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---
title: CVaRMeasurement
description: API reference for qiskit.aqua.operators.state_fns.CVaRMeasurement
in_page_toc_min_heading_level: 1
python_api_type: class
python_api_name: qiskit.aqua.operators.state_fns.CVaRMeasurement
---
<span id="qiskit-aqua-operators-state-fns-cvarmeasurement" />
# qiskit.aqua.operators.state\_fns.CVaRMeasurement
<Class id="qiskit.aqua.operators.state_fns.CVaRMeasurement" isDedicatedPage={true} github="https://github.com/qiskit-community/qiskit-aqua/tree/stable/0.8/qiskit/aqua/operators/state_fns/cvar_measurement.py" signature="CVaRMeasurement(primitive=None, alpha=1.0, coeff=1.0)" modifiers="class">
**A specialized measurement class to compute CVaR expectation values.**
See [https://arxiv.org/pdf/1907.04769.pdf](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`\[`int`, `float`, `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].
* [**AquaError**](qiskit.aqua.AquaError "qiskit.aqua.AquaError") If the primitive is not diagonal.
### \_\_init\_\_
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.__init__" signature="__init__(primitive=None, alpha=1.0, coeff=1.0)">
**Parameters**
* **primitive** (`Optional`\[`OperatorBase`]) The `OperatorBase` which defines the diagonal operator measurement.
* **coeff** (`Union`\[`int`, `float`, `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].
* [**AquaError**](qiskit.aqua.AquaError "qiskit.aqua.AquaError") If the primitive is not diagonal.
</Function>
## Methods
| | |
| -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| [`__init__`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.__init__ "qiskit.aqua.operators.state_fns.CVaRMeasurement.__init__")(\[primitive, alpha, coeff]) | **type primitive**`Optional`\[`OperatorBase`] |
| [`add`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.add "qiskit.aqua.operators.state_fns.CVaRMeasurement.add")(other) | Return Operator addition of self and other, overloaded by `+`. |
| [`adjoint`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.adjoint "qiskit.aqua.operators.state_fns.CVaRMeasurement.adjoint")() | The adjoint of a CVaRMeasurement is not defined. |
| [`assign_parameters`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.assign_parameters "qiskit.aqua.operators.state_fns.CVaRMeasurement.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`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.bind_parameters "qiskit.aqua.operators.state_fns.CVaRMeasurement.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`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.compose "qiskit.aqua.operators.state_fns.CVaRMeasurement.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. |
| [`equals`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.equals "qiskit.aqua.operators.state_fns.CVaRMeasurement.equals")(other) | Evaluate Equality between Operators, overloaded by `==`. |
| [`eval`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.eval "qiskit.aqua.operators.state_fns.CVaRMeasurement.eval")(\[front]) | Evaluate the Operators underlying function, either on a binary string or another Operator. |
| [`mul`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.mul "qiskit.aqua.operators.state_fns.CVaRMeasurement.mul")(scalar) | Returns the scalar multiplication of the Operator, overloaded by `*`, including support for Terras `Parameters`, which can be bound to values later (via `bind_parameters`). |
| [`neg`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.neg "qiskit.aqua.operators.state_fns.CVaRMeasurement.neg")() | Return the Operators negation, effectively just multiplying by -1.0, overloaded by `-`. |
| [`permute`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.permute "qiskit.aqua.operators.state_fns.CVaRMeasurement.permute")(permutation) | Permute the qubits of the state function. |
| [`power`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.power "qiskit.aqua.operators.state_fns.CVaRMeasurement.power")(exponent) | Compose with Self Multiple Times, undefined for StateFns. |
| [`primitive_strings`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.primitive_strings "qiskit.aqua.operators.state_fns.CVaRMeasurement.primitive_strings")() | Return a set of strings describing the primitives contained in the Operator. |
| [`reduce`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.reduce "qiskit.aqua.operators.state_fns.CVaRMeasurement.reduce")() | Try collapsing the Operator structure, usually after some type of conversion, e.g. |
| [`sample`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.sample "qiskit.aqua.operators.state_fns.CVaRMeasurement.sample")(\[shots, massive, reverse\_endianness]) | Sample the state function as a normalized probability distribution. |
| [`tensor`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.tensor "qiskit.aqua.operators.state_fns.CVaRMeasurement.tensor")(other) | Return tensor product between self and other, overloaded by `^`. |
| [`tensorpower`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.tensorpower "qiskit.aqua.operators.state_fns.CVaRMeasurement.tensorpower")(other) | Return tensor product with self multiple times, overloaded by `^`. |
| [`to_circuit_op`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.to_circuit_op "qiskit.aqua.operators.state_fns.CVaRMeasurement.to_circuit_op")() | Not defined. |
| [`to_density_matrix`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.to_density_matrix "qiskit.aqua.operators.state_fns.CVaRMeasurement.to_density_matrix")(\[massive]) | Not defined. |
| [`to_legacy_op`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.to_legacy_op "qiskit.aqua.operators.state_fns.CVaRMeasurement.to_legacy_op")(\[massive]) | Attempt to return the Legacy Operator representation of the Operator. |
| [`to_matrix`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.to_matrix "qiskit.aqua.operators.state_fns.CVaRMeasurement.to_matrix")(\[massive]) | Not defined. |
| [`to_matrix_op`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.to_matrix_op "qiskit.aqua.operators.state_fns.CVaRMeasurement.to_matrix_op")(\[massive]) | Not defined. |
| [`traverse`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.traverse "qiskit.aqua.operators.state_fns.CVaRMeasurement.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`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.alpha "qiskit.aqua.operators.state_fns.CVaRMeasurement.alpha") | A real-valued parameter between 0 and 1 which specifies the |
| [`coeff`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.coeff "qiskit.aqua.operators.state_fns.CVaRMeasurement.coeff") | A coefficient by which the state function is multiplied. |
| [`is_measurement`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.is_measurement "qiskit.aqua.operators.state_fns.CVaRMeasurement.is_measurement") | Whether the StateFn object is a measurement Operator. |
| [`num_qubits`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.num_qubits "qiskit.aqua.operators.state_fns.CVaRMeasurement.num_qubits") | The number of qubits over which the Operator is defined. |
| [`parameters`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.parameters "qiskit.aqua.operators.state_fns.CVaRMeasurement.parameters") | Return a set of Parameter objects contained in the Operator. |
| [`primitive`](#qiskit.aqua.operators.state_fns.CVaRMeasurement.primitive "qiskit.aqua.operators.state_fns.CVaRMeasurement.primitive") | The primitive which defines the behavior of the underlying State function. |
### add
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.add" signature="add(other)">
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**
`OperatorBase`
**Returns**
An `OperatorBase` equivalent to the sum of self and other.
</Function>
### adjoint
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.adjoint" signature="adjoint()">
The adjoint of a CVaRMeasurement is not defined.
**Return type**
`OperatorBase`
**Returns**
Does not return anything, raises an error.
**Raises**
[**AquaError**](qiskit.aqua.AquaError "qiskit.aqua.AquaError") The adjoint of a CVaRMeasurement is not defined.
</Function>
### alpha
<Attribute id="qiskit.aqua.operators.state_fns.CVaRMeasurement.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
</Attribute>
### assign\_parameters
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.assign_parameters" signature="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 Terras `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`.
</Function>
### bind\_parameters
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.bind_parameters" signature="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`
</Function>
### coeff
<Attribute id="qiskit.aqua.operators.state_fns.CVaRMeasurement.coeff">
A coefficient by which the state function is multiplied.
**Return type**
`Union`\[`int`, `float`, `complex`, `ParameterExpression`]
</Attribute>
### compose
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.compose" signature="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.
</Function>
### equals
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.equals" signature="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.
</Function>
### eval
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.eval" signature="eval(front=None)">
Evaluate the Operators underlying function, either on a binary string or another Operator. A square binary Operator can be defined as a function taking a binary function to another binary function. This method returns the value of that function for a given StateFn or binary string. For example, `op.eval('0110').eval('1110')` can be seen as querying the Operators matrix representation by row 6 and column 14, and will return the complex value at those “indices.” Similarly for a StateFn, `op.eval('1011')` will return the complex value at row 11 of the vector representation of the StateFn, as all StateFns are defined to be evaluated from Zero implicitly (i.e. it is as if `.eval('0000')` is already called implicitly to always “indexing” from column 0).
If `front` is None, the matrix-representation of the operator is returned.
**Parameters**
**front** (`Union`\[`str`, `dict`, `ndarray`, `OperatorBase`, `None`]) The bitstring, dict of bitstrings (with values being coefficients), or StateFn to evaluated by the Operators underlying function, or None.
**Return type**
`Union`\[`OperatorBase`, `float`, `complex`]
**Returns**
The output of the Operators evaluation function. If self is a `StateFn`, the result is a float or complex. If self is an Operator (`PrimitiveOp, ComposedOp, SummedOp, EvolvedOp,` etc.), the result is a StateFn. If `front` is None, the matrix-representation of the operator is returned, which is a `MatrixOp` for the operators and a `VectorStateFn` for state-functions. If either self or front contain proper `ListOps` (not ListOp subclasses), the result is an n-dimensional list of complex or StateFn results, resulting from the recursive evaluation by each OperatorBase in the ListOps.
</Function>
### is\_measurement
<Attribute id="qiskit.aqua.operators.state_fns.CVaRMeasurement.is_measurement">
Whether the StateFn object is a measurement Operator.
**Return type**
`bool`
</Attribute>
### mul
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.mul" signature="mul(scalar)">
Returns the scalar multiplication of the Operator, overloaded by `*`, including support for Terras `Parameters`, which can be bound to values later (via `bind_parameters`).
**Parameters**
**scalar** (`Union`\[`int`, `float`, `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**
`OperatorBase`
**Returns**
An `OperatorBase` equivalent to product of self and scalar.
</Function>
### neg
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.neg" signature="neg()">
Return the Operators negation, effectively just multiplying by -1.0, overloaded by `-`.
**Return type**
`OperatorBase`
**Returns**
An `OperatorBase` equivalent to the negation of self.
</Function>
### num\_qubits
<Attribute id="qiskit.aqua.operators.state_fns.CVaRMeasurement.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 Operators underlying function.
</Attribute>
### parameters
<Attribute id="qiskit.aqua.operators.state_fns.CVaRMeasurement.parameters">
Return a set of Parameter objects contained in the Operator.
</Attribute>
### permute
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.permute" signature="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.
</Function>
### power
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.power" signature="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`
</Function>
### primitive
<Attribute id="qiskit.aqua.operators.state_fns.CVaRMeasurement.primitive">
The primitive which defines the behavior of the underlying State function.
</Attribute>
### primitive\_strings
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.primitive_strings" signature="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.
</Function>
### reduce
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.reduce" signature="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`.
</Function>
### sample
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.sample" signature="sample(shots=1024, massive=False, reverse_endianness=False)">
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 Terras big-endianness.
**Return type**
`dict`
**Returns**
A dict containing pairs sampled strings from the State function and sampling frequency divided by shots.
</Function>
### tensor
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.tensor" signature="tensor(other)">
Return tensor product between self and other, overloaded by `^`. Note: You must be conscious of Qiskits 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**
`OperatorBase`
**Returns**
An `OperatorBase` equivalent to the tensor product of self and other.
</Function>
### tensorpower
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.tensorpower" signature="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.
</Function>
### to\_circuit\_op
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.to_circuit_op" signature="to_circuit_op()">
Not defined.
**Return type**
`OperatorBase`
</Function>
### to\_density\_matrix
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.to_density_matrix" signature="to_density_matrix(massive=False)">
Not defined.
**Return type**
`ndarray`
</Function>
### to\_legacy\_op
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.to_legacy_op" signature="to_legacy_op(massive=False)">
Attempt to return the Legacy Operator representation of the Operator. If self is a `SummedOp` of `PauliOps`, will attempt to convert to `WeightedPauliOperator`, and otherwise will simply convert to `MatrixOp` and then to `MatrixOperator`. The Legacy Operators cannot represent `StateFns` or proper `ListOps` (meaning not one of the `ListOp` subclasses), so an error will be thrown if this method is called on such an Operator. Also, Legacy Operators cannot represent unbound Parameter coeffs, so an error will be thrown if any are present in self.
Warn if more than 16 qubits to force having to set `massive=True` if such a large vector is desired.
**Return type**
`LegacyBaseOperator`
**Returns**
The `LegacyBaseOperator` representing this Operator.
**Raises**
**TypeError** self is an Operator which cannot be represented by a `LegacyBaseOperator`, such as `StateFn`, proper (non-subclass) `ListOp`, or an Operator with an unbound coeff Parameter.
</Function>
### to\_matrix
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.to_matrix" signature="to_matrix(massive=False)">
Not defined.
**Return type**
`ndarray`
</Function>
### to\_matrix\_op
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.to_matrix_op" signature="to_matrix_op(massive=False)">
Not defined.
**Return type**
`OperatorBase`
</Function>
### traverse
<Function id="qiskit.aqua.operators.state_fns.CVaRMeasurement.traverse" signature="traverse(convert_fn, coeff=None)">
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`\[`int`, `float`, `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.
</Function>
</Class>