that I can't figure out.

To test the matrix construction part, I have brute-force built up the entire matrix for the H2 6-31++G 12 qubit problem and diagonalized that, and received the correct ground state energy.

So something is missing in my understanding of the Occupation -> BK basis transformation when NQubits is not a power of 2.

[ndattani]

Thanks Alex,
It is already nice that it's working for JW, though JW for Li2 in an aug-cc-pCV6Z basis set already has more than 1000 spin orbitals, and will therefore have 1000-local terms, whereas BK is O(log(M))-local and may therefore only have log_2(1000) = 10-local terms for the same molecule.

10-local seems much better than 1000-local, so I do think there's value to doing the tapering in the BK picture, since BK would probably be used for most practical applications.