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# PhaseEstimation¶

class PhaseEstimation(num_evaluation_qubits, unitary, iqft=None, name='QPE')[source]

Bases: QuantumCircuit

Phase Estimation circuit.

In the Quantum Phase Estimation (QPE) algorithm [1, 2, 3], the Phase Estimation circuit is used to estimate the phase $$\phi$$ of an eigenvalue $$e^{2\pi i\phi}$$ of a unitary operator $$U$$, provided with the corresponding eigenstate $$|psi\rangle$$. That is

$U|\psi\rangle = e^{2\pi i\phi} |\psi\rangle$

This estimation (and thereby this circuit) is a central routine to several well-known algorithms, such as Shor’s algorithm or Quantum Amplitude Estimation.

References:

: Kitaev, A. Y. (1995). Quantum measurements and the Abelian Stabilizer Problem. 1–22.

quant-ph/9511026

: Michael A. Nielsen and Isaac L. Chuang. 2011.

Quantum Computation and Quantum Information: 10th Anniversary Edition (10th ed.). Cambridge University Press, New York, NY, USA.

: Qiskit

textbook

Parameters
• num_evaluation_qubits (int) – The number of evaluation qubits.

• unitary (QuantumCircuit) – The unitary operation $$U$$ which will be repeated and controlled.

• iqft (Optional[QuantumCircuit]) – A inverse Quantum Fourier Transform, per default the inverse of QFT is used. Note that the QFT should not include the usual swaps!

• name (str) – The name of the circuit.

Note

The inverse QFT should not include a swap of the qubit order.

Reference Circuit: 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 circuit in radians.

instances = 311
layout

Return any associated layout information anout 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 – 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 unituitive 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.