def _expval_params(operator, variance=False):
# Convert O to SparsePauliOp representation
if isinstance(operator, Pauli):
operator = SparsePauliOp(operator)
elif not isinstance(operator, SparsePauliOp):
operator = SparsePauliOp.from_operator(Operator(operator))
if not isinstance(operator, SparsePauliOp):
raise ExtensionError("Invalid input operator")
params = {}
# Add Pauli basis components of O
for pauli, coeff in operator.label_iter():
if pauli in params:
coeff1 = params[pauli][0]
params[pauli] = (coeff1 + coeff.real, 0)
else:
params[pauli] = (coeff.real, 0)
# Add Pauli basis components of O^2
if variance:
for pauli, coeff in operator.dot(operator).label_iter():
if pauli in params:
coeff1, coeff2 = params[pauli]
params[pauli] = (coeff1, coeff2 + coeff.real)
else:
params[pauli] = (0, coeff.real)
# Convert to list
return list(params.items())
def to_pauli_op(self, massive: bool = False) -> OperatorBase:
""" Returns a sum of ``PauliOp`` s equivalent to this Operator. """
# pylint: disable=import-outside-toplevel,cyclic-import
from ..list_ops.summed_op import SummedOp
mat_op = self.to_matrix_op(massive=massive)
sparse_pauli = SparsePauliOp.from_operator(
mat_op.primitive) # type: ignore
if not sparse_pauli.to_list():
# pylint: disable=import-outside-toplevel
from ..operator_globals import I
return (I ^ self.num_qubits) * 0.0
if len(sparse_pauli) == 1:
label, coeff = sparse_pauli.to_list()[0]
coeff = coeff.real if np.isreal(coeff) else coeff
return PrimitiveOp(Pauli(label), coeff * self.coeff)
return SummedOp(
[
PrimitiveOp(
Pauli(label),
coeff.real if coeff == coeff.real else coeff,
) for (label, coeff) in sparse_pauli.to_list()
],
self.coeff,
)
def init_observable(observable: BaseOperator | PauliSumOp) -> SparsePauliOp:
"""Initialize observable by converting the input to a :class:`~qiskit.quantum_info.SparsePauliOp`.
Args:
observable: The observable.
Returns:
The observable as :class:`~qiskit.quantum_info.SparsePauliOp`.
Raises:
TypeError: If the observable is a :class:`~qiskit.opflow.PauliSumOp` and has a parameterized
coefficient.
"""
if isinstance(observable, SparsePauliOp):
return observable
elif isinstance(observable, PauliSumOp):
if isinstance(observable.coeff, ParameterExpression):
raise TypeError(
f"Observable must have numerical coefficient, not {type(observable.coeff)}."
)
return observable.coeff * observable.primitive
elif isinstance(observable, BasePauli):
return SparsePauliOp(observable)
elif isinstance(observable, BaseOperator):
return SparsePauliOp.from_operator(observable)
else:
return SparsePauliOp(observable)
def to_pauli_op(self, massive: bool = False) -> OperatorBase:
""" Returns a sum of ``PauliOp`` s equivalent to this Operator. """
mat_op = self.to_matrix_op(massive=massive)
sparse_pauli = SparsePauliOp.from_operator(mat_op.primitive)
return sum([
PrimitiveOp(Pauli.from_label(label),
coeff.real if coeff == coeff.real else coeff)
for (label, coeff) in sparse_pauli.to_list()
]) * self.coeff
def to_pauli_op(self, massive: bool = False) -> OperatorBase:
""" Returns a sum of ``PauliOp`` s equivalent to this Operator. """
mat_op = self.to_matrix_op(massive=massive)
sparse_pauli = SparsePauliOp.from_operator(mat_op.primitive) # type: ignore
if not sparse_pauli.to_list():
# pylint: disable=import-outside-toplevel
from ..operator_globals import I
return (I ^ self.num_qubits) * 0.0
return sum([PrimitiveOp(Pauli.from_label(label), # type: ignore
coeff.real if coeff == coeff.real else coeff)
for (label, coeff) in sparse_pauli.to_list()]) * self.coeff
def init_observable(observable: BaseOperator | PauliSumOp) -> SparsePauliOp:
"""Initialize observable"""
if isinstance(observable, SparsePauliOp):
return observable
if isinstance(observable, PauliSumOp):
if isinstance(observable.coeff, ParameterExpression):
raise TypeError(
f"observable must have numerical coefficient, not {type(observable.coeff)}"
)
return observable.coeff * observable.primitive
if isinstance(observable, BaseOperator):
return SparsePauliOp.from_operator(observable)
return SparsePauliOp(observable)
def __init__(self,
operator,
label="expectation_value_variance",
unnormalized=False,
pershot=False,
conditional=False):
r"""Instruction to save the expectation value and variance of a Hermitian operator.
The expectation value of a Hermitian operator :math:`H` for a
simulator in quantum state :math`\rho`is given by
:math:`\langle H\rangle = \mbox{Tr}[H.\rho]`. The variance is given by
:math:`\sigma^2 = \langle H^2 \rangle - \langle H \rangle>^2`.
Args:
operator (Pauli or SparsePauliOp or Operator): a Hermitian operator.
label (str): the key for retrieving saved data from results.
unnormalized (bool): If True return save the unnormalized accumulated
or conditional accumulated expectation value
over all shot [Default: False].
pershot (bool): if True save a list of expectation values for each shot
of the simulation rather than the average over
all shots [Default: False].
conditional (bool): if True save the average or pershot data
conditional on the current classical register
values [Default: False].
Raises:
ExtensionError: if the input operator is invalid or not Hermitian.
.. note::
This instruction can be directly appended to a circuit using
the :func:`save_expectation_value` circuit method.
"""
# Convert O to SparsePauliOp representation
if isinstance(operator, Pauli):
operator = SparsePauliOp(operator)
elif not isinstance(operator, SparsePauliOp):
operator = SparsePauliOp.from_operator(Operator(operator))
if not allclose(operator.coeffs.imag, 0):
raise ExtensionError("Input operator is not Hermitian.")
params = _expval_params(operator, variance=True)
super().__init__('save_expval_var',
operator.num_qubits,
label,
unnormalized=unnormalized,
pershot=pershot,
conditional=conditional,
params=params)