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braids_test.py
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braids_test.py
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import numpy as np
from qutip import basis, snot, controlled_gate, sigmaz, tensor, rand_ket
# functions related to quantum mechanical concepts
from qm import bloch
from qm import deriveUnitary
from qm import evolve
from qm import Sz
# Hamiltonian generators
from hamiltonians import constructHadamardH
from hamiltonians import constructHadamardCorr
from hamiltonians import constructCZH
# helper functions
from helpers import are_close
# functions that generate our circuit and time evolutions
from teleportation import continuousTeleportationSimulation
from teleportation import continuousXXBraidingCorrectionSimulation
from teleportation import continuousZBraidingCorrectionSimulation
from teleportation import continuousDecodingSimulation
from teleportation import circuitTeleportationSimulation
from teleportation import circuitXXBraidingCorrectionSimulation
from teleportation import circuitZBraidingCorrectionSimulation
from teleportation import circuitDecodingSimulation
from teleportation import simulateTeleportation
z0, z1, xp, xm, yp, ym = bloch(basis(2, 0), basis(2, 1))
class TestCZandH(object):
def testHadamardUnitary(self):
H = constructHadamardH(1, [0])
U = snot()
U2 = deriveUnitary(H, np.pi)
Ucorr = constructHadamardCorr(1, [0])
assert Ucorr*U2 == U
assert H.isherm
def testHadamardUnitaryMulti(self):
H = constructHadamardH(2, [0, 1])
UH1 = snot(N=2, target=0)
UH2 = snot(N=2, target=1)
U2 = deriveUnitary(H, np.pi)
Ucorr = constructHadamardCorr(2, [0, 1])
assert Ucorr*U2 == UH1*UH2
assert H.isherm
def testHadamardHamiltonian(self):
t = np.pi
H = constructHadamardH(1, [0])
U = snot()
Ucorr = constructHadamardCorr(1, [0])
for psi0 in [z0, z1, xp, xm, yp, ym, rand_ket(2)]:
psiu = U*psi0
psif = evolve(H, t/2., psi0)
psic = Ucorr*psif
overl = psiu.overlap(psic)
assert are_close(overl, 1.)
assert H.isherm
def testCZUnitary(self):
H = constructCZH(2, [0], [1])
U = controlled_gate(sigmaz(), N=2, control=0, target=1)
U2 = deriveUnitary(H, np.pi)
assert U == U2
assert H.isherm
def testCZHamiltonian(self):
t = np.pi
H = constructCZH(2, [0], [1])
U = controlled_gate(sigmaz(), N=2, control=0, target=1)
states = [z0, z1, xp, xm, yp, ym, rand_ket(2)]
for psiA in states:
for psiB in states:
psi0 = tensor([psiA, psiB])
psiu = U*psi0
psic = evolve(H, t/2., psi0)
overl = psiu.overlap(psic)
assert are_close(overl, 1., atol=1e-04)
assert H.isherm
def testCZHamiltonianMore(self):
t = np.pi
H1 = constructCZH(4, [0], [1])
H2 = constructCZH(4, [2], [3])
U1 = controlled_gate(sigmaz(), N=4, control=0, target=1)
U2 = controlled_gate(sigmaz(), N=4, control=2, target=3)
for psiA in [z0, z1]:
for psiB in [xp, xm]:
for psiC in [z0, z1]:
for psiD in [xp, xm]:
psi0 = tensor([psiA, psiB, psiC, psiD])
psiu = U2*U1*psi0
psic = evolve(H1, t/2., psi0)
psic = evolve(H2, t/2., psic)
overl = psiu.overlap(psic)
assert are_close(overl, 1., atol=1e-04)
assert H1.isherm
assert H2.isherm
class TestCompareCircuitEvolutions(object):
def test_teleportation_component(self):
states = [z0, z1, xp, xm, yp, ym, rand_ket(2)]
for psi in states:
psift = continuousTeleportationSimulation(psi, 0.)
psifc = circuitTeleportationSimulation(psi)
overl = psifc.overlap(psift)
assert are_close(overl, 1., atol=1e-04)
def test_unitary_teleportation(self):
states = [z0, z1, xp, xm, yp, ym, rand_ket(2)]
for psi in states:
fidelity0000, fidelity = simulateTeleportation(
psi,
circuitTeleportationSimulation,
circuitXXBraidingCorrectionSimulation,
circuitZBraidingCorrectionSimulation,
circuitDecodingSimulation)
assert are_close(fidelity0000, 1.)
assert are_close(fidelity, 1.)
def test_time_teleportation(self):
states = [z0, z1, xp, xm, yp, ym, rand_ket(2)]
for psi in states:
fidelity0000, fidelity = simulateTeleportation(
psi,
continuousTeleportationSimulation,
continuousXXBraidingCorrectionSimulation,
continuousZBraidingCorrectionSimulation,
continuousDecodingSimulation)
assert are_close(fidelity0000, 1.)
assert fidelity < fidelity0000
def test_noisy_time_teleportation_z0(self):
N = 8
gamma = 0.05
c_ops = [np.sqrt(gamma)*Sz(N, i) for i in range(N)]
psi = z0
fidelity0000, fidelity = simulateTeleportation(
psi,
continuousTeleportationSimulation,
continuousXXBraidingCorrectionSimulation,
continuousZBraidingCorrectionSimulation,
continuousDecodingSimulation,
c_ops=c_ops)
assert fidelity0000 > fidelity
def test_noisy_time_teleportation_z1(self):
N = 8
gamma = 0.05
c_ops = [np.sqrt(gamma)*Sz(N, i) for i in range(N)]
psi = z1
fidelity0000, fidelity = simulateTeleportation(
psi,
continuousTeleportationSimulation,
continuousXXBraidingCorrectionSimulation,
continuousZBraidingCorrectionSimulation,
continuousDecodingSimulation,
c_ops=c_ops)
assert fidelity0000 > fidelity
def test_noisy_time_teleportation_xp(self):
N = 8
gamma = 0.05
c_ops = [np.sqrt(gamma)*Sz(N, i) for i in range(N)]
psi = xp
fidelity0000, fidelity = simulateTeleportation(
psi,
continuousTeleportationSimulation,
continuousXXBraidingCorrectionSimulation,
continuousZBraidingCorrectionSimulation,
continuousDecodingSimulation,
c_ops=c_ops)
assert fidelity0000 > fidelity
def test_noisy_time_teleportation_xm(self):
N = 8
gamma = 0.05
c_ops = [np.sqrt(gamma)*Sz(N, i) for i in range(N)]
psi = xm
fidelity0000, fidelity = simulateTeleportation(
psi,
continuousTeleportationSimulation,
continuousXXBraidingCorrectionSimulation,
continuousZBraidingCorrectionSimulation,
continuousDecodingSimulation,
c_ops=c_ops)
assert fidelity0000 > fidelity
def test_noisy_time_teleportation_yp(self):
N = 8
gamma = 0.05
c_ops = [np.sqrt(gamma)*Sz(N, i) for i in range(N)]
psi = yp
fidelity0000, fidelity = simulateTeleportation(
psi,
continuousTeleportationSimulation,
continuousXXBraidingCorrectionSimulation,
continuousZBraidingCorrectionSimulation,
continuousDecodingSimulation,
c_ops=c_ops)
assert fidelity0000 > fidelity
def test_noisy_time_teleportation_ym(self):
N = 8
gamma = 0.05
c_ops = [np.sqrt(gamma)*Sz(N, i) for i in range(N)]
psi = ym
fidelity0000, fidelity = simulateTeleportation(
psi,
continuousTeleportationSimulation,
continuousXXBraidingCorrectionSimulation,
continuousZBraidingCorrectionSimulation,
continuousDecodingSimulation,
c_ops=c_ops)
assert fidelity0000 > fidelity
def test_noisy_time_teleportation_rand(self):
N = 8
gamma = 0.05
c_ops = [np.sqrt(gamma)*Sz(N, i) for i in range(N)]
psi = rand_ket(2)
fidelity0000, fidelity = simulateTeleportation(
psi,
continuousTeleportationSimulation,
continuousXXBraidingCorrectionSimulation,
continuousZBraidingCorrectionSimulation,
continuousDecodingSimulation,
c_ops=c_ops)
assert fidelity0000 > fidelity