def create_densop():
mat_1 = np.array([[0.75, 0.25], [0.25, 0.25]])
de_1 = DensOp(matrix=mat_1)
de_ini = de_1.composite(num=4)
de_1.free()
return de_ini
def decoder(de_comp, id_all, theta, iperm_mat):
qs_0 = QState(1)
de_0 = DensOp(qstate=[qs_0])
de_fin = de_0.tenspro(de_comp) # add 1-qubit (|0>)
de_fin.apply(iperm_mat)
[de_fin.ry(i, phase=theta) for i in id_all]
qs_0.free()
de_0.free()
return de_fin
dim = 2**qnum
vec = np.array([0.0]*dim)
vec[0] = 1.0
mat = unitary_group.rvs(dim)
vec = np.dot(mat, vec)
qs = QState(vector=vec)
return qs
if __name__ == '__main__':
qnum_A = 2
qnum_B = 2
id_A = list(range(qnum_A))
id_B = [i+qnum_A for i in range(qnum_B)]
qs = random_qstate(qnum_A+qnum_B)
de = DensOp(qstate=[qs], prob=[1.0])
ent = de.entropy()
ent_A = de.entropy(id_A)
ent_B = de.entropy(id_B)
print("** S(A,B) = {:.4f}".format(ent))
print("** S(A) = {:.4f}".format(ent_A))
print("** S(B) = {:.4f}".format(ent_B))
qs.free()
de.free()
return densop_est
if __name__ == '__main__':
# settings
qubit_num = 1
mixed_num = 2
shots = 100
# quantum state ensemble (original)
qstate, prob = random_qstate_ensemble(qubit_num, mixed_num)
# density operator (original)
densop_ori = DensOp(qstate=qstate, prob=prob)
# density operator estimation only from quantum state ensemble
# (quantum state tomography)
densop_est = estimate_densop(prob, qstate, shots)
print("** density operator (original)")
densop_ori.show()
print("** density operator (estimated)")
densop_est.show()
print("** fidelity =", densop_ori.fidelity(densop_est))
for q in qstate:
q.free()
densop_ori.free()
densop_est.free()
from qlazypy import QState, DensOp
qs_pure = QState(1).h(0) # (|0> + |1>) / sqrt(2.0)
de_pure = DensOp(qstate=[qs_pure], prob=[1.0])
qs_pure_1 = QState(1) # |0>
qs_pure_2 = QState(1).x(0) # |1>
de_mixed = DensOp(qstate=[qs_pure_1, qs_pure_2], prob=[0.5, 0.5])
print("== pure state ==")
de_pure.show()
print("* trace =", de_pure.trace())
print("* square trace =", de_pure.sqtrace())
print("")
print("== mixed state ==")
de_mixed.show()
print("* trace =", de_mixed.trace())
print("* square trace =", de_mixed.sqtrace())
qs_pure.free()
qs_pure_1.free()
qs_pure_2.free()
de_pure.free()
de_mixed.free()
qs = QState(4)
qs.h(0).h(1) # unitary operation for 0,1-system
qs.x(2).z(3) # unitary operation for 2,3-system
de1 = DensOp(qstate=[qs], prob=[1.0]) # product state
de1_reduced = de1.patrace([0, 1]) # trace-out 0,1-system
print("== partial trace of product state ==")
print(" * trace = ", de1_reduced.trace())
print(" * square trace = ", de1_reduced.sqtrace())
qs.cx(1, 3).cx(0, 2) # entangle between 0,1-system and 2,3-system
de2 = DensOp(qstate=[qs], prob=[1.0]) # entangled state
de2_reduced = de2.patrace([0, 1]) # trace-out 0,1-system
print("== partial trace of entangled state ==")
print(" * trace = ", de2_reduced.trace())
print(" * square trace = ", de2_reduced.sqtrace())
print("== partial state of entangled state ==")
qs.show([2, 3])
qs.free()
de1.free()
de2.free()
de1_reduced.free()
de2_reduced.free()
