QFT

class QFT(num_qubits=None, approximation_degree=0, do_swaps=True, inverse=False, insert_barriers=False, name=None)

Bases : BlueprintCircuit

Quantum Fourier Transform Circuit.

The Quantum Fourier Transform (QFT) on \(n\) qubits is the operation

\[|j\rangle \mapsto \frac{1}{2^{n/2}} \sum_{k=0}^{2^n - 1} e^{2\pi ijk / 2^n} |k\rangle\]

The circuit that implements this transformation can be implemented using Hadamard gates on each qubit, a series of controlled-U1 (or Z, depending on the phase) gates and a layer of Swap gates. The layer of Swap gates can in principle be dropped if the QFT appears at the end of the circuit, since then the re-ordering can be done classically. They can be turned off using the do_swaps attribute.

For 4 qubits, the circuit that implements this transformation is:

(Source code)

The inverse QFT can be obtained by calling the inverse method on this class. The respective circuit diagram is:

(Source code)

One method to reduce circuit depth is to implement the QFT approximately by ignoring controlled-phase rotations where the angle is beneath a threshold. This is discussed in more detail in https://arxiv.org/abs/quant-ph/9601018 or https://arxiv.org/abs/quant-ph/0403071.

Here, this can be adjusted using the approximation_degree attribute: the smallest approximation_degree rotation angles are dropped from the QFT. For instance, a QFT on 5 qubits with approximation degree 2 yields (the barriers are dropped in this example):

(Source code)

Construct a new QFT circuit.

Paramètres

• num_qubits (Optional[int]) – The number of qubits on which the QFT acts.

• approximation_degree (int) – The degree of approximation (0 for no approximation).

• do_swaps (bool) – Whether to include the final swaps in the QFT.

• inverse (bool) – If True, the inverse Fourier transform is constructed.

• insert_barriers (bool) – If True, barriers are inserted as visualization improvement.

• name (Optional[str]) – The name of the circuit.

Methods Defined Here

inverse	Invert this circuit.
is_inverse	Whether the inverse Fourier transform is implemented.

Attributes

ancillas

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

approximation_degree

The approximation degree of the QFT.

Renvoie

The currently set approximation degree.

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

do_swaps

Whether the final swaps of the QFT are applied or not.

Renvoie

True, if the final swaps are applied, False if not.

extension_lib = 'include "qelib1.inc";'

global_phase

Return the global phase of the circuit in radians.

header = 'OPENQASM 2.0;'

insert_barriers

Whether barriers are inserted for better visualization or not.

Renvoie

True, if barriers are inserted, False if not.

instances = 258

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.

metadata

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

num_qubits

The number of qubits in the QFT circuit.

Renvoie

The number of qubits in the circuit.

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.

Renvoie

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

Lève

AttributeError – When circuit is not scheduled.

parameters

prefix = 'circuit'

qregs: list[QuantumRegister]

A list of the quantum registers associated with the circuit.

qubits

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