qiskit.opflow.state_fns.CVaRMeasurement¶

class CVaRMeasurement(primitive=None, alpha=1.0, coeff=1.0)[source]¶

A specialized measurement class to compute CVaR expectation values.: See https://arxiv.org/pdf/1907.04769.pdf for further details.

Used in CVaRExpectation, see there for more details.

Parameters

primitive (Optional[OperatorBase]) – The OperatorBase which defines the diagonal operator measurement.
coeff (Union[complex, ParameterExpression]) – A coefficient by which to multiply the state function
alpha (float) – A real-valued parameter between 0 and 1 which specifies the fraction of observed samples to include when computing the objective value. alpha = 1 corresponds to a standard observable expectation value. alpha = 0 corresponds to only using the single sample with the lowest energy. alpha = 0.5 corresponds to ranking each observation by lowest energy and using the best

Raises

ValueError – TODO remove that this raises an error
ValueError – If alpha is not in [0, 1].
OpflowError – If the primitive is not diagonal.

__init__(primitive=None, alpha=1.0, coeff=1.0)[source]¶

Parameters

primitive (Optional[OperatorBase]) – The OperatorBase which defines the diagonal operator measurement.
coeff (Union[complex, ParameterExpression]) – A coefficient by which to multiply the state function
alpha (float) – A real-valued parameter between 0 and 1 which specifies the fraction of observed samples to include when computing the objective value. alpha = 1 corresponds to a standard observable expectation value. alpha = 0 corresponds to only using the single sample with the lowest energy. alpha = 0.5 corresponds to ranking each observation by lowest energy and using the best

Raises

ValueError – TODO remove that this raises an error
ValueError – If alpha is not in [0, 1].
OpflowError – If the primitive is not diagonal.

Methods

`__init__`([primitive, alpha, coeff])	type primitive `Optional`[`OperatorBase`]
`add`(other)	Return Operator addition of self and other, overloaded by `+`.
`adjoint`()	The adjoint of a CVaRMeasurement is not defined.
`assign_parameters`(param_dict)	Binds scalar values to any Terra `Parameters` in the coefficients or primitives of the Operator, or substitutes one `Parameter` for another.
`bind_parameters`(param_dict)	Same as assign_parameters, but maintained for consistency with QuantumCircuit in Terra (which has both assign_parameters and bind_parameters).
`compose`(other[, permutation, front])	Composition (Linear algebra-style: A@B(x) = A(B(x))) is not well defined for states in the binary function model, but is well defined for measurements.
`compute_cvar`(energies, probabilities)	Given the energies of each sampled measurement outcome (H_i) as well as the sampling probability of each measurement outcome (p_i, we can compute the CVaR.
`copy`()	Return a deep copy of the Operator.
`equals`(other)	Evaluate Equality between Operators, overloaded by `==`.
`eval`([front])	Given the energies of each sampled measurement outcome (H_i) as well as the sampling probability of each measurement outcome (p_i, we can compute the CVaR as H_j + 1/α(sum_i<j p_i(H_i - H_j)).
`eval_variance`([front])	Given the energies of each sampled measurement outcome (H_i) as well as the sampling probability of each measurement outcome (p_i, we can compute the variance of the CVaR estimator as H_j^2 + 1/α * (sum_i<j p_i*(H_i^2 - H_j^2)).
`get_outcome_energies_probabilities`([front])	In order to compute the CVaR of an observable expectation, we require the energies of each sampled measurement outcome as well as the sampling probability of each measurement outcome.
`mul`(scalar)	Returns the scalar multiplication of the Operator, overloaded by `*`, including support for Terra’s `Parameters`, which can be bound to values later (via `bind_parameters`).
`neg`()	Return the Operator’s negation, effectively just multiplying by -1.0, overloaded by `-`.
`permute`(permutation)	Permute the qubits of the state function.
`power`(exponent)	Compose with Self Multiple Times, undefined for StateFns.
`primitive_strings`()	Return a set of strings describing the primitives contained in the Operator.
`reduce`()	Try collapsing the Operator structure, usually after some type of conversion, e.g.
`sample`([shots, massive, reverse_endianness])	Sample the state function as a normalized probability distribution.
`tensor`(other)	Return tensor product between self and other, overloaded by `^`.
`tensorpower`(other)	Return tensor product with self multiple times, overloaded by `^`.
`to_circuit_op`()	Not defined.
`to_density_matrix`([massive])	Not defined.
`to_matrix`([massive])	Not defined.
`to_matrix_op`([massive])	Not defined.
`to_spmatrix`()	Return SciPy sparse matrix representation of the Operator.
`traverse`(convert_fn[, coeff])	Apply the convert_fn to the internal primitive if the primitive is an Operator (as in the case of `OperatorStateFn`).

Attributes

`INDENTATION`
`alpha`	A real-valued parameter between 0 and 1 which specifies the
`coeff`	A coefficient by which the state function is multiplied.
`instance_id`	Return the unique instance id.
`is_measurement`	Whether the StateFn object is a measurement Operator.
`num_qubits`	The number of qubits over which the Operator is defined.
`parameters`	Return a set of Parameter objects contained in the Operator.
`primitive`	The primitive which defines the behavior of the underlying State function.

add(other)[source]¶

Return Operator addition of self and other, overloaded by +.

Parameters: other (OperatorBase) – An OperatorBase with the same number of qubits as self, and in the same ‘Operator’, ‘State function’, or ‘Measurement’ category as self (i.e. the same type of underlying function).
Return type: SummedOp
Returns: An OperatorBase equivalent to the sum of self and other.

adjoint()[source]¶

The adjoint of a CVaRMeasurement is not defined.

Returns: Does not return anything, raises an error.
Raises: OpflowError – The adjoint of a CVaRMeasurement is not defined.

property alpha¶

A real-valued parameter between 0 and 1 which specifies the: fraction of observed samples to include when computing the objective value. alpha = 1 corresponds to a standard observable expectation value. alpha = 0 corresponds to only using the single sample with the lowest energy. alpha = 0.5 corresponds to ranking each observation by lowest energy and using the best half.

Return type: float
Returns: The parameter alpha which was given at initialization

assign_parameters(param_dict)¶

Binds scalar values to any Terra Parameters in the coefficients or primitives of the Operator, or substitutes one Parameter for another. This method differs from Terra’s assign_parameters in that it also supports lists of values to assign for a give Parameter, in which case self will be copied for each parameterization in the binding list(s), and all the copies will be returned in an OpList. If lists of parameterizations are used, every Parameter in the param_dict must have the same length list of parameterizations.

Parameters: param_dict (dict) – The dictionary of Parameters to replace, and values or lists of values by which to replace them.
Return type: OperatorBase
Returns: The OperatorBase with the Parameters in self replaced by the values or Parameters in param_dict. If param_dict contains parameterization lists, this OperatorBase is an OpList.

bind_parameters(param_dict)¶

Same as assign_parameters, but maintained for consistency with QuantumCircuit in Terra (which has both assign_parameters and bind_parameters).

Return type: OperatorBase

property coeff¶

A coefficient by which the state function is multiplied.

Return type: Union[complex, ParameterExpression]

compose(other, permutation=None, front=False)¶

Composition (Linear algebra-style: A@B(x) = A(B(x))) is not well defined for states in the binary function model, but is well defined for measurements.

Parameters

other (OperatorBase) – The Operator to compose with self.
permutation (Optional[List[int]]) – List[int] which defines permutation on other operator.
front (bool) – If front==True, return other.compose(self).

Return type

OperatorBase

Returns

An Operator equivalent to the function composition of self and other.

Raises

ValueError – If self is not a measurement, it cannot be composed from the right.

compute_cvar(energies, probabilities)[source]¶

Given the energies of each sampled measurement outcome (H_i) as well as the sampling probability of each measurement outcome (p_i, we can compute the CVaR. Note that the sampling probabilities serve as an alternative to knowing the counts of each observation and that the input energies are assumed to be sorted in increasing order.

Consider the outcome with index j, such that only some of the samples with measurement outcome j will be used in computing CVaR. The CVaR calculation can then be separated into two parts. First we sum each of the energies for outcomes i < j, weighted by the probability of observing that outcome (i.e the normalized counts). Second, we add the energy for outcome j, weighted by the difference (α - sum_i<j p_i)

Parameters

energies (list) – A list containing the energies (H_i) of each sample measurement outcome, sorted in increasing order.
probabilities (list) – The sampling probabilities (p_i) for each corresponding measurement outcome.

Return type

complex

Returns

The CVaR of the diagonal observable specified by self.primitive and: the sampled quantum state described by the inputs (energies, probabilities). For index j (described above), the CVaR is computed as H_j + 1/α * (sum_i<j p_i*(H_i - H_j))

Raises

ValueError – front isn’t a DictStateFn or VectorStateFn

copy()¶

Return a deep copy of the Operator.

Return type: OperatorBase

equals(other)¶

Evaluate Equality between Operators, overloaded by ==. Only returns True if self and other are of the same representation (e.g. a DictStateFn and CircuitStateFn will never be equal, even if their vector representations are equal), their underlying primitives are equal (this means for ListOps, OperatorStateFns, or EvolvedOps the equality is evaluated recursively downwards), and their coefficients are equal.

Parameters: other (OperatorBase) – The OperatorBase to compare to self.
Return type: bool
Returns: A bool equal to the equality of self and other.

eval(front=None)[source]¶

Given the energies of each sampled measurement outcome (H_i) as well as the sampling probability of each measurement outcome (p_i, we can compute the CVaR as H_j + 1/α*(sum_i<j p_i*(H_i - H_j)). Note that index j corresponds to the measurement outcome such that only some of the samples with measurement outcome j will be used in computing CVaR. Note also that the sampling probabilities serve as an alternative to knowing the counts of each observation.

This computation is broken up into two subroutines. One which evaluates each measurement outcome and determines the sampling probabilities of each. And one which carries out the above calculation. The computation is split up this way to enable a straightforward calculation of the variance of this estimator.

Parameters

front (Union[str, dict, ndarray, OperatorBase, Statevector, None]) – A StateFn or primitive which specifies the results of evaluating a quantum state.

Return type

complex

Returns

The CVaR of the diagonal observable specified by self.primitive and: the sampled quantum state described by the inputs (energies, probabilities). For index j (described above), the CVaR is computed as H_j + 1/α*(sum_i<j p_i*(H_i - H_j))

eval_variance(front=None)[source]¶

Given the energies of each sampled measurement outcome (H_i) as well as the sampling probability of each measurement outcome (p_i, we can compute the variance of the CVaR estimator as H_j^2 + 1/α * (sum_i<j p_i*(H_i^2 - H_j^2)). This follows from the definition that Var[X] = E[X^2] - E[X]^2. In this case, X = E[<bi|H|bi>], where H is the diagonal observable and bi corresponds to measurement outcome i. Given this, E[X^2] = E[<bi|H|bi>^2]

Parameters

front (Union[str, dict, ndarray, OperatorBase, None]) – A StateFn or primitive which specifies the results of evaluating a quantum state.

Return type

complex

Returns

The Var[CVaR] of the diagonal observable specified by self.primitive: and the sampled quantum state described by the inputs (energies, probabilities). For index j (described above), the CVaR is computed as H_j^2 + 1/α*(sum_i<j p_i*(H_i^2 - H_j^2))

get_outcome_energies_probabilities(front=None)[source]¶

In order to compute the CVaR of an observable expectation, we require the energies of each sampled measurement outcome as well as the sampling probability of each measurement outcome. Note that the counts for each measurement outcome will also suffice (and this is often how the CVaR is presented).

Parameters

front (Union[str, dict, ndarray, OperatorBase, Statevector, None]) – A StateFn or a primitive which defines a StateFn. This input holds the results of a sampled/simulated circuit.

Return type

Tuple[list, list]

Returns

Two lists of equal length. energies contains the energy of each: unique measurement outcome computed against the diagonal observable stored in self.primitive. probabilities contains the corresponding sampling probability for each measurement outcome in energies.

Raises

ValueError – front isn’t a DictStateFn or VectorStateFn

property instance_id¶

Return the unique instance id.

Return type: int

property is_measurement¶

Whether the StateFn object is a measurement Operator.

Return type: bool

mul(scalar)[source]¶

Returns the scalar multiplication of the Operator, overloaded by *, including support for Terra’s Parameters, which can be bound to values later (via bind_parameters).

Parameters: scalar (Union[complex, ParameterExpression]) – The real or complex scalar by which to multiply the Operator, or the ParameterExpression to serve as a placeholder for a scalar factor.
Return type: CVaRMeasurement
Returns: An OperatorBase equivalent to product of self and scalar.

neg()¶

Return the Operator’s negation, effectively just multiplying by -1.0, overloaded by -.

Return type: OperatorBase
Returns: An OperatorBase equivalent to the negation of self.

property num_qubits¶

The number of qubits over which the Operator is defined. If op.num_qubits == 5, then op.eval('1' * 5) will be valid, but op.eval('11') will not.

Return type: int
Returns: The number of qubits accepted by the Operator’s underlying function.

property parameters¶: Return a set of Parameter objects contained in the Operator.

permute(permutation)¶

Permute the qubits of the state function.

Parameters: permutation (List[int]) – A list defining where each qubit should be permuted. The qubit at index j of the circuit should be permuted to position permutation[j].
Return type: OperatorStateFn
Returns: A new StateFn containing the permuted primitive.

power(exponent)¶

Compose with Self Multiple Times, undefined for StateFns.

Parameters: exponent (int) – The number of times to compose self with self.
Raises: ValueError – This function is not defined for StateFns.
Return type: OperatorBase

property primitive¶: The primitive which defines the behavior of the underlying State function.

primitive_strings()¶

Return a set of strings describing the primitives contained in the Operator. For example, {'QuantumCircuit', 'Pauli'}. For hierarchical Operators, such as ListOps, this can help illuminate the primitives represented in the various recursive levels, and therefore which conversions can be applied.

Return type: Set[str]
Returns: A set of strings describing the primitives contained within the Operator.

reduce()¶

Try collapsing the Operator structure, usually after some type of conversion, e.g. trying to add Operators in a SummedOp or delete needless IGates in a CircuitOp. If no reduction is available, just returns self.

Return type: OperatorBase
Returns: The reduced OperatorBase.

sample(shots=1024, massive=False, reverse_endianness=False)[source]¶

Sample the state function as a normalized probability distribution. Returns dict of bitstrings in order of probability, with values being probability.

Parameters

shots (int) – The number of samples to take to approximate the State function.
massive (bool) – Whether to allow large conversions, e.g. creating a matrix representing over 16 qubits.
reverse_endianness (bool) – Whether to reverse the endianness of the bitstrings in the return dict to match Terra’s big-endianness.

Returns

A dict containing pairs sampled strings from the State function and sampling frequency divided by shots.

tensor(other)[source]¶

Return tensor product between self and other, overloaded by ^. Note: You must be conscious of Qiskit’s big-endian bit printing convention. Meaning, Plus.tensor(Zero) produces a |+⟩ on qubit 0 and a |0⟩ on qubit 1, or |+⟩⨂|0⟩, but would produce a QuantumCircuit like

|0⟩– |+⟩–

Because Terra prints circuits and results with qubit 0 at the end of the string or circuit.

Parameters: other (OperatorBase) – The OperatorBase to tensor product with self.
Return type: Union[OperatorStateFn, TensoredOp]
Returns: An OperatorBase equivalent to the tensor product of self and other.

tensorpower(other)¶

Return tensor product with self multiple times, overloaded by ^.

Parameters: other (int) – The int number of times to tensor product self with itself via tensorpower.
Return type: Union[OperatorBase, int]
Returns: An OperatorBase equivalent to the tensorpower of self by other.

to_circuit_op()[source]¶: Not defined.

to_density_matrix(massive=False)[source]¶: Not defined.

to_matrix(massive=False)[source]¶: Not defined.

to_matrix_op(massive=False)[source]¶: Not defined.

to_spmatrix()¶

Return SciPy sparse matrix representation of the Operator. Represents the evaluation of the Operator’s underlying function on every combination of basis binary strings.

Return type: spmatrix
Returns: The SciPy spmatrix equivalent to this Operator.

traverse(convert_fn, coeff=None)[source]¶

Apply the convert_fn to the internal primitive if the primitive is an Operator (as in the case of OperatorStateFn). Otherwise do nothing. Used by converters.

Parameters

convert_fn (Callable) – The function to apply to the internal OperatorBase.
coeff (Union[complex, ParameterExpression, None]) – A coefficient to multiply by after applying convert_fn. If it is None, self.coeff is used instead.

Return type

OperatorBase

Returns

The converted StateFn.