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kendall_tau_form.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Wed May 5 13:42:23 2021
@author: paulxie
"""
import numpy as np
from gurobipy import *
from networkx import DiGraph
import networkx as nx
class kt_solver:
def __init__(self, arcs, operations, K_dir, S, K_rev = None):
G = DiGraph()
for a in arcs:
G.add_edge(a[0], a[1])
self.V = list(G.nodes())
self.A = list(G.edges())
self.A_rev = []
for a in self.A:
self.A_rev.append((a[1], a[0]))
self.gates_layout = {}
self.C = []
self.gates_id = list(operations.keys())
self.K_rev = {}
self.Q = []
Layers = []
for o in operations:
Layers.append(operations[o][-1])
self.K_rev[o] = operations[o][2]
self.C.append((operations[o][0], operations[o][1]))
if operations[o][0] not in self.Q:
self.Q.append(operations[o][0])
if operations[o][1] not in self.Q:
self.Q.append(operations[o][1])
self.Q.sort()
self.Layers = range(min(Layers), max(Layers)+1)
for l in self.Layers:
self.gates_layout[l] = []
for o in operations:
if operations[o][-1] == l:
self.gates_layout[l].append(o)
if K_rev != None:
for k in self.K_rev.keys():
self.K_rev[k] = K_rev
self.K_dir = K_dir
self.S = S
self.operations = operations
def solve_it(self, TimeLimit = 10800):
M = len(self.V) + 2
m = Model('KT_Formulation')
x = m.addVars(self.Q, self.Layers, lb = min(self.V), ub = max(self.V), vtype = GRB.INTEGER, name = 'x')
z = m.addVars(self.Q, self.Q, self.Layers, vtype = GRB.BINARY, name = 'z')
# for i,j,t in z.keys():
# z[i,j,t] = -z[j,i,t]
y_dir = m.addVars(self.A, self.gates_id, self.Layers, vtype = GRB.BINARY, name ='y')
y_rev = m.addVars(self.A_rev, self.gates_id, self.Layers, vtype = GRB.BINARY, name = 'y*')
r = m.addVars(self.Q, self.V, self.Layers, vtype = GRB.BINARY, name = 'r')
k = m.addVars(self.Q, self.Q, self.Layers[:-1], vtype = GRB.BINARY, name = 'k')
# for i,j,t in k.keys():
# k[i,j,t] = k[j,i,t]
m._cost_1 = 0
for a in self.A:
for c in self.gates_id:
for t in self.Layers:
m._cost_1 += self.K_dir * y_dir[a[0],a[1],c,t] + self.K_rev[c] * y_rev[a[1],a[0],c,t]
m._cost_2 = 0
for i in self.Q:
for j in self.Q:
if i != j:
for t in self.Layers[:-1]:
m._cost_2 += 0.5 * self.S * k[i,j,t]
m.setObjective(m._cost_1 + m._cost_2, GRB.MINIMIZE)
for t in self.Layers:
for c in self.gates_layout[t]:
p,q = self.operations[c][0], self.operations[c][1]
for (i,j) in self.A:
m.addConstr((r[p,i,t] + r[q,j,t] >= 2*y_dir[i,j,c,t]), 'constr_1')
m.addConstr((r[p,j,t] + r[q,i,t] >= 2*y_rev[j,i,c,t]), 'constr_2')
# m.addConstr((x[p,t] - x[j,t] >= -1), 'constr_6_L')
# m.addConstr((x[p,t] - x[j,t] <= 1), 'constr_6_R')
m.addConstr((sum(y_dir[a[0],a[1],c,t]+ y_rev[a[1],a[0],c,t] for a in self.A) == 1), 'constr_3')
for i in self.Q:
for j in self.Q:
if i != j:
m.addConstr((x[i,t] - x[j,t] <= M*z[i,j,t] -1), 'constr_4')
# m.addConstr((x[j,t] - x[i,t] <= M*(1-z[i,j,t]) -1), 'constr_5')
for q in self.Q:
m.addConstr((x[q,t] == quicksum(i* r[q,i,t] for i in self.V)), 'constr_7')
m.addConstr((quicksum(r[q,i,t] for i in self.V) == 1), 'constr_10')
m.addConstrs((quicksum(r[q,i,t] for q in self.Q) <= 1 for i in self.V), 'constr_9')
for i in self.Q:
for j in self.Q:
if i != j :
m.addConstr((z[i,j,t] + z[j,i,t] == 1), 'constr_11')
for t in self.Layers[:-1]:
for i in self.Q:
for j in self.Q:
if i != j :
m.addConstr((z[i,j,t] - z[i,j,t+1] >= -k[i,j,t]), 'constr_8_L')
m.addConstr((z[i,j,t] - z[i,j,t+1] <= k[i,j,t]), 'constr_8_R')
m.Params.TimeLimit = TimeLimit
m.optimize()
return m, x, z, y_dir, y_rev, r, k
def print_results(self, m, x, z, y_dir, y_rev, r, k):
if m.status != GRB.OPTIMAL:
print('\nThe model is infeasible or was not solved to optimality.')
else:
print('\n')
print('Optimal objective value is {}'.format(m.ObjVal, 2))
swap_count = 0
for q1, q2, t in k.keys():
if (k[q1,q2,t].x == 1) and (q1<q2):
swap_count += 1
print('A swap gate was implemented on qubits {} between layer {} and {}'.format((q1,q2), t, t+1))
dir_count = 0
m_value = [] # record the m value needed for each layer
for t in self.Layers[:-1]:
steps = {1:[]} # track which qubits were swaped at each step
for q1 in self.Q:
for q2 in self.Q:
if q1 < q2:
max_inst = max(steps.keys())
if (k[q1,q2,t].x == 1):
if (q1 not in steps[max_inst]) and (q2 not in steps[max_inst]):
steps[max_inst].extend([q1, q2])
else:
steps[max_inst + 1] = [q1, q2]
max_inst = max(steps.keys())
if steps[max_inst] != []:
m_value.append(max_inst)
print('{} steps is needed between layers {} and {}'.format(max_inst, t, t+1))
for t in self.Layers:
for a in self.A:
for c in self.gates_id:
if y_dir[a[0], a[1], c, t].x == 1:
print('Gate {} is directly implemented on arc {} at layer {}'.format(c, a, t))
dir_count += 1
elif y_rev[a[1], a[0], c, t].x == 1:
print('Gate {} is reversely implemented on arc {} at layer {}'.format(c, a, t))
print('\nGates directly implemented: {}/{}'.format(dir_count, len(self.operations)))
print('Number of swap gates used: {}'.format(swap_count))
print('m value needed to for feasible soluiton: ', max(m_value))
def get_m_value(self, k):
m_value = [] # record the m value needed for each layer
for t in self.Layers[:-1]:
steps = {1:[]} # track which qubits were swaped at each step
for q1 in self.Q:
for q2 in self.Q:
if q1 < q2:
max_inst = max(steps.keys())
if (k[q1,q2,t].x == 1):
if (q1 not in steps[max_inst]) and (q2 not in steps[max_inst]):
steps[max_inst].extend([q1, q2])
else:
steps[max_inst + 1] = [q1, q2]
max_inst = max(steps.keys())
if steps[max_inst] != []:
m_value.append(max_inst)
else:
m_value.append(1)
return max(m_value)
ARCS = [(1,3), (4,1), (2,4), (5,2)]
OPERATIONS = {
23: [3, 4, 11, 1],
26: [4, 3, 12, 2],
28: [3, 4, 11, 3],
33: [0, 1, 11, 1],
36: [1, 0, 12, 2],
38: [0, 1, 11, 3],
43: [2, 0, 11, 4],
46: [0, 2, 12, 5],
48: [2, 0, 11, 6],
53: [4, 1, 11, 4],
56: [1, 4, 12, 5],
58: [4, 1, 11, 6],
63: [4, 3, 11, 7],
66: [3, 4, 12, 8],
68: [4, 3, 11, 9],
73: [0, 2, 11, 7],
76: [2, 0, 12, 8],
78: [0, 2, 11, 9],
83: [4, 0, 11, 10],
86: [0, 4, 12, 11],
88: [4, 0, 11, 12],
93: [2, 1, 11, 10],
96: [1, 2, 12, 11],
98: [2, 1, 11, 12],
103: [2, 1, 11, 13],
106: [1, 2, 12, 14],
108: [2, 1, 11, 15],
113: [4, 0, 11, 13],
116: [0, 4, 12, 14],
118: [4, 0, 11, 15]
}
soln = kt_solver(ARCS, OPERATIONS, 10, 34)
m, x, z, y_dir, y_rev, r, k = soln.solve_it()
soln.print_results(m, x, z, y_dir, y_rev, r, k)
m_val = soln.get_m_value(k)
print('Runtime = ', m.runtime)