# UnitaryOverlap

qiskit.circuit.library.UnitaryOverlap(unitary1, unitary2, prefix1='p1', prefix2='p2')

Bases: QuantumCircuit

Circuit that returns the overlap between two unitaries $U_2^{\dag} U_1$.

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 $|0\rangle\langle 0|$.

Example:

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 = sampler.run(overlap).result()

# the fidelity is the probability to measure 0
fidelity = result.quasi_dists.get(0, 0)

Parameters

• 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".

Raises

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

## Attributes

### ancillas

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

### calibrations

Return calibration dictionary.

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

### clbits

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

### data

Return the circuit data (instructions and context).

Returns

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

Return type

QuantumCircuitData

### extension_lib

= 'include "qelib1.inc";'

### global_phase

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

= 'OPENQASM 2.0;'

### instances

= 293

### layout

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 PassManager.run() 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.

### num_ancillas

Return the number of ancilla qubits.

### num_clbits

Return number of classical bits.

### num_parameters

The number of parameter objects in the circuit.

### num_qubits

Return number of qubits.

### op_start_times

Return a list of operation start times.

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

Returns

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

Raises

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

### parameters

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.

## Examples

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()
┌─────────────────────────────┐
q: ┤ U(angle_1,angle_2,angle_10) ├
└─────────────────────────────┘
>>> 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
ParameterView([
ParameterVectorElement(x), ParameterVectorElement(x),
ParameterVectorElement(x), ParameterVectorElement(x),
..., ParameterVectorElement(x)
])

Returns

The sorted Parameter objects in the circuit.

### prefix

= 'circuit'

### qubits

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