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qiskit.circuit.library.UnitaryOverlap(unitary1, unitary2, prefix1='p1', prefix2='p2')GitHub(opens in a new tab)

Bases: QuantumCircuit

Circuit that returns the overlap between two unitaries U2U1U_2^{\dag} U_1.

The input quantum circuits must represent unitary operations, since they must be invertible. If the inputs will have parameters, they are replaced by ParameterVectors with names “p1” (for circuit unitary1) and “p2” (for circuit unitary_2) in the output circuit.

This circuit is usually employed in computing the fidelity:

.. math::
    \left|\langle 0| U_2^{\dag} U_1|0\rangle\right|^{2}

by computing the probability of being in the all-zeros bit-string, or equivalently, the expectation value of projector 00|0\rangle\langle 0|.


import numpy as np
from qiskit.circuit.library import EfficientSU2, UnitaryOverlap
from qiskit.primitives import Sampler
# get two circuit to prepare states of which we comput the overlap
circuit = EfficientSU2(2, reps=1)
unitary1 = circuit.assign_parameters(np.random.random(circuit.num_parameters))
unitary2 = circuit.assign_parameters(np.random.random(circuit.num_parameters))
# create the overlap circuit
overlap = UnitaryOverap(unitary1, unitary2)
# sample from the overlap
sampler = Sampler(options={"shots": 100})
result =
# the fidelity is the probability to measure 0
fidelity = result.quasi_dists[0].get(0, 0)


  • unitary1 (QuantumCircuit) – Unitary acting on the ket vector.
  • unitary2 (QuantumCircuit) – Unitary whose inverse operates on the bra vector.
  • prefix1 – The name of the parameter vector associated to unitary1, if it is parameterized. Defaults to "p1".
  • prefix2 – The name of the parameter vector associated to unitary2, if it is parameterized. Defaults to "p2".


  • CircuitError – Number of qubits in unitary1 and unitary2 does not match.
  • CircuitError – Inputs contain measurements and/or resets.



Returns a list of ancilla bits in the order that the registers were added.


Return calibration dictionary.

The custom pulse definition of a given gate is of the form {'gate_name': {(qubits, params): schedule}}


Returns a list of classical bits in the order that the registers were added.


Return the circuit data (instructions and context).


a list-like object containing the CircuitInstructions for each instruction.

Return type



Return the global phase of the current circuit scope in radians.


= 158


Return any associated layout information about the circuit

This attribute contains an optional TranspileLayout object. This is typically set on the output from transpile() or to retain information about the permutations caused on the input circuit by transpilation.

There are two types of permutations caused by the transpile() function, an initial layout which permutes the qubits based on the selected physical qubits on the Target, and a final layout which is an output permutation caused by SwapGates inserted during routing.


The user provided metadata associated with the circuit.

The metadata for the circuit is a user provided dict of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.


Return the number of ancilla qubits.


Return number of classical bits.


The number of parameter objects in the circuit.


Return number of qubits.


Return a list of operation start times.

This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.


List of integers representing instruction start times. The index corresponds to the index of instruction in


AttributeError(opens in a new tab) – When circuit is not scheduled.


The parameters defined in the circuit.

This attribute returns the Parameter objects in the circuit sorted alphabetically. Note that parameters instantiated with a ParameterVector are still sorted numerically.


The snippet below shows that insertion order of parameters does not matter.

>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> a, b, elephant = Parameter("a"), Parameter("b"), Parameter("elephant")
>>> circuit = QuantumCircuit(1)
>>> circuit.rx(b, 0)
>>> circuit.rz(elephant, 0)
>>> circuit.ry(a, 0)
>>> circuit.parameters  # sorted alphabetically!
ParameterView([Parameter(a), Parameter(b), Parameter(elephant)])

Bear in mind that alphabetical sorting might be unintuitive when it comes to numbers. The literal “10” comes before “2” in strict alphabetical sorting.

>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> angles = [Parameter("angle_1"), Parameter("angle_2"), Parameter("angle_10")]
>>> circuit = QuantumCircuit(1)
>>> circuit.u(*angles, 0)
>>> circuit.draw()
>>> circuit.parameters
ParameterView([Parameter(angle_1), Parameter(angle_10), Parameter(angle_2)])

To respect numerical sorting, a ParameterVector can be used.

>>> from qiskit.circuit import QuantumCircuit, Parameter, ParameterVector
>>> x = ParameterVector("x", 12)
>>> circuit = QuantumCircuit(1)
>>> for x_i in x:
...     circuit.rx(x_i, 0)
>>> circuit.parameters
    ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
    ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
    ..., ParameterVectorElement(x[11])


The sorted Parameter objects in the circuit.


= 'circuit'


Returns a list of quantum bits in the order that the registers were added.

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