# qiskit.opflow.state_fns.CVaRMeasurement¶

class CVaRMeasurement(primitive=None, alpha=1.0, coeff=1.0)[Quellcode]
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.

Parameter
• 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

Verursacht
• 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)[Quellcode]
Parameter
• 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

Verursacht
• 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 +. 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. 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

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. settings Return settings.
add(other)[Quellcode]

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

Parameter

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).

Rückgabetyp

SummedOp

Rückgabe

An OperatorBase equivalent to the sum of self and other.

adjoint()[Quellcode]

The adjoint of a CVaRMeasurement is not defined.

Rückgabe

Does not return anything, raises an error.

Verursacht

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.

Rückgabetyp

float

Rückgabe

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.

Parameter

param_dict (dict) – The dictionary of Parameters to replace, and values or lists of values by which to replace them.

Rückgabetyp

OperatorBase

Rückgabe

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).

Rückgabetyp

OperatorBase

property coeff

A coefficient by which the state function is multiplied.

Rückgabetyp

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.

Parameter
• 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).

Rückgabetyp

OperatorBase

Rückgabe

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

Verursacht

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

compute_cvar(energies, probabilities)[Quellcode]

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)

Parameter
• 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.

Rückgabetyp

complex

Rückgabe

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))

Verursacht

ValueError – front isn’t a DictStateFn or VectorStateFn

copy()

Return a deep copy of the Operator.

Rückgabetyp

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.

Parameter

other (OperatorBase) – The OperatorBase to compare to self.

Rückgabetyp

bool

Rückgabe

A bool equal to the equality of self and other.

eval(front=None)[Quellcode]

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.

Parameter

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

Rückgabetyp

complex

Rückgabe

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)[Quellcode]

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]

Parameter

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

Rückgabetyp

complex

Rückgabe

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)[Quellcode]

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).

Parameter

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.

Rückgabetyp

Tuple[list, list]

Rückgabe

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.

Verursacht

ValueError – front isn’t a DictStateFn or VectorStateFn

property instance_id

Return the unique instance id.

Rückgabetyp

int

property is_measurement

Whether the StateFn object is a measurement Operator.

Rückgabetyp

bool

mul(scalar)[Quellcode]

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).

Parameter

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.

Rückgabetyp

CVaRMeasurement

Rückgabe

An OperatorBase equivalent to product of self and scalar.

neg()

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

Rückgabetyp

OperatorBase

Rückgabe

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.

Rückgabetyp

int

Rückgabe

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.

Parameter

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].

Rückgabetyp

OperatorStateFn

Rückgabe

A new StateFn containing the permuted primitive.

power(exponent)

Compose with Self Multiple Times, undefined for StateFns.

Parameter

exponent (int) – The number of times to compose self with self.

Verursacht

ValueError – This function is not defined for StateFns.

Rückgabetyp

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.

Rückgabetyp

Set[str]

Rückgabe

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.

Rückgabetyp

OperatorBase

Rückgabe

The reduced OperatorBase.

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

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

Parameter
• 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.

Rückgabe

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

property settings

Return settings.

Rückgabetyp

Dict

tensor(other)[Quellcode]

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.

Parameter

other (OperatorBase) – The OperatorBase to tensor product with self.

Rückgabetyp

Union[OperatorStateFn, TensoredOp]

Rückgabe

An OperatorBase equivalent to the tensor product of self and other.

tensorpower(other)

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

Parameter

other (int) – The int number of times to tensor product self with itself via tensorpower.

Rückgabetyp

Union[OperatorBase, int]

Rückgabe

An OperatorBase equivalent to the tensorpower of self by other.

to_circuit_op()[Quellcode]

Not defined.

to_density_matrix(massive=False)[Quellcode]

Not defined.

to_matrix(massive=False)[Quellcode]

Not defined.

to_matrix_op(massive=False)[Quellcode]

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.

Rückgabetyp

spmatrix

Rückgabe

The SciPy spmatrix equivalent to this Operator.

traverse(convert_fn, coeff=None)[Quellcode]

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.

Parameter
• 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.

Rückgabetyp

OperatorBase

Rückgabe

The converted StateFn.