def main():
# parameters for generating random state: |psi>
alpha, beta, gamma = random.random(), random.random(), random.random()
# reference state: T|psi>
qs_expect = QState(1)
qs_expect.rz(0, phase=alpha).rx(0, phase=beta).rz(0, phase=gamma).t(0)
# prepare initial state
qs = QState(3)
qs.h(0).s(0) # |Y>
qs.h(1).t(1) # |A>
qs.rz(2, phase=alpha).rx(2, phase=beta).rz(2, phase=gamma) # |psi>
# T gate (only with X,Z,H,CNOT and measurement)
qs.cx(1, 2)
mval = qs.m(qid=[2]).last
if mval == '1':
qs.cx(1, 0).h(0).cx(1, 0).h(0)
qs.x(1).z(1)
qs_actual = qs.partial(qid=[1])
# show the result
print("== expect ==")
qs_expect.show()
print("== actual ==")
qs_actual.show()
print("== fidelity ==")
print("{:.6f}".format(qs_actual.fidelity(qs_expect)))
def test_operate_xyz(self):
"""test 'operate' (xyz)
"""
qs_expect = QState(qubit_num=3)
qs_actual = QState(qubit_num=3)
pp = PauliProduct(pauli_str="XYZ", qid=[2, 0, 1])
qs_expect.x(2).y(0).z(1)
qs_actual.operate(pp=pp)
ans = equal_qstates(qs_expect, qs_actual)
self.assertEqual(ans, True)
def test_operate_h_x(self):
"""test 'operate' (x followed by h)
"""
qs_expect = QState(qubit_num=1).h(0)
qs_actual = QState(qubit_num=1).h(0)
pp = PauliProduct(pauli_str="X")
qs_expect.x(0)
qs_actual.operate(pp=pp)
ans = equal_qstates(qs_expect, qs_actual)
self.assertEqual(ans, True)
qs.h(1).cx(1,2)
# initial state (before teleportation)
print("== Alice (initial) ==")
qs.show([0])
print("== Bob (initial) ==")
qs.show([2])
# Alice execute Bell-measurement to her qubits 0,1
print("== Bell measurement ==")
result = qs.mb([0,1],shots=1).lst
# Bob operate his qubit (id=2) according to the result
if result == BELL_PHI_PLUS:
print("result: phi+")
elif result == BELL_PSI_PLUS:
print("result: psi+")
qs.x(2)
elif result == BELL_PSI_MINUS:
print("result: psi-")
qs.x(2).z(2)
elif result == BELL_PHI_MINUS:
print("result: phi-")
qs.z(2)
# final state (before teleportation)
print("== Alice (final) ==")
qs.show([0])
print("== Bob (final) ==")
qs.show([2])
def logical_zero():
anc = [0, 1, 2, 3, 4, 5, 6] # registers for ancila
cod = [7, 8, 9, 10, 11, 12, 13] # registers for steane code
qs_total = QState(14)
# g1
qs_total.h(anc[0])
[qs_total.cx(anc[0], anc[i]) for i in range(1, 4)]
qs_total.cx(anc[0], cod[3]).cx(anc[1],
cod[4]).cx(anc[2],
cod[5]).cx(anc[3], cod[6])
[qs_total.cx(anc[0], anc[i]) for i in range(1, 4)]
qs_total.h(anc[0])
mval = qs_total.m(qid=[anc[0]]).last
if mval == '1': qs_total.z(cod[0]).z(cod[1]).z(cod[2]).z(cod[3])
qs_total.reset(qid=anc)
# g2
qs_total.h(anc[0])
[qs_total.cx(anc[0], anc[i]) for i in range(1, 4)]
qs_total.cx(anc[0], cod[1]).cx(anc[1],
cod[2]).cx(anc[2],
cod[5]).cx(anc[3], cod[6])
[qs_total.cx(anc[0], anc[i]) for i in range(1, 4)]
qs_total.h(anc[0])
mval = qs_total.m(qid=[anc[0]]).last
if mval == '1': qs_total.z(cod[0]).z(cod[1]).z(cod[4]).z(cod[5])
qs_total.reset(qid=anc)
# g3
qs_total.h(anc[0])
[qs_total.cx(anc[0], anc[i]) for i in range(1, 4)]
qs_total.cx(anc[0], cod[0]).cx(anc[1],
cod[2]).cx(anc[2],
cod[4]).cx(anc[3], cod[6])
[qs_total.cx(anc[0], anc[i]) for i in range(1, 4)]
qs_total.h(anc[0])
mval = qs_total.m(qid=[anc[0]]).last
if mval == '1': qs_total.z(cod[2]).z(cod[4]).z(cod[6])
qs_total.reset(qid=anc)
# g4
qs_total.h(anc[0])
[qs_total.cx(anc[0], anc[i]) for i in range(1, 4)]
qs_total.cz(anc[0], cod[3]).cz(anc[1],
cod[4]).cz(anc[2],
cod[5]).cz(anc[3], cod[6])
[qs_total.cx(anc[0], anc[i]) for i in range(1, 4)]
qs_total.h(anc[0])
mval = qs_total.m(qid=[anc[0]]).last
if mval == '1': qs_total.x(cod[0]).x(cod[1]).x(cod[2]).x(cod[3])
qs_total.reset(qid=anc)
# g5
qs_total.h(anc[0])
[qs_total.cx(anc[0], anc[i]) for i in range(1, 4)]
qs_total.cz(anc[0], cod[1]).cz(anc[1],
cod[2]).cz(anc[2],
cod[5]).cz(anc[3], cod[6])
[qs_total.cx(anc[0], anc[i]) for i in range(1, 4)]
qs_total.h(anc[0])
mval = qs_total.m(qid=[anc[0]]).last
if mval == '1': qs_total.x(cod[0]).x(cod[1]).x(cod[4]).x(cod[5])
qs_total.reset(qid=anc)
# g6
qs_total.h(anc[0])
[qs_total.cx(anc[0], anc[i]) for i in range(1, 4)]
qs_total.cz(anc[0], cod[0]).cz(anc[1],
cod[2]).cz(anc[2],
cod[4]).cz(anc[3], cod[6])
[qs_total.cx(anc[0], anc[i]) for i in range(1, 4)]
qs_total.h(anc[0])
mval = qs_total.m(qid=[anc[0]]).last
if mval == '1': qs_total.x(cod[2]).x(cod[4]).x(cod[6])
qs_total.reset(qid=anc)
# g7
qs_total.h(anc[0])
[qs_total.cx(anc[0], anc[i]) for i in range(1, 7)]
[qs_total.cz(anc[i], cod[i]) for i in range(7)]
[qs_total.cx(anc[0], anc[i]) for i in range(1, 7)]
qs_total.h(anc[0])
mval = qs_total.m(qid=[anc[0]]).last
if mval == '1': [qs_total.x(q) for q in cod]
qs_total.reset(qid=anc)
qs = qs_total.partial(qid=cod)
return qs
from qlazy import QState, DensOp
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])
