def test_CheckMulType():
"Qobj multiplication type"
# ket-bra and bra-ket multiplication
psi = basis(5)
dm = psi * psi.dag()
assert_(dm.isoper)
assert_(dm.isherm)
nrm = psi.dag() * psi
assert_equal(np.prod(nrm.shape), 1)
assert_((abs(nrm) == 1)[0, 0])
# operator-operator multiplication
H1 = rand_herm(3)
H2 = rand_herm(3)
out = H1 * H2
assert_(out.isoper)
out = H1 * H1
assert_(out.isoper)
assert_(out.isherm)
out = H2 * H2
assert_(out.isoper)
assert_(out.isherm)
U = rand_unitary(5)
out = U.dag() * U
assert_(out.isoper)
assert_(out.isherm)
N = num(5)
out = N * N
assert_(out.isoper)
assert_(out.isherm)
# operator-ket and bra-operator multiplication
op = sigmax()
ket1 = basis(2)
ket2 = op * ket1
assert_(ket2.isket)
bra1 = basis(2).dag()
bra2 = bra1 * op
assert_(bra2.isbra)
assert_(bra2.dag() == ket2)
# superoperator-operket and operbra-superoperator multiplication
sop = to_super(sigmax())
opket1 = operator_to_vector(fock_dm(2))
opket2 = sop * opket1
assert(opket2.isoperket)
opbra1 = operator_to_vector(fock_dm(2)).dag()
opbra2 = opbra1 * sop
assert(opbra2.isoperbra)
assert_(opbra2.dag() == opket2)
def testOperatorListState(self):
"""
expect: operator list and state
"""
res = expect([sigmax(), sigmay(), sigmaz()], fock(2, 0))
assert_(len(res) == 3)
assert_(all(abs(res - [0, 0, 1]) < 1e-12))
res = expect([sigmax(), sigmay(), sigmaz()], fock_dm(2, 1))
assert_(len(res) == 3)
assert_(all(abs(res - [0, 0, -1]) < 1e-12))
def __init__(self, N, correct_global_phase=True,
sx=None, sz=None, sxsy=None):
"""
Parameters
----------
sx: Integer/List
The delta for each of the qubits in the system.
sz: Integer/List
The epsilon for each of the qubits in the system.
sxsy: Integer/List
The interaction strength for each of the qubit pair in the system.
"""
super(SpinChain, self).__init__(N, correct_global_phase)
self.sx_ops = [tensor([sigmax() if m == n else identity(2)
for n in range(N)])
for m in range(N)]
self.sz_ops = [tensor([sigmaz() if m == n else identity(2)
for n in range(N)])
for m in range(N)]
self.sxsy_ops = []
for n in range(N - 1):
x = [identity(2)] * N
x[n] = x[n + 1] = sigmax()
y = [identity(2)] * N
y[n] = y[n + 1] = sigmay()
self.sxsy_ops.append(tensor(x) + tensor(y))
if sx is None:
self.sx_coeff = [0.25 * 2 * np.pi] * N
elif not isinstance(sx, list):
self.sx_coeff = [sx * 2 * np.pi] * N
else:
self.sx_coeff = sx
if sz is None:
self.sz_coeff = [1.0 * 2 * np.pi] * N
elif not isinstance(sz, list):
self.sz_coeff = [sz * 2 * np.pi] * N
else:
self.sz_coeff = sz
if sxsy is None:
self.sxsy_coeff = [0.1 * 2 * np.pi] * (N - 1)
elif not isinstance(sxsy, list):
self.sxsy_coeff = [sxsy * 2 * np.pi] * (N - 1)
else:
self.sxsy_coeff = sxsy
def test_unitarity_known():
"""
Metrics: Unitarity for known cases.
"""
def case(q_oper, known_unitarity):
assert_almost_equal(unitarity(q_oper), known_unitarity)
yield case, to_super(sigmax()), 1.0
yield case, sum(map(
to_super, [qeye(2), sigmax(), sigmay(), sigmaz()]
)) / 4, 0.0
yield case, sum(map(
to_super, [qeye(2), sigmax()]
)) / 2, 1 / 3.0
def test_known_iscptp(self):
"""
Superoperator: iscp, istp and iscptp known cases.
"""
# Check that unitaries are CPTP.
assert_(identity(2).iscptp)
assert_(sigmax().iscptp)
# The partial transpose map, whose Choi matrix is SWAP, is TP but not
# CP.
W = Qobj(swap(), type='super', superrep='choi')
assert_(W.istp)
assert_(not W.iscp)
assert_(not W.iscptp)
# Subnormalized maps (representing erasure channels, for instance)
# can be CP but not TP.
subnorm_map = Qobj(identity(4) * 0.9, type='super', superrep='super')
assert_(subnorm_map.iscp)
assert_(not subnorm_map.istp)
assert_(not subnorm_map.iscptp)
# Check that things which aren't even operators aren't identified as
# CPTP.
assert_(not (basis(2).iscptp))
def add_annotation(self, state_or_vector, text, **kwargs):
"""Add a text or LaTeX annotation to Bloch sphere,
parametrized by a qubit state or a vector.
Parameters
----------
state_or_vector : Qobj/array/list/tuple
Position for the annotaion.
Qobj of a qubit or a vector of 3 elements.
text : str/unicode
Annotation text.
You can use LaTeX, but remember to use raw string
e.g. r"$\\langle x \\rangle$"
or escape backslashes
e.g. "$\\\\langle x \\\\rangle$".
**kwargs :
Options as for mplot3d.axes3d.text, including:
fontsize, color, horizontalalignment, verticalalignment.
"""
if isinstance(state_or_vector, Qobj):
vec = [expect(sigmax(), state_or_vector),
expect(sigmay(), state_or_vector),
expect(sigmaz(), state_or_vector)]
elif isinstance(state_or_vector, (list, ndarray, tuple)) \
and len(state_or_vector) == 3:
vec = state_or_vector
else:
raise Exception("Position needs to be specified by a qubit " +
"state or a 3D vector.")
self.annotations.append({'position': vec,
'text': text,
'opts': kwargs})
def testExpandGate3toN_permutation(self):
"""
gates: expand 3 to 3 with permuTation (using toffoli)
"""
for _p in itertools.permutations([0, 1, 2]):
controls, target = [_p[0], _p[1]], _p[2]
controls = [1, 2]
target = 0
p = [1, 2, 3]
p[controls[0]] = 0
p[controls[1]] = 1
p[target] = 2
U = toffoli(N=3, controls=controls, target=target)
ops = [basis(2, 0).dag(), basis(2, 0).dag(), identity(2)]
P = tensor(ops[p[0]], ops[p[1]], ops[p[2]])
assert_(P * U * P.dag() == identity(2))
ops = [basis(2, 1).dag(), basis(2, 0).dag(), identity(2)]
P = tensor(ops[p[0]], ops[p[1]], ops[p[2]])
assert_(P * U * P.dag() == identity(2))
ops = [basis(2, 0).dag(), basis(2, 1).dag(), identity(2)]
P = tensor(ops[p[0]], ops[p[1]], ops[p[2]])
assert_(P * U * P.dag() == identity(2))
ops = [basis(2, 1).dag(), basis(2, 1).dag(), identity(2)]
P = tensor(ops[p[0]], ops[p[1]], ops[p[2]])
assert_(P * U * P.dag() == sigmax())
def test_stinespring_dims(self):
"""
Stinespring: Check that dims of channels are preserved.
"""
# FIXME: not the most general test, since this assumes a map
# from square matrices to square matrices on the same space.
chan = super_tensor(to_super(sigmax()), to_super(qeye(3)))
A, B = to_stinespring(chan)
assert_equal(A.dims, [[2, 3, 1], [2, 3]])
assert_equal(B.dims, [[2, 3, 1], [2, 3]])
def case_is_clifford(self, U):
paulis = (identity(2), sigmax(), sigmay(), sigmaz())
for P in paulis:
U_P = U * P * U.dag()
assert_(any(
self._prop_identity(U_P * Q)
for Q in paulis
))
def case_is_clifford(self, U):
paulis = (identity(2), sigmax(), sigmay(), sigmaz())
for P in paulis:
U_P = U * P * U.dag()
out = (np.any(
np.array([self._prop_identity(U_P * Q) for Q in paulis])
))
return out
def qubit_clifford_group(N=None, target=0):
"""
Generates the Clifford group on a single qubit,
using the presentation of the group given by Ross and Selinger
(http://www.mathstat.dal.ca/~selinger/newsynth/).
Parameters
-----------
N : int or None
Number of qubits on which each operator is to be defined
(default: 1).
target : int
Index of the target qubit on which the single-qubit
Clifford operators are to act.
Yields
------
op : Qobj
Clifford operators, represented as Qobj instances.
"""
# The Ross-Selinger presentation of the single-qubit Clifford
# group expresses each element in the form C_{ijk} = E^i X^j S^k
# for gates E, X and S, and for i in range(3), j in range(2) and
# k in range(4).
#
# We start by defining these gates. E is defined in terms of H,
# \omega and S, so we define \omega and H first.
w = np.exp(1j * 2 * np.pi / 8)
H = snot()
X = sigmax()
S = phasegate(np.pi / 2)
E = H * (S ** 3) * w ** 3
for op in map(
# partial(reduce, mul) returns a function that takes products of its argument,
# by analogy to sum. Note that by analogy, sum can be written partial(reduce, add).
partial(reduce, mul),
# product(...) yields the Cartesian product of its arguments. Here, each element is
# a tuple (E**i, X**j, S**k) such that partial(reduce, mul) acting on the tuple
# yields E**i * X**j * S**k.
product(_powers(E, 3), _powers(X, 2), _powers(S, 4))
):
# Finally, we optionally expand the gate.
if N is not None:
yield gate_expand_1toN(op, N, target)
else:
yield op
def TestUserNoise(self):
"""
Test for the user-defined noise object
"""
dr_noise = DriftNoise(sigmax())
proc = Processor(1)
proc.add_noise(dr_noise)
proc.tlist = np.array([0, np.pi / 2.])
result = proc.run_state(rho0=basis(2, 0))
assert_allclose(fidelity(result.states[-1], basis(2, 1)),
1,
rtol=1.0e-6)
def test_chi_known(self):
"""
Superoperator: Chi-matrix for known cases is correct.
"""
def case(S, chi_expected, silent=True):
chi_actual = to_chi(S)
chiq = Qobj(chi_expected,
dims=[[[2], [2]], [[2], [2]]],
superrep='chi')
if not silent:
print(chi_actual)
print(chi_expected)
assert_almost_equal((chi_actual - chiq).norm('tr'), 0)
case(sigmax(),
[[0, 0, 0, 0], [0, 4, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]])
case(to_super(sigmax()),
[[0, 0, 0, 0], [0, 4, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]])
case(qeye(2), [[4, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]])
case((-1j * sigmax() * pi / 4).expm(),
[[2, 2j, 0, 0], [-2j, 2, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]])
def add_states(self, state, kind="vector"):
"""Add a state vector Qobj to Bloch sphere.
Parameters
----------
state : qobj
Input state vector.
kind : str {'vector','point'}
Type of object to plot.
"""
if isinstance(state, Qobj):
state = [state]
for st in state:
if kind == "vector":
vec = [expect(sigmax(), st), expect(sigmay(), st), expect(sigmaz(), st)]
self.add_vectors(vec)
elif kind == "point":
pnt = [expect(sigmax(), st), expect(sigmay(), st), expect(sigmaz(), st)]
self.add_points(pnt)
def test_QobjHerm():
"Qobj Hermicity"
N = 10
data = np.random.random(
(N, N)) + 1j * np.random.random((N, N)) - (0.5 + 0.5j)
q = Qobj(data)
assert_equal(q.isherm, False)
data = data + data.conj().T
q = Qobj(data)
assert_(q.isherm)
q_a = destroy(5)
assert_(not q_a.isherm)
q_ad = create(5)
assert_(not q_ad.isherm)
# test addition of two nonhermitian operators adding up to a hermitian one
q_x = q_a + q_ad
assert_hermicity(q_x, True)
# test addition of one hermitan and one nonhermitian operator
q = q_x + q_a
assert_hermicity(q, False)
# test addition of two hermitan operators
q = q_x + q_x
assert_hermicity(q, True)
# Test multiplication of two Hermitian operators.
# This results in a skew-Hermitian operator, so
# we're checking here that __mul__ doesn't set wrong
# metadata.
q = sigmax() * sigmay()
assert_hermicity(q, False, "Expected iZ = X * Y to be skew-Hermitian.")
# Similarly, we need to check that -Z = X * iY is correctly
# identified as Hermitian.
q = sigmax() * (1j * sigmay())
assert_hermicity(q, True, "Expected -Z = X * iY to be Hermitian.")
def test_QobjHerm():
"Qobj Hermicity"
N = 10
data = np.random.random(
(N, N)) + 1j * np.random.random((N, N)) - (0.5 + 0.5j)
q = Qobj(data)
assert_equal(q.isherm, False)
data = data + data.conj().T
q = Qobj(data)
assert_(q.isherm)
q_a = destroy(5)
assert_(not q_a.isherm)
q_ad = create(5)
assert_(not q_ad.isherm)
# test addition of two nonhermitian operators adding up to a hermitian one
q_x = q_a + q_ad
assert_hermicity(q_x, True)
# test addition of one hermitan and one nonhermitian operator
q = q_x + q_a
assert_hermicity(q, False)
# test addition of two hermitan operators
q = q_x + q_x
assert_hermicity(q, True)
# Test multiplication of two Hermitian operators.
# This results in a skew-Hermitian operator, so
# we're checking here that __mul__ doesn't set wrong
# metadata.
q = sigmax() * sigmay()
assert_hermicity(q, False, "Expected iZ = X * Y to be skew-Hermitian.")
# Similarly, we need to check that -Z = X * iY is correctly
# identified as Hermitian.
q = sigmax() * (1j * sigmay())
assert_hermicity(q, True, "Expected -Z = X * iY to be Hermitian.")
def TestDecoherenceNoise(self):
"""
Test for the decoherence noise
"""
tlist = np.array([1, 2, 3, 4, 5, 6])
coeffs = [np.array([1, 1, 1, 1, 1, 1])]
# Time-dependent
decnoise = DecoherenceNoise(sigmaz(),
coeffs=coeffs,
tlist=tlist,
targets=[1])
noise_list = decnoise.get_noise(2)
assert_allclose(noise_list[0].ops[0].qobj, tensor(qeye(2), sigmaz()))
assert_allclose(noise_list[0].ops[0].coeff, coeffs[0])
assert_allclose(noise_list[0].tlist, tlist)
# Time-indenpendent and all qubits
decnoise = DecoherenceNoise(sigmax(), all_qubits=True)
noise_list = decnoise.get_noise(2)
assert_(tensor([qeye(2), sigmax()]) in noise_list)
assert_(tensor([sigmax(), qeye(2)]) in noise_list)
# Time-denpendent and all qubits
decnoise = DecoherenceNoise(sigmax(),
all_qubits=True,
coeffs=coeffs * 2,
tlist=tlist)
noise_list = decnoise.get_noise(2)
assert_allclose(noise_list[0].ops[0].qobj, tensor(sigmax(), qeye(2)))
assert_allclose(noise_list[0].ops[0].coeff, coeffs[0])
assert_allclose(noise_list[0].tlist, tlist)
assert_allclose(noise_list[1].ops[0].qobj, tensor(qeye(2), sigmax()))
def TestNoisyPulse():
"""
Test for lindblad noise and different tlist
"""
coeff = np.array([0.1, 0.2, 0.3, 0.4])
tlist = np.array([0., 1., 2., 3.])
ham = sigmaz()
pulse1 = Pulse(ham, 1, tlist, coeff)
# Add coherent noise and lindblad noise with different tlist
pulse1.spline_kind = "step_func"
tlist_noise = np.array([1., 2.5, 3.])
coeff_noise = np.array([0.5, 0.1, 0.5])
pulse1.add_coherent_noise(sigmay(), 0, tlist_noise, coeff_noise)
tlist_noise2 = np.array([0.5, 2, 3.])
coeff_noise2 = np.array([0.1, 0.2, 0.3])
pulse1.add_lindblad_noise(sigmax(), 1, coeff=True)
pulse1.add_lindblad_noise(
sigmax(), 0, tlist=tlist_noise2, coeff=coeff_noise2)
assert_allclose(
pulse1.get_ideal_qobjevo(2).ops[0].qobj, tensor(identity(2), sigmaz()))
noise_qu, c_ops = pulse1.get_noisy_qobjevo(2)
assert_allclose(noise_qu.tlist, np.array([0., 0.5, 1., 2., 2.5, 3.]))
for ele in noise_qu.ops:
if ele.qobj == tensor(identity(2), sigmaz()):
assert_allclose(
ele.coeff, np.array([0.1, 0.1, 0.2, 0.3, 0.3, 0.4]))
elif ele.qobj == tensor(sigmay(), identity(2)):
assert_allclose(
ele.coeff, np.array([0., 0., 0.5, 0.5, 0.1, 0.5]))
for c_op in c_ops:
if len(c_op.ops) == 0:
assert_allclose(c_ops[0].cte, tensor(identity(2), sigmax()))
else:
assert_allclose(
c_ops[1].ops[0].qobj, tensor(sigmax(), identity(2)))
assert_allclose(
c_ops[1].tlist, np.array([0., 0.5, 1., 2., 2.5, 3.]))
assert_allclose(
c_ops[1].ops[0].coeff, np.array([0., 0.1, 0.1, 0.2, 0.2, 0.3]))
def qubit_clifford_group(N=None, target=0):
"""
Generates the Clifford group on a single qubit,
using the presentation of the group given by Ross and Selinger
(http://www.mathstat.dal.ca/~selinger/newsynth/).
Parameters
-----------
N : int or None
Number of qubits on which each operator is to be defined
(default: 1).
target : int
Index of the target qubit on which the single-qubit
Clifford operators are to act.
Yields
------
op : Qobj
Clifford operators, represented as Qobj instances.
"""
# The Ross-Selinger presentation of the single-qubit Clifford
# group expresses each element in the form C_{ijk} = E^i X^j S^k
# for gates E, X and S, and for i in range(3), j in range(2) and
# k in range(4).
#
# We start by defining these gates. E is defined in terms of H,
# \omega and S, so we define \omega and H first.
w = np.exp(1j * 2 * np.pi / 8)
H = snot()
X = sigmax()
S = phasegate(np.pi / 2)
E = H * (S**3) * w**3
for op in map(
# partial(reduce, mul) returns a function that takes products of its argument,
# by analogy to sum. Note that by analogy, sum can be written partial(reduce, add).
partial(reduce, mul),
# product(...) yields the Cartesian product of its arguments. Here, each element is
# a tuple (E**i, X**j, S**k) such that partial(reduce, mul) acting on the tuple
# yields E**i * X**j * S**k.
product(_powers(E, 3), _powers(X, 2), _powers(S, 4))):
# Finally, we optionally expand the gate.
if N is not None:
yield gate_expand_1toN(op, N, target)
else:
yield op
def TestChooseSolver(self):
# setup and fidelity without noise
init_state = qubit_states(2, [0, 0, 0, 0])
tlist = np.array([0., np.pi/2.])
a = destroy(2)
proc = Processor(N=2)
proc.add_control(sigmax(), targets=1)
proc.pulses[0].tlist = tlist
proc.pulses[0].coeff = np.array([1])
result = proc.run_state(init_state=init_state, solver="mcsolve")
assert_allclose(
fidelity(result.states[-1], qubit_states(2, [0, 1, 0, 0])),
1, rtol=1.e-7)
def testExpectSolverCompatibility(self):
"""
expect: operator list and state list
"""
c_ops = [0.0001 * sigmaz()]
e_ops = [sigmax(), sigmay(), sigmaz(), sigmam(), sigmap()]
times = np.linspace(0, 10, 100)
res1 = mesolve(sigmax(), fock(2, 0), times, c_ops, e_ops)
res2 = mesolve(sigmax(), fock(2, 0), times, c_ops, [])
e1 = res1.expect
e2 = expect(e_ops, res2.states)
assert_(len(e1) == len(e2))
for n in range(len(e1)):
assert_(len(e1[n]) == len(e2[n]))
assert_(isinstance(e1[n], np.ndarray))
assert_(isinstance(e2[n], np.ndarray))
assert_(e1[n].dtype == e2[n].dtype)
assert_(all(abs(e1[n] - e2[n]) < 1e-12))
def testExpectSolverCompatibility(self):
"""
expect: operator list and state list
"""
c_ops = [0.0001 * sigmaz()]
e_ops = [sigmax(), sigmay(), sigmaz(), sigmam(), sigmap()]
times = np.linspace(0, 10, 100)
res1 = mesolve(sigmax(), fock(2, 0), times, c_ops, e_ops)
res2 = mesolve(sigmax(), fock(2, 0), times, c_ops, [])
e1 = res1.expect
e2 = expect(e_ops, res2.states)
assert_(len(e1) == len(e2))
for n in range(len(e1)):
assert_(len(e1[n]) == len(e2[n]))
assert_(isinstance(e1[n], np.ndarray))
assert_(isinstance(e2[n], np.ndarray))
assert_(e1[n].dtype == e2[n].dtype)
assert_(all(abs(e1[n] - e2[n]) < 1e-12))
def test_user_defined_noise(self):
"""
Test for the user-defined noise object
"""
dr_noise = DriftNoise(sigmax())
proc = Processor(1)
proc.add_noise(dr_noise)
tlist = np.array([0, np.pi / 2.])
proc.add_pulse(Pulse(identity(2), 0, tlist, False))
result = proc.run_state(init_state=basis(2, 0))
assert_allclose(fidelity(result.states[-1], basis(2, 1)),
1,
rtol=1.0e-6)
def TestControlAmpNoise(self):
"""
Test for the control amplitude noise
"""
tlist = np.array([1, 2, 3, 4, 5, 6])
coeff = np.array([1, 1, 1, 1, 1, 1])
# use external operators and no expansion
dummy_qobjevo = QobjEvo(sigmaz(), tlist=tlist)
connoise = ControlAmpNoise(ops=sigmax(), coeffs=[coeff], tlist=tlist)
noise = connoise.get_noise(N=1, proc_qobjevo=dummy_qobjevo)
assert_allclose(noise.ops[0].qobj, sigmax())
assert_allclose(noise.tlist, tlist)
assert_allclose(noise.ops[0].coeff, coeff)
dummy_qobjevo = QobjEvo(tensor([sigmaz(), sigmaz()]), tlist=tlist)
connoise = ControlAmpNoise(ops=[sigmay()],
coeffs=[coeff],
tlist=tlist,
targets=1)
noise = connoise.get_noise(N=2, proc_qobjevo=dummy_qobjevo)
assert_allclose(noise.ops[0].qobj, tensor([qeye(2), sigmay()]))
# use external operators with expansion
dummy_qobjevo = QobjEvo(sigmaz(), tlist=tlist)
connoise = ControlAmpNoise(ops=sigmaz(),
coeffs=[coeff] * 2,
tlist=tlist,
cyclic_permutation=True)
noise = connoise.get_noise(N=2, proc_qobjevo=dummy_qobjevo)
assert_allclose(noise.ops[0].qobj, tensor([sigmaz(), qeye(2)]))
assert_allclose(noise.ops[1].qobj, tensor([qeye(2), sigmaz()]))
# use proc_qobjevo
proc_qobjevo = QobjEvo([[sigmaz(), coeff]], tlist=tlist)
connoise = ControlAmpNoise(coeffs=[coeff], tlist=tlist)
noise = connoise.get_noise(N=2, proc_qobjevo=proc_qobjevo)
assert_allclose(noise.ops[0].qobj, sigmaz())
assert_allclose(noise.ops[0].coeff, coeff[0])
def x_gate(N=None, target=0):
"""Pauli-X gate or sigmax operator.
Returns
-------
result : :class:`qutip.Qobj`
Quantum object for operator describing
a single-qubit rotation through pi radians around the x-axis.
"""
if N is not None:
return gate_expand_1toN(x_gate(), N, target)
return sigmax()
def set_up_ops(self, N):
"""
Generate the Hamiltonians for the spinchain model and save them in the
attribute `ctrls`.
Parameters
----------
N: int
The number of qubits in the system.
"""
# sx_ops
for m in range(N):
self.pulses.append(
Pulse(sigmax(), m, spline_kind=self.spline_kind))
# sz_ops
for m in range(N):
self.pulses.append(
Pulse(sigmaz(), m, spline_kind=self.spline_kind))
# sxsy_ops
operator = tensor([sigmax(), sigmax()]) + tensor([sigmay(), sigmay()])
for n in range(N - 1):
self.pulses.append(
Pulse(operator, [n, n+1], spline_kind=self.spline_kind))
def add_states(self, state, kind='vector'):
"""Add a state vector Qobj to Bloch sphere.
Parameters
----------
state : qobj
Input state vector.
kind : str {'vector','point'}
Type of object to plot.
"""
if isinstance(state, Qobj):
state = [state]
for st in state:
if kind == 'vector':
vec = [expect(sigmax(), st), expect(sigmay(), st),
expect(sigmaz(), st)]
self.add_vectors(vec)
elif kind == 'point':
pnt = [expect(sigmax(), st), expect(sigmay(), st),
expect(sigmaz(), st)]
self.add_points(pnt)
def TestNoise(self):
"""
Test for Processor with noise
"""
# setup and fidelity without noise
rho0 = qubit_states(2, [0, 0, 0, 0])
tlist = np.array([0., np.pi / 2.])
a = destroy(2)
proc = Processor(N=2)
proc.tlist = tlist
proc.coeffs = np.array([1]).reshape((1, 1))
proc.add_ctrl(sigmax(), targets=1)
result = proc.run_state(rho0=rho0)
assert_allclose(fidelity(result.states[-1],
qubit_states(2, [0, 1, 0, 0])),
1,
rtol=1.e-7)
# decoherence noise
dec_noise = DecoherenceNoise([0.25 * a], targets=1)
proc.add_noise(dec_noise)
result = proc.run_state(rho0=rho0)
assert_allclose(fidelity(result.states[-1],
qubit_states(2, [0, 1, 0, 0])),
0.981852,
rtol=1.e-3)
# white noise with internal/external operators
proc.noise = []
white_noise = RandomNoise(loc=0.1, scale=0.1)
proc.add_noise(white_noise)
result = proc.run_state(rho0=rho0)
proc.noise = []
white_noise = RandomNoise(loc=0.1, scale=0.1, ops=sigmax(), targets=1)
proc.add_noise(white_noise)
result = proc.run_state(rho0=rho0)
def testPulseConstructor(self):
"""
Test for creating empty Pulse, Pulse with constant coefficients etc.
"""
coeff = np.array([0.1, 0.2, 0.3, 0.4])
tlist = np.array([0., 1., 2., 3.])
ham = sigmaz()
# Special ways of initializing pulse
pulse2 = Pulse(sigmax(), 0, tlist, True)
assert_allclose(
pulse2.get_ideal_qobjevo(2).ops[0].qobj,
tensor(sigmax(), identity(2)))
pulse3 = Pulse(sigmay(), 0)
assert_allclose(pulse3.get_ideal_qobjevo(2).cte.norm(), 0.)
pulse4 = Pulse(None, None) # Dummy empty ham
assert_allclose(pulse4.get_ideal_qobjevo(2).cte.norm(), 0.)
tlist_noise = np.array([1., 2.5, 3.])
coeff_noise = np.array([0.5, 0.1, 0.5])
tlist_noise2 = np.array([0.5, 2, 3.])
coeff_noise2 = np.array([0.1, 0.2, 0.3])
# Pulse with different dims
random_qobj = Qobj(np.random.random((3, 3)))
pulse5 = Pulse(sigmaz(), 1, tlist, True)
pulse5.add_coherent_noise(sigmay(), 1, tlist_noise, coeff_noise)
pulse5.add_lindblad_noise(random_qobj,
0,
tlist=tlist_noise2,
coeff=coeff_noise2)
qu, c_ops = pulse5.get_noisy_qobjevo(dims=[3, 2])
assert_allclose(qu.ops[0].qobj, tensor([identity(3), sigmaz()]))
assert_allclose(qu.ops[1].qobj, tensor([identity(3), sigmay()]))
assert_allclose(c_ops[0].ops[0].qobj,
tensor([random_qobj, identity(2)]))
def test_chi_known(self):
"""
Superoperator: Chi-matrix for known cases is correct.
"""
def case(S, chi_expected, silent=True):
chi_actual = to_chi(S)
chiq = Qobj(chi_expected, dims=[[[2], [2]], [[2], [2]]], superrep='chi')
if not silent:
print(chi_actual)
print(chi_expected)
assert_almost_equal((chi_actual - chiq).norm('tr'), 0)
yield case, sigmax(), [
[0, 0, 0, 0],
[0, 4, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]
]
yield case, to_super(sigmax()), [
[0, 0, 0, 0],
[0, 4, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]
]
yield case, qeye(2), [
[4, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]
]
yield case, (-1j * sigmax() * pi / 4).expm(), [
[2, 2j, 0, 0],
[-2j, 2, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]
]
def _spin_hamiltonian(N):
from qutip.tensor import tensor
from qutip.operators import qeye, sigmax, sigmay, sigmaz
# array of spin energy splittings and coupling strengths. here we use
# uniform parameters, but in general we don't have too
h = 1.0 * 2 * np.pi * np.ones(N)
Jz = 0.1 * 2 * np.pi * np.ones(N)
Jx = 0.1 * 2 * np.pi * np.ones(N)
Jy = 0.1 * 2 * np.pi * np.ones(N)
# dephasing rate
gamma = 0.01 * np.ones(N)
si = qeye(2)
sx = sigmax()
sy = sigmay()
sz = sigmaz()
sx_list = []
sy_list = []
sz_list = []
for n in range(N):
op_list = []
for m in range(N):
op_list.append(si)
op_list[n] = sx
sx_list.append(tensor(op_list))
op_list[n] = sy
sy_list.append(tensor(op_list))
op_list[n] = sz
sz_list.append(tensor(op_list))
# construct the hamiltonian
H = 0
# energy splitting terms
for n in range(N):
H += - 0.5 * h[n] * sz_list[n]
# interaction terms
for n in range(N-1):
H += - 0.5 * Jx[n] * sx_list[n] * sx_list[n+1]
H += - 0.5 * Jy[n] * sy_list[n] * sy_list[n+1]
H += - 0.5 * Jz[n] * sz_list[n] * sz_list[n+1]
return H
def _spin_hamiltonian(N):
from qutip.tensor import tensor
from qutip.operators import qeye, sigmax, sigmay, sigmaz
# array of spin energy splittings and coupling strengths. here we use
# uniform parameters, but in general we don't have too
h = 1.0 * 2 * np.pi * np.ones(N)
Jz = 0.1 * 2 * np.pi * np.ones(N)
Jx = 0.1 * 2 * np.pi * np.ones(N)
Jy = 0.1 * 2 * np.pi * np.ones(N)
# dephasing rate
gamma = 0.01 * np.ones(N)
si = qeye(2)
sx = sigmax()
sy = sigmay()
sz = sigmaz()
sx_list = []
sy_list = []
sz_list = []
for n in range(N):
op_list = []
for m in range(N):
op_list.append(si)
op_list[n] = sx
sx_list.append(tensor(op_list))
op_list[n] = sy
sy_list.append(tensor(op_list))
op_list[n] = sz
sz_list.append(tensor(op_list))
# construct the hamiltonian
H = 0
# energy splitting terms
for n in range(N):
H += -0.5 * h[n] * sz_list[n]
# interaction terms
for n in range(N - 1):
H += -0.5 * Jx[n] * sx_list[n] * sx_list[n + 1]
H += -0.5 * Jy[n] * sy_list[n] * sy_list[n + 1]
H += -0.5 * Jz[n] * sz_list[n] * sz_list[n + 1]
return H
def test_heom():
"""
heom: Tests the HEOM method.
"""
Q = sigmax()
wq = 1.0
lam, gamma, w0 = 0.2, 0.05, 1.0
tlist = np.linspace(0, 200, 1000)
Nc = 9
# zero temperature case
beta = np.inf
Hsys = 0.5 * wq * sigmaz()
initial_ket = basis(2, 1)
rho0 = initial_ket * initial_ket.dag()
omega = np.sqrt(w0 ** 2 - (gamma / 2.0) ** 2)
a = omega + 1j * gamma / 2.0
lam_coeff = lam ** 2 / (2 * (omega))
options = Options(nsteps=1500, store_states=True, atol=1e-12, rtol=1e-12)
ck1, vk1 = nonmatsubara_exponents(lam, gamma, w0, beta)
mats_data_zero = matsubara_zero_analytical(lam, gamma, w0, tlist)
ck20, vk20 = biexp_fit(tlist, mats_data_zero)
hsolver = HeomUB(
Hsys,
Q,
lam_coeff,
np.concatenate([ck1, ck20]),
np.concatenate([-vk1, -vk20]),
ncut=Nc,
)
output = hsolver.solve(rho0, tlist)
result = np.real(expect(output.states, sigmaz()))
# Ignore Matsubara
hsolver2 = HeomUB(Hsys, Q, lam_coeff, ck1, -vk1, ncut=Nc)
output2 = hsolver2.solve(rho0, tlist)
result2 = np.real(expect(output2.states, sigmaz()))
steady_state_error = np.abs(result[-1] - result2[-1])
assert_(steady_state_error > 0.0)
def test_QobjUnitaryOper():
"Qobj unitarity"
# Check some standard operators
Sx = sigmax()
Sy = sigmay()
assert_unitarity(qeye(4), True)
assert_unitarity(Sx, True)
assert_unitarity(Sy, True)
assert_unitarity(sigmam(), False)
assert_unitarity(destroy(10), False)
# Check multiplcation of unitary is unitary
assert_unitarity(Sx * Sy, True)
# Check some other operations clear unitarity
assert_unitarity(Sx + Sy, False)
assert_unitarity(4 * Sx, False)
assert_unitarity(Sx * 4, False)
assert_unitarity(4 + Sx, False)
assert_unitarity(Sx + 4, False)
def __init__(self, N, correct_global_phase=True,
sx=None, sz=None, sxsy=None):
super(CircularSpinChain, self).__init__(N, correct_global_phase,
sx, sz, sxsy)
x = [identity(2)] * N
x[0] = x[N - 1] = sigmax()
y = [identity(2)] * N
y[0] = y[N - 1] = sigmay()
self.sxsy_ops.append(tensor(x) + tensor(y))
if sxsy is None:
self.sxsy_coeff = [0.1 * 2 * np.pi] * N
elif not isinstance(sxsy, list):
self.sxsy_coeff = [sxsy * 2 * np.pi] * N
else:
self.sxsy_coeff = sxsy
def test_QobjUnitaryOper():
"Qobj unitarity"
# Check some standard operators
Sx = sigmax()
Sy = sigmay()
assert_unitarity(qeye(4), True, "qeye(4) should be unitary.")
assert_unitarity(Sx, True, "sigmax() should be unitary.")
assert_unitarity(Sy, True, "sigmax() should be unitary.")
assert_unitarity(sigmam(), False, "sigmam() should NOT be unitary.")
assert_unitarity(destroy(10), False, "destroy(10) should NOT be unitary.")
# Check multiplcation of unitary is unitary
assert_unitarity(Sx*Sy, True, "sigmax()*sigmay() should be unitary.")
# Check some other operations clear unitarity
assert_unitarity(Sx+Sy, False, "sigmax()+sigmay() should NOT be unitary.")
assert_unitarity(4*Sx, False, "4*sigmax() should NOT be unitary.")
assert_unitarity(Sx*4, False, "sigmax()*4 should NOT be unitary.")
assert_unitarity(4+Sx, False, "4+sigmax() should NOT be unitary.")
assert_unitarity(Sx+4, False, "sigmax()+4 should NOT be unitary.")
def test_QobjUnitaryOper():
"Qobj unitarity"
# Check some standard operators
Sx = sigmax()
Sy = sigmay()
assert_unitarity(qeye(4), True, "qeye(4) should be unitary.")
assert_unitarity(Sx, True, "sigmax() should be unitary.")
assert_unitarity(Sy, True, "sigmax() should be unitary.")
assert_unitarity(sigmam(), False, "sigmam() should NOT be unitary.")
assert_unitarity(destroy(10), False, "destroy(10) should NOT be unitary.")
# Check multiplcation of unitary is unitary
assert_unitarity(Sx*Sy, True, "sigmax()*sigmay() should be unitary.")
# Check some other operations clear unitarity
assert_unitarity(Sx+Sy, False, "sigmax()+sigmay() should NOT be unitary.")
assert_unitarity(4*Sx, False, "4*sigmax() should NOT be unitary.")
assert_unitarity(Sx*4, False, "sigmax()*4 should NOT be unitary.")
assert_unitarity(4+Sx, False, "4+sigmax() should NOT be unitary.")
assert_unitarity(Sx+4, False, "sigmax()+4 should NOT be unitary.")
def test_dnorm_qubit_simple_known_cases(self):
"""
Metrics: check agreement for known qubit channels.
"""
id_chan = to_choi(qeye(2))
X_chan = to_choi(sigmax())
depol = to_choi(
Qobj(diag(ones((4, ))),
dims=[[[2], [2]], [[2], [2]]],
superrep='chi'))
# We need to restrict the number of iterations for things on the
# boundary, such as perfectly distinguishable channels.
assert 2 == pytest.approx(dnorm(id_chan, X_chan), abs=1e-7)
assert 1.5 == pytest.approx(dnorm(id_chan, depol), abs=1e-7)
# Finally, we add a known case from Johnston's QETLAB documentation,
# || Phi - I ||_♢,
# where Phi(X) = UXU⁺ and U = [[1, 1], [-1, 1]] / sqrt(2).
assert np.sqrt(2) == pytest.approx(
dnorm(Qobj([[1, 1], [-1, 1]]) / np.sqrt(2), qeye(2)))
def dict_to_qutip(dictH):
"""
Converts ising H to QuTip Hz and makes QuTip Hx of D-Wave
in the process to avoid redundant function calls.
"""
# make useful operators
X = qto.sigmax()
Z = qto.sigmaz()
nqbits = len([key for key in dictH.keys() if key[0] == key[1]])
Hx = sum([nqubit_1pauli(X, m, nqbits) for m in range(nqbits)])
zeros = [qto.qzero(2) for m in range(nqbits)]
Hz = qt.tensor(*zeros)
for key, value in dictH.items():
if key[0] == key[1]:
Hz += value*nqubit_1pauli(Z, key[0], nqbits)
else:
Hz += value*nqubit_2pauli(Z, Z, key[0], key[1], nqbits)
return [Hz, Hx]
def testOperatorListStateList(self):
"""
expect: operator list and state list
"""
operators = [sigmax(), sigmay(), sigmaz(), sigmam(), sigmap()]
states = [fock(2, 0), fock(2, 1), fock_dm(2, 0), fock_dm(2, 1)]
res = expect(operators, states)
assert_(len(res) == len(operators))
for r_idx, r in enumerate(res):
assert_(isinstance(r, np.ndarray))
if operators[r_idx].isherm:
assert_(r.dtype == np.float64)
else:
assert_(r.dtype == np.complex128)
for s_idx, s in enumerate(states):
assert_(r[s_idx] == expect(operators[r_idx], states[s_idx]))
def testOperatorListStateList(self):
"""
expect: operator list and state list
"""
operators = [sigmax(), sigmay(), sigmaz(), sigmam(), sigmap()]
states = [fock(2, 0), fock(2, 1), fock_dm(2, 0), fock_dm(2, 1)]
res = expect(operators, states)
assert_(len(res) == len(operators))
for r_idx, r in enumerate(res):
assert_(isinstance(r, np.ndarray))
if operators[r_idx].isherm:
assert_(r.dtype == np.float64)
else:
assert_(r.dtype == np.complex128)
for s_idx, s in enumerate(states):
assert_(r[s_idx] == expect(operators[r_idx], states[s_idx]))
def add_annotation(self, state_or_vector, text, **kwargs):
"""
Add a text or LaTeX annotation to Bloch sphere, parametrized by a qubit
state or a vector.
Parameters
----------
state_or_vector : Qobj/array/list/tuple
Position for the annotaion.
Qobj of a qubit or a vector of 3 elements.
text : str
Annotation text.
You can use LaTeX, but remember to use raw string
e.g. r"$\\langle x \\rangle$"
or escape backslashes
e.g. "$\\\\langle x \\\\rangle$".
kwargs :
Options as for mplot3d.axes3d.text, including:
fontsize, color, horizontalalignment, verticalalignment.
"""
if isinstance(state_or_vector, Qobj):
vec = [
expect(sigmax(), state_or_vector),
expect(sigmay(), state_or_vector),
expect(sigmaz(), state_or_vector)
]
elif isinstance(state_or_vector, (list, ndarray, tuple)) \
and len(state_or_vector) == 3:
vec = state_or_vector
else:
raise Exception("Position needs to be specified by a qubit " +
"state or a 3D vector.")
self.annotations.append({
'position': vec,
'text': text,
'opts': kwargs
})
def __init__(self,
N,
correct_global_phase=True,
sx=None,
sz=None,
sxsy=None):
super(CircularSpinChain, self).__init__(N, correct_global_phase, sx,
sz, sxsy)
x = [identity(2)] * N
x[0] = x[N - 1] = sigmax()
y = [identity(2)] * N
y[0] = y[N - 1] = sigmay()
self.sxsy_ops.append(tensor(x) + tensor(y))
if sxsy is None:
self.sxsy_coeff = [0.1 * 2 * np.pi] * N
elif not isinstance(sxsy, list):
self.sxsy_coeff = [sxsy * 2 * np.pi] * N
else:
self.sxsy_coeff = sxsy
def test_multi_gates(self):
N = 2
H_d = tensor([sigmaz()] * 2)
H_c = []
test = OptPulseProcessor(N)
test.add_drift(H_d, [0, 1])
test.add_control(sigmax(), cyclic_permutation=True)
test.add_control(sigmay(), cyclic_permutation=True)
test.add_control(tensor([sigmay(), sigmay()]))
# qubits circuit with 3 gates
setting_args = {
"SNOT": {
"num_tslots": 10,
"evo_time": 1
},
"SWAP": {
"num_tslots": 30,
"evo_time": 3
},
"CNOT": {
"num_tslots": 30,
"evo_time": 3
}
}
qc = QubitCircuit(N)
qc.add_gate("SNOT", 0)
qc.add_gate("SWAP", targets=[0, 1])
qc.add_gate('CNOT', controls=1, targets=[0])
test.load_circuit(qc, setting_args=setting_args, merge_gates=False)
rho0 = rand_ket(4) # use random generated ket state
rho0.dims = [[2, 2], [1, 1]]
U = gate_sequence_product(qc.propagators())
rho1 = U * rho0
result = test.run_state(rho0)
assert_(fidelity(result.states[-1], rho1) > 1 - 1.0e-6)
def set_up_ops(self, N):
"""
Generate the Hamiltonians for the spinchain model and save them in the
attribute `ctrls`.
Parameters
----------
N: int
The number of qubits in the system.
"""
self.pulse_dict = {}
index = 0
# single qubit terms
for m in range(N):
self.pulses.append(
Pulse(sigmax(), [m + 1], spline_kind=self.spline_kind))
self.pulse_dict["sx" + str(m)] = index
index += 1
for m in range(N):
self.pulses.append(
Pulse(sigmaz(), [m + 1], spline_kind=self.spline_kind))
self.pulse_dict["sz" + str(m)] = index
index += 1
# coupling terms
a = tensor([destroy(self.num_levels)] +
[identity(2) for n in range(N)])
for n in range(N):
sm = tensor(
[identity(self.num_levels)] +
[destroy(2) if m == n else identity(2) for m in range(N)])
self.pulses.append(
Pulse(a.dag() * sm + a * sm.dag(),
list(range(N + 1)),
spline_kind=self.spline_kind))
self.pulse_dict["g" + str(n)] = index
index += 1
def test_decoherence_noise(self):
"""
Test for the decoherence noise
"""
tlist = np.array([1, 2, 3, 4, 5, 6])
coeff = np.array([1, 1, 1, 1, 1, 1])
# Time-dependent
decnoise = DecoherenceNoise(sigmaz(),
coeff=coeff,
tlist=tlist,
targets=[1])
dims = [2] * 2
pulses, systematic_noise = decnoise.get_noisy_dynamics(dims=dims)
noisy_qu, c_ops = systematic_noise.get_noisy_qobjevo(dims=dims)
assert_allclose(c_ops[0].ops[0].qobj, tensor(qeye(2), sigmaz()))
assert_allclose(c_ops[0].ops[0].coeff, coeff)
assert_allclose(c_ops[0].tlist, tlist)
# Time-indenpendent and all qubits
decnoise = DecoherenceNoise(sigmax(), all_qubits=True)
pulses, systematic_noise = decnoise.get_noisy_dynamics(dims=dims)
noisy_qu, c_ops = systematic_noise.get_noisy_qobjevo(dims=dims)
c_ops = [qu.cte for qu in c_ops]
assert_(tensor([qeye(2), sigmax()]) in c_ops)
assert_(tensor([sigmax(), qeye(2)]) in c_ops)
# Time-denpendent and all qubits
decnoise = DecoherenceNoise(sigmax(),
all_qubits=True,
coeff=coeff * 2,
tlist=tlist)
pulses, systematic_noise = decnoise.get_noisy_dynamics(dims=dims)
noisy_qu, c_ops = systematic_noise.get_noisy_qobjevo(dims=dims)
assert_allclose(c_ops[0].ops[0].qobj, tensor(sigmax(), qeye(2)))
assert_allclose(c_ops[0].ops[0].coeff, coeff * 2)
assert_allclose(c_ops[0].tlist, tlist)
assert_allclose(c_ops[1].ops[0].qobj, tensor(qeye(2), sigmax()))
def test_dnorm_qubit_known_cases():
"""
Metrics: check agreement for known qubit channels.
"""
def case(chan1, chan2, expected, significant=4):
# We again take a generous tolerance so that we don't kill off
# SCS solvers.
assert_approx_equal(
dnorm(chan1, chan2), expected,
significant=significant
)
id_chan = to_choi(qeye(2))
S_eye = to_super(id_chan)
X_chan = to_choi(sigmax())
depol = to_choi(Qobj(
diag(ones((4,))),
dims=[[[2], [2]], [[2], [2]]], superrep='chi'
))
S_H = to_super(hadamard_transform())
W = swap()
# We need to restrict the number of iterations for things on the boundary,
# such as perfectly distinguishable channels.
yield case, id_chan, X_chan, 2
yield case, id_chan, depol, 1.5
# Next, we'll generate some test cases based on comparisons to pre-existing
# dnorm() implementations. In particular, the targets for the following
# test cases were generated using QuantumUtils for MATLAB (https://goo.gl/oWXhO9).
def overrotation(x):
return to_super((1j * np.pi * x * sigmax() / 2).expm())
for x, target in {
1.000000e-03: 3.141591e-03,
3.100000e-03: 9.738899e-03,
1.000000e-02: 3.141463e-02,
3.100000e-02: 9.735089e-02,
1.000000e-01: 3.128689e-01,
3.100000e-01: 9.358596e-01
}.items():
yield case, overrotation(x), id_chan, target
def had_mixture(x):
return (1 - x) * S_eye + x * S_H
for x, target in {
1.000000e-03: 2.000000e-03,
3.100000e-03: 6.200000e-03,
1.000000e-02: 2.000000e-02,
3.100000e-02: 6.200000e-02,
1.000000e-01: 2.000000e-01,
3.100000e-01: 6.200000e-01
}.items():
yield case, had_mixture(x), id_chan, target
def swap_map(x):
S = (1j * x * W).expm()
S._type = None
S.dims = [[[2], [2]], [[2], [2]]]
S.superrep = 'super'
return S
for x, target in {
1.000000e-03: 2.000000e-03,
3.100000e-03: 6.199997e-03,
1.000000e-02: 1.999992e-02,
3.100000e-02: 6.199752e-02,
1.000000e-01: 1.999162e-01,
3.100000e-01: 6.173918e-01
}.items():
yield case, swap_map(x), id_chan, target
# Finally, we add a known case from Johnston's QETLAB documentation,
# || Phi - I ||,_♢ where Phi(X) = UXU⁺ and U = [[1, 1], [-1, 1]] / sqrt(2).
yield case, Qobj([[1, 1], [-1, 1]]) / np.sqrt(2), qeye(2), np.sqrt(2)
CPTP, expand to arbitrary dimensional systems, etc.
"""
return Qobj(dims=[[[2], [2]], [[2], [2]]],
inpt=array([[1. - pe / 2., 0., 0., 1. - pe],
[0., pe / 2., 0., 0.],
[0., 0., pe / 2., 0.],
[1. - pe, 0., 0., 1. - pe / 2.]]),
superrep='choi')
# CHANGE OF BASIS FUNCTIONS ---------------------------------------------------
# These functions find change of basis matrices, and are useful in converting
# between (for instance) Choi and chi matrices. At some point, these should
# probably be moved out to another module.
_SINGLE_QUBIT_PAULI_BASIS = (identity(2), sigmax(), sigmay(), sigmaz())
def _pauli_basis(nq=1):
# NOTE: This is slow as can be.
# TODO: Make this sparse. CSR format was causing problems for the [idx, :]
# slicing below.
B = zeros((4 ** nq, 4 ** nq), dtype=complex)
dims = [[[2] * nq] * 2] * 2
for idx, op in enumerate(starmap(tensor,
product(_SINGLE_QUBIT_PAULI_BASIS,
repeat=nq))):
B[:, idx] = operator_to_vector(op).dag().data.todense()
return Qobj(B, dims=dims)
TODO: if this is going into production (hopefully it isn't) then check
CPTP, expand to arbitrary dimensional systems, etc.
"""
return Qobj(dims=[[[2], [2]], [[2], [2]]],
inpt=array([[1. - pe / 2., 0., 0., 1. - pe],
[0., pe / 2., 0., 0.], [0., 0., pe / 2., 0.],
[1. - pe, 0., 0., 1. - pe / 2.]]),
superrep='choi')
# CHANGE OF BASIS FUNCTIONS ---------------------------------------------------
# These functions find change of basis matrices, and are useful in converting
# between (for instance) Choi and chi matrices. At some point, these should
# probably be moved out to another module.
_SINGLE_QUBIT_PAULI_BASIS = (identity(2), sigmax(), sigmay(), sigmaz())
def _pauli_basis(nq=1):
# NOTE: This is slow as can be.
# TODO: Make this sparse. CSR format was causing problems for the [idx, :]
# slicing below.
B = zeros((4**nq, 4**nq), dtype=complex)
dims = [[[2] * nq] * 2] * 2
for idx, op in enumerate(
starmap(tensor, product(_SINGLE_QUBIT_PAULI_BASIS, repeat=nq))):
B[:, idx] = operator_to_vector(op).dag().full()
return Qobj(B, dims=dims)
def test_known_iscptp(self):
"""
Superoperator: ishp, iscp, istp and iscptp known cases.
"""
def case(qobj, shouldhp, shouldcp, shouldtp):
hp = qobj.ishp
cp = qobj.iscp
tp = qobj.istp
cptp = qobj.iscptp
shouldcptp = shouldcp and shouldtp
if (
hp == shouldhp and
cp == shouldcp and
tp == shouldtp and
cptp == shouldcptp
):
return
fails = []
if hp != shouldhp:
fails.append(("ishp", shouldhp, hp))
if tp != shouldtp:
fails.append(("istp", shouldtp, tp))
if cp != shouldcp:
fails.append(("iscp", shouldcp, cp))
if cptp != shouldcptp:
fails.append(("iscptp", shouldcptp, cptp))
raise AssertionError("Expected {}.".format(" and ".join([
"{} == {} (got {})".format(fail, expected, got)
for fail, expected, got in fails
])))
# Conjugation by a creation operator should
# have be CP (and hence HP), but not TP.
a = create(2).dag()
S = sprepost(a, a.dag())
yield case, S, True, True, False
# A single off-diagonal element should not be CP,
# nor even HP.
S = sprepost(a, a)
yield case, S, False, False, False
# Check that unitaries are CPTP and HP.
yield case, identity(2), True, True, True
yield case, sigmax(), True, True, True
# The partial transpose map, whose Choi matrix is SWAP, is TP
# and HP but not CP (one negative eigenvalue).
W = Qobj(swap(), type='super', superrep='choi')
yield case, W, True, False, True
# Subnormalized maps (representing erasure channels, for instance)
# can be CP but not TP.
subnorm_map = Qobj(identity(4) * 0.9, type='super', superrep='super')
yield case, subnorm_map, True, True, False
# Check that things which aren't even operators aren't identified as
# CPTP.
yield case, basis(2), False, False, False
def overrotation(x):
return to_super((1j * np.pi * x * sigmax() / 2).expm())
def set_up_ops(self, N):
super(CircularSpinChain, self).set_up_ops(N)
operator = tensor([sigmax(), sigmax()]) + tensor([sigmay(), sigmay()])
self.pulses.append(
Pulse(operator, [N-1, 0], spline_kind=self.spline_kind))
self.pulse_dict["g" + str(N-1)] = len(self.pulses) - 1
def test_known_iscptp(self):
"""
Superoperator: ishp, iscp, istp and iscptp known cases.
"""
def case(qobj, shouldhp, shouldcp, shouldtp):
hp = qobj.ishp
cp = qobj.iscp
tp = qobj.istp
cptp = qobj.iscptp
shouldcptp = shouldcp and shouldtp
if (hp == shouldhp and cp == shouldcp and tp == shouldtp
and cptp == shouldcptp):
return
fails = []
if hp != shouldhp:
fails.append(("ishp", shouldhp, hp))
if tp != shouldtp:
fails.append(("istp", shouldtp, tp))
if cp != shouldcp:
fails.append(("iscp", shouldcp, cp))
if cptp != shouldcptp:
fails.append(("iscptp", shouldcptp, cptp))
raise AssertionError("Expected {}.".format(" and ".join([
"{} == {} (got {})".format(fail, expected, got)
for fail, expected, got in fails
])))
# Conjugation by a creation operator should
# have be CP (and hence HP), but not TP.
a = create(2).dag()
S = sprepost(a, a.dag())
case(S, True, True, False)
# A single off-diagonal element should not be CP,
# nor even HP.
S = sprepost(a, a)
case(S, False, False, False)
# Check that unitaries are CPTP and HP.
case(identity(2), True, True, True)
case(sigmax(), True, True, True)
# Check that unitaries on bipartite systems are CPTP and HP.
case(tensor(sigmax(), identity(2)), True, True, True)
# Check that a linear combination of bipartitie unitaries is CPTP and HP.
S = (to_super(tensor(sigmax(), identity(2))) +
to_super(tensor(identity(2), sigmay()))) / 2
case(S, True, True, True)
# The partial transpose map, whose Choi matrix is SWAP, is TP
# and HP but not CP (one negative eigenvalue).
W = Qobj(swap(), type='super', superrep='choi')
case(W, True, False, True)
# Subnormalized maps (representing erasure channels, for instance)
# can be CP but not TP.
subnorm_map = Qobj(identity(4) * 0.9, type='super', superrep='super')
case(subnorm_map, True, True, False)
# Check that things which aren't even operators aren't identified as
# CPTP.
case(basis(2), False, False, False)
