def _compare_multiply_to_superop(self, rep, dim, samples, unitary=False):
"""Test channel scalar multiplication is equivalent to SuperOp"""
for _ in range(samples):
if unitary:
mat1 = self.rand_matrix(dim, dim)
sop1 = np.kron(np.conj(mat1), mat1)
else:
sop1 = self.rand_matrix(dim * dim, dim * dim)
val = 2 * (np.random.rand() - 0.5)
targ = SuperOp(val * sop1)
channel = SuperOp(rep(SuperOp(sop1)).multiply(val))
self.assertEqual(channel, targ)
def test_ptm_to_superop(self):
"""Test PTM to SuperOp transformation."""
# Test unitary channels
for ptm, sop in zip(self.unitary_ptm, self.unitary_sop):
chan1 = SuperOp(sop)
chan2 = SuperOp(PTM(ptm))
self.assertEqual(chan1, chan2)
# Test depolarizing channels
for p in [0.25, 0.5, 0.75, 1]:
chan1 = SuperOp(self.depol_sop(p))
chan2 = SuperOp(PTM(self.depol_ptm(p)))
self.assertEqual(chan1, chan2)
def _superop_to_other(self, rep, qubits_test_cases, repetitions):
"""Test SuperOp to Other evolution."""
for nq in qubits_test_cases:
dim = 2**nq
for _ in range(repetitions):
rho = self.rand_rho(dim)
mat = self.rand_matrix(dim**2, dim**2)
chan1 = SuperOp(mat)
rho1 = chan1._evolve(rho)
chan2 = rep(chan1)
rho2 = chan2._evolve(rho)
self.assertAllClose(rho1, rho2)
def test_chi_to_superop(self):
"""Test Chi to SuperOp transformation."""
# Test unitary channels
for chi, sop in zip(self.unitary_chi, self.unitary_sop):
chan1 = SuperOp(sop)
chan2 = SuperOp(Chi(chi))
self.assertEqual(chan1, chan2)
# Test depolarizing channels
for p in [0.25, 0.5, 0.75, 1]:
chan1 = SuperOp(self.depol_sop(p))
chan2 = SuperOp(Chi(self.depol_chi(p)))
self.assertEqual(chan1, chan2)
def test_stinespring_to_superop(self):
"""Test Stinespring to SuperOp transformation."""
# Test unitary channels
for mat, sop in zip(self.unitary_mat, self.unitary_sop):
chan1 = SuperOp(sop)
chan2 = SuperOp(Kraus(mat))
self.assertEqual(chan1, chan2)
# Test depolarizing channels
for p in [0.25, 0.5, 0.75, 1]:
chan1 = SuperOp(self.depol_sop(p))
chan2 = SuperOp(Stinespring(self.depol_stine(p)))
self.assertEqual(chan1, chan2)
def test_superop_to_ptm(self):
"""Test SuperOp to PTM transformation."""
# Test unitary channels
for sop, ptm in zip(self.unitary_sop, self.unitary_ptm):
chan1 = PTM(ptm)
chan2 = PTM(SuperOp(sop))
self.assertEqual(chan1, chan2)
# Test depolarizing channels
for p in [0.25, 0.5, 0.75, 1]:
chan1 = PTM(self.depol_ptm(p))
chan2 = PTM(SuperOp(self.depol_sop(p)))
self.assertEqual(chan1, chan2)
def test_superop_to_superop(self):
"""Test SuperOp to SuperOp transformation."""
# Test unitary channels
for sop in self.unitary_sop:
chan1 = SuperOp(sop)
chan2 = SuperOp(chan1)
self.assertEqual(chan1, chan2)
# Test depolarizing channels
for p in [0, 0.25, 0.5, 0.75, 1]:
chan1 = SuperOp(self.depol_sop(p))
chan2 = SuperOp(chan1)
self.assertEqual(chan1, chan2)
def test_superop_to_choi(self):
"""Test SuperOp to Choi transformation."""
# Test unitary channels
for choi, sop in zip(self.unitary_choi, self.unitary_sop):
chan1 = Choi(choi)
chan2 = Choi(SuperOp(sop))
self.assertEqual(chan1, chan2)
# Test depolarizing channels
for p in [0, 0.25, 0.5, 0.75, 1]:
chan1 = Choi(self.depol_choi(p))
chan2 = Choi(SuperOp(self.depol_sop(p)))
self.assertEqual(chan1, chan2)
def test_superop_to_stinespring(self):
"""Test SuperOp to Stinespring transformation."""
# Test unitary channels
for mat, sop in zip(self.unitary_mat, self.unitary_sop):
chan1 = Stinespring(mat)
chan2 = Stinespring(SuperOp(sop))
self.assertTrue(
matrix_equal(chan2.data[0], chan1.data[0], ignore_phase=True))
# Test depolarizing channels
rho = DensityMatrix(np.diag([1, 0]))
for p in [0.25, 0.5, 0.75, 1]:
target = rho.evolve(Stinespring(self.depol_stine(p)))
output = rho.evolve(Stinespring(SuperOp(self.depol_sop(p))))
self.assertEqual(output, target)
def test_superop_to_stinespring(self):
"""Test SuperOp to Stinespring transformation."""
# Test unitary channels
for mat, sop in zip(self.unitary_mat, self.unitary_sop):
chan1 = Stinespring(mat)
chan2 = Stinespring(SuperOp(sop))
self.assertTrue(
matrix_equal(chan2.data[0], chan1.data[0], ignore_phase=True))
# Test depolarizing channels
rho = np.diag([1, 0])
for p in [0.25, 0.5, 0.75, 1]:
targ = Stinespring(self.depol_stine(p))._evolve(rho)
chan = Stinespring(SuperOp(self.depol_sop(p)))
self.assertAllClose(chan._evolve(rho), targ)
def _compare_subtract_to_superop(self, rep, dim, samples, unitary=False):
"""Test channel subtraction is equivalent to SuperOp"""
for _ in range(samples):
if unitary:
mat1 = self.rand_matrix(dim, dim)
mat2 = self.rand_matrix(dim, dim)
sop1 = np.kron(np.conj(mat1), mat1)
sop2 = np.kron(np.conj(mat2), mat2)
else:
sop1 = self.rand_matrix(dim * dim, dim * dim)
sop2 = self.rand_matrix(dim * dim, dim * dim)
targ = SuperOp(sop1 - sop2)
channel = SuperOp(rep(SuperOp(sop1))._add(rep(-SuperOp(sop2))))
self.assertEqual(channel, targ)
def test_compose_both_kraus(self):
"""Test composition of two kraus errors"""
A0 = np.array([[1, 0], [0, np.sqrt(1 - 0.3)]], dtype=complex)
A1 = np.array([[0, 0], [0, np.sqrt(0.3)]], dtype=complex)
B0 = np.array([[1, 0], [0, np.sqrt(1 - 0.5)]], dtype=complex)
B1 = np.array([[0, 0], [0, np.sqrt(0.5)]], dtype=complex)
# Use quantum channels for reference
target = SuperOp(Kraus([A0, A1]).compose(Kraus([B0, B1])))
error = QuantumError([A0, A1]).compose(QuantumError([B0, B1]))
kraus, p = error.error_term(0)
self.assertEqual(p, 1)
self.assertEqual(kraus[0]['name'], 'kraus')
self.assertEqual(kraus[0]['qubits'], [0])
error_superop = SuperOp(Kraus(kraus[0]['params']))
self.assertEqual(target, error_superop, msg="Incorrect compose kraus")
def test_expand_both_kraus(self):
"""Test expand of two kraus errors"""
a_0 = np.array([[1, 0], [0, np.sqrt(1 - 0.3)]], dtype=complex)
a_1 = np.array([[0, 0], [0, np.sqrt(0.3)]], dtype=complex)
b_0 = np.array([[1, 0], [0, np.sqrt(1 - 0.5)]], dtype=complex)
b_1 = np.array([[0, 0], [0, np.sqrt(0.5)]], dtype=complex)
# Use quantum channels for reference
target = SuperOp(Kraus([a_0, a_1]).expand(Kraus([b_0, b_1])))
error = QuantumError([a_0, a_1]).expand(QuantumError([b_0, b_1]))
kraus, prob = error.error_term(0)
self.assertEqual(prob, 1)
self.assertEqual(kraus[0]['name'], 'kraus')
self.assertEqual(kraus[0]['qubits'], [0, 1])
error_superop = SuperOp(Kraus(kraus[0]['params']))
self.assertEqual(target, error_superop, msg="Incorrect expand kraus")
def compose(self, other, qargs=None, front=False):
"""Return the composed quantum channel self @ other.
Args:
other (QuantumChannel): a quantum channel.
qargs (list or None): a list of subsystem positions to apply
other on. If None apply on all
subsystems [default: None].
front (bool): If True compose using right operator multiplication,
instead of left multiplication [default: False].
Returns:
PTM: The quantum channel self @ other.
Raises:
QiskitError: if other has incompatible dimensions.
Additional Information:
Composition (``@``) is defined as `left` matrix multiplication for
:class:`SuperOp` matrices. That is that ``A @ B`` is equal to ``B * A``.
Setting ``front=True`` returns `right` matrix multiplication
``A * B`` and is equivalent to the :meth:`dot` method.
"""
if qargs is not None:
return PTM(SuperOp(self).compose(other, qargs=qargs, front=front))
# Convert other to PTM
if not isinstance(other, PTM):
other = PTM(other)
input_dims, output_dims = self._get_compose_dims(other, qargs, front)
if front:
data = np.dot(self._data, other.data)
else:
data = np.dot(other.data, self._data)
return PTM(data, input_dims, output_dims)
def compose(self, other, qargs=None, front=False):
if qargs is None:
qargs = getattr(other, "qargs", None)
if qargs is not None:
return Choi(SuperOp(self).compose(other, qargs=qargs, front=front))
if not isinstance(other, Choi):
other = Choi(other)
new_shape = self._op_shape.compose(other._op_shape, qargs, front)
output_dim, input_dim = new_shape.shape
if front:
first = np.reshape(other._data, other._bipartite_shape)
second = np.reshape(self._data, self._bipartite_shape)
else:
first = np.reshape(self._data, self._bipartite_shape)
second = np.reshape(other._data, other._bipartite_shape)
# Contract Choi matrices for composition
data = np.reshape(
np.einsum("iAjB,AkBl->ikjl", first, second),
(input_dim * output_dim, input_dim * output_dim),
)
ret = Choi(data)
ret._op_shape = new_shape
return ret
def compose(self, other, qargs=None, front=False):
"""Return the composed quantum channel self @ other.
Args:
other (QuantumChannel): a quantum channel.
qargs (list or None): a list of subsystem positions to apply
other on. If None apply on all
subsystems [default: None].
front (bool): If True compose using right operator multiplication,
instead of left multiplication [default: False].
Returns:
Chi: The quantum channel self @ other.
Raises:
QiskitError: if other has incompatible dimensions.
Additional Information:
Composition (``@``) is defined as `left` matrix multiplication for
:class:`SuperOp` matrices. That is that ``A @ B`` is equal to ``B * A``.
Setting ``front=True`` returns `right` matrix multiplication
``A * B`` and is equivalent to the :meth:`dot` method.
"""
if qargs is not None:
return Chi(SuperOp(self).compose(other, qargs=qargs, front=front))
# If no qargs we compose via Choi representation to avoid an additional
# representation conversion to SuperOp and then convert back to Chi
return Chi(Choi(self).compose(other, front=front))
def compose(self, other, qargs=None, front=False):
if qargs is None:
qargs = getattr(other, 'qargs', None)
if qargs is not None:
return Kraus(
SuperOp(self).compose(other, qargs=qargs, front=front))
if not isinstance(other, Kraus):
other = Kraus(other)
new_shape = self._op_shape.compose(other._op_shape, qargs, front)
input_dims = new_shape.dims_r()
output_dims = new_shape.dims_l()
if front:
ka_l, ka_r = self._data
kb_l, kb_r = other._data
else:
ka_l, ka_r = other._data
kb_l, kb_r = self._data
kab_l = [np.dot(a, b) for a in ka_l for b in kb_l]
if ka_r is None and kb_r is None:
kab_r = None
elif ka_r is None:
kab_r = [np.dot(a, b) for a in ka_l for b in kb_r]
elif kb_r is None:
kab_r = [np.dot(a, b) for a in ka_r for b in kb_l]
else:
kab_r = [np.dot(a, b) for a in ka_r for b in kb_r]
ret = Kraus((kab_l, kab_r), input_dims, output_dims)
ret._op_shape = new_shape
return ret
def compose(self, other, qargs=None, front=False):
"""Return the composition channel self∘other.
Args:
other (QuantumChannel): a quantum channel subclass.
qargs (list): a list of subsystem positions to compose other on.
front (bool): If False compose in standard order other(self(input))
otherwise compose in reverse order self(other(input))
[default: False]
Returns:
Stinespring: The composition channel as a Stinespring object.
Raises:
QiskitError: if other cannot be converted to a channel or
has incompatible dimensions.
"""
if qargs is not None:
return Stinespring(
SuperOp(self).compose(other, qargs=qargs, front=front))
# Convert other to Kraus
if not isinstance(other, Kraus):
other = Kraus(other)
# Check dimensions match up
if front and self._input_dim != other._output_dim:
raise QiskitError(
'input_dim of self must match output_dim of other')
if not front and self._output_dim != other._input_dim:
raise QiskitError(
'input_dim of other must match output_dim of self')
# Since we cannot directly compose two channels in Stinespring
# representation we convert to the Kraus representation
return Stinespring(Kraus(self).compose(other, front=front))
def _append_instruction(self, other, qargs=None):
"""Update the current Statevector by applying an instruction."""
# Try evolving by a matrix operator (unitary-like evolution)
mat = Operator._instruction_to_matrix(other)
if mat is not None:
self._data = self._evolve_operator(Operator(mat), qargs=qargs).data
return
# Otherwise try evolving by a Superoperator
chan = SuperOp._instruction_to_superop(other)
if chan is not None:
# Evolve current state by the superoperator
self._data = chan._evolve(self, qargs=qargs).data
return
# If the instruction doesn't have a matrix defined we use its
# circuit decomposition definition if it exists, otherwise we
# cannot compose this gate and raise an error.
if other.definition is None:
raise QiskitError('Cannot apply Instruction: {}'.format(
other.name))
for instr, qregs, cregs in other.definition:
if cregs:
raise QiskitError(
'Cannot apply instruction with classical registers: {}'.
format(instr.name))
# Get the integer position of the flat register
if qargs is None:
new_qargs = [tup.index for tup in qregs]
else:
new_qargs = [qargs[tup.index] for tup in qregs]
self._append_instruction(instr, qargs=new_qargs)
def _chanmul(self, other, qargs=None, left_multiply=False):
"""Multiply two quantum channels.
Args:
other (QuantumChannel): a quantum channel.
qargs (list): a list of subsystem positions to compose other on.
left_multiply (bool): If True return other * self
If False return self * other [Default:False]
Returns:
Choi: The composition channel as a Chi object.
Raises:
QiskitError: if other is not a QuantumChannel subclass, or
has incompatible dimensions.
"""
if qargs is not None:
return Chi(
SuperOp(self)._chanmul(other,
qargs=qargs,
left_multiply=left_multiply))
# Convert other to Choi since we convert via Choi
if not isinstance(other, Choi):
other = Choi(other)
# Check dimensions match up
if not left_multiply and self._input_dim != other._output_dim:
raise QiskitError(
'input_dim of self must match output_dim of other')
if left_multiply and self._output_dim != other._input_dim:
raise QiskitError(
'input_dim of other must match output_dim of self')
# Since we cannot directly multiply two channels in the Chi
# representation we convert to the Choi representation
return Chi(Choi(self)._chanmul(other, left_multiply=left_multiply))
def _compare_subtract_operator_to_superop(self,
rep,
dim,
samples,
unitary=False):
"""Test channel addition is equivalent to SuperOp"""
for _ in range(samples):
if unitary:
mat1 = self.rand_matrix(dim, dim)
sop1 = np.kron(np.conj(mat1), mat1)
else:
sop1 = self.rand_matrix(dim * dim, dim * dim)
mat2 = self.rand_matrix(dim, dim)
target = SuperOp(sop1) - SuperOp(Operator(mat2))
channel = SuperOp(rep(SuperOp(sop1)) - Operator(mat2))
self.assertEqual(channel, target)
def compose(self, other, qargs=None, front=False):
"""Return the composition channel self∘other.
Args:
other (QuantumChannel): a quantum channel.
qargs (list): a list of subsystem positions to compose other on.
front (bool): If False compose in standard order other(self(input))
otherwise compose in reverse order self(other(input))
[default: False]
Returns:
Chi: The composition channel as a Chi object.
Raises:
QiskitError: if other is not a QuantumChannel subclass, or
has incompatible dimensions.
"""
if qargs is not None:
return Chi(SuperOp(self).compose(other, qargs=qargs, front=front))
# Convert other to Choi since we convert via Choi
if not isinstance(other, Choi):
other = Choi(other)
# Check dimensions match up
if front and self._input_dim != other._output_dim:
raise QiskitError(
'input_dim of self must match output_dim of other')
if not front and self._output_dim != other._input_dim:
raise QiskitError(
'input_dim of other must match output_dim of self')
# Since we cannot directly add two channels in the Chi
# representation we convert to the Choi representation
return Chi(Choi(self).compose(other, front=front))
def _evolve(self, state, qargs=None):
"""Evolve a quantum state by the QuantumChannel.
Args:
state (QuantumState): The input statevector or density matrix.
qargs (list): a list of QuantumState subsystem positions to apply
the operator on.
Returns:
DensityMatrix: the output quantum state as a density matrix.
Raises:
QiskitError: if the operator dimension does not match the
specified QuantumState subsystem dimensions.
"""
# If subsystem evolution we use the SuperOp representation
if qargs is not None:
return SuperOp(self)._evolve(state, qargs)
# Otherwise we compute full evolution directly
state = self._format_state(state, density_matrix=True)
if state.shape[0] != self._input_dim:
raise QiskitError(
"QuantumChannel input dimension is not equal to state dimension."
)
return np.einsum('AB,AiBj->ij', state,
np.reshape(self._data, self._bipartite_shape))
def compose(self, other, qargs=None, front=False):
"""Return the composed quantum channel self @ other.
Args:
other (QuantumChannel): a quantum channel.
qargs (list or None): a list of subsystem positions to apply
other on. If None apply on all
subsystems [default: None].
front (bool): If True compose using right operator multiplication,
instead of left multiplication [default: False].
Returns:
Stinespring: The quantum channel self @ other.
Raises:
QiskitError: if other cannot be converted to a Stinespring or has
incompatible dimensions.
Additional Information:
Composition (``@``) is defined as `left` matrix multiplication for
:class:`SuperOp` matrices. That is that ``A @ B`` is equal to ``B * A``.
Setting ``front=True`` returns `right` matrix multiplication
``A * B`` and is equivalent to the :meth:`dot` method.
"""
if qargs is None:
qargs = getattr(other, 'qargs', None)
if qargs is not None:
return Stinespring(
SuperOp(self).compose(other, qargs=qargs, front=front))
# Otherwise we convert via Kraus representation rather than
# superoperator to avoid unnecessary representation conversions
return Stinespring(Kraus(self).compose(other, front=front))
def test_superop_compose(self):
"""Test compose of SuperOp matrices is correct."""
mats = [self.matI, self.matX, self.matY, self.matZ, self.matH]
chans = [
SuperOp(mat)
for mat in [self.sopI, self.sopX, self.sopY, self.sopZ, self.sopH]
]
self._compare_compose_to_unitary(chans, mats)
def compose(self, other, qargs=None, front=False):
if qargs is None:
qargs = getattr(other, "qargs", None)
if qargs is not None:
return Chi(SuperOp(self).compose(other, qargs=qargs, front=front))
# If no qargs we compose via Choi representation to avoid an additional
# representation conversion to SuperOp and then convert back to Chi
return Chi(Choi(self).compose(other, front=front))
def test_superop_compose(self):
"""Test compose of SuperOp matrices is correct."""
mats = [self.UI, self.UX, self.UY, self.UZ, self.UH]
chans = [
SuperOp(mat)
for mat in [self.sopI, self.sopX, self.sopY, self.sopZ, self.sopH]
]
self._compare_compose_to_operator(chans, mats)
def compose(self, other, qargs=None, front=False):
if qargs is None:
qargs = getattr(other, "qargs", None)
if qargs is not None:
return Stinespring(
SuperOp(self).compose(other, qargs=qargs, front=front))
# Otherwise we convert via Kraus representation rather than
# superoperator to avoid unnecessary representation conversions
return Stinespring(Kraus(self).compose(other, front=front))
def reset_superop(num_qubits):
"""Return a N-qubit reset SuperOp."""
reset = SuperOp(
np.array([[1, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]]))
if num_qubits == 1:
return reset
reset_n = reset
for _ in range(num_qubits - 1):
reset_n.tensor(reset)
return reset_n
def to_channel(self):
"""Convet the QuantumError to a SuperOp quantum channel."""
# Initialize as an empty superoperator of the correct size
dim = 2**self.number_of_qubits
channel = SuperOp(np.zeros([dim * dim, dim * dim]))
for circuit, prob in zip(self._noise_circuits,
self._noise_probabilities):
component = prob * circuit2superop(circuit, self.number_of_qubits)
channel = channel + component
return channel