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QFT

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

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Bases: BlueprintCircuit

Quantum Fourier Transform Circuit.

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

j12n/2k=02n1e2πijk/2nk|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:

Diagram illustrating the previously described circuit.

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

Diagram illustrating the previously described circuit.

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):

Diagram illustrating the previously described circuit.

Construct a new QFT circuit.

Deprecated since version 1.3_pending

The class qiskit.circuit.library.basis_change.qft.QFT is pending deprecation as of qiskit 1.3. It will be marked deprecated in a future release, and then removed no earlier than 3 months after the release date. (‘Use qiskit.circuit.library.QFTGate or qiskit.synthesis.qft.synth_qft_full instead, for access to all previous arguments.’,)

Parameters

  • num_qubits (int | None) – 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 (str | None) – The name of the circuit.

Attributes

ancillas

A list of AncillaQubits in the order that they were added. You should not mutate this.

approximation_degree

The approximation degree of the QFT.

Returns

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}}

Deprecated since version 1.3

The property qiskit.circuit.quantumcircuit.QuantumCircuit.calibrations is deprecated as of Qiskit 1.3. It will be removed in Qiskit 2.0. The entire Qiskit Pulse package is being deprecated and will be moved to the Qiskit Dynamics repository: https://github.com/qiskit-community/qiskit-dynamics. Note that once removed, qiskit.circuit.quantumcircuit.QuantumCircuit.calibrations will have no alternative in Qiskit.

clbits

A list of Clbits in the order that they were added. You should not mutate this.

data

The circuit data (instructions and context).

Returns

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

Return type

QuantumCircuitData

do_swaps

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

Returns

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

duration

The total duration of the circuit, set by a scheduling transpiler pass. Its unit is specified by unit.

Deprecated since version 1.3.0

The property qiskit.circuit.quantumcircuit.QuantumCircuit.duration is deprecated as of qiskit 1.3.0. It will be removed in Qiskit 2.0.0.

global_phase

The global phase of the current circuit scope in radians.

insert_barriers

Whether barriers are inserted for better visualization or not.

Returns

True, if barriers are inserted, False if not.

instances

Default value: 160

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.

metadata

Arbitrary user-defined metadata for the circuit.

Qiskit will not examine the content of this mapping, but it will pass it through the transpiler and reattach it to the output, so you can track your own metadata.

num_ancillas

Return the number of ancilla qubits.

num_captured_vars

The number of real-time classical variables in the circuit marked as captured from an enclosing scope.

This is the length of the iter_captured_vars() iterable. If this is non-zero, num_input_vars must be zero.

num_clbits

Return number of classical bits.

num_declared_vars

The number of real-time classical variables in the circuit that are declared by this circuit scope, excluding inputs or captures.

This is the length of the iter_declared_vars() iterable.

num_input_vars

The number of real-time classical variables in the circuit marked as circuit inputs.

This is the length of the iter_input_vars() iterable. If this is non-zero, num_captured_vars must be zero.

num_parameters

The number of parameter objects in the circuit.

num_qubits

The number of qubits in the QFT circuit.

Returns

The number of qubits in the circuit.

num_vars

The number of real-time classical variables in the circuit.

This is the length of the iter_vars() iterable.

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 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[0]), ParameterVectorElement(x[1]),
    ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
    ..., ParameterVectorElement(x[11])
])

Returns

The sorted Parameter objects in the circuit.

prefix

Default value: 'circuit'

qregs

Type: list[QuantumRegister]

A list of the QuantumRegisters in this circuit. You should not mutate this.

qubits

A list of Qubits in the order that they were added. You should not mutate this.

unit

The unit that duration is specified in.

Deprecated since version 1.3.0

The property qiskit.circuit.quantumcircuit.QuantumCircuit.unit is deprecated as of qiskit 1.3.0. It will be removed in Qiskit 2.0.0.

name

Type: str

A human-readable name for the circuit.

cregs

Type: list[ClassicalRegister]

A list of the ClassicalRegisters in this circuit. You should not mutate this.


Methods

inverse

inverse(annotated=False)

GitHub

Invert this circuit.

Parameters

annotated (bool) – indicates whether the inverse gate can be implemented as an annotated gate. The value of this argument is ignored as the inverse of a QFT is an IQFT which is just another instance of QFT.

Returns

The inverted circuit.

Return type

QFT

is_inverse

is_inverse()

GitHub

Whether the inverse Fourier transform is implemented.

Returns

True, if the inverse Fourier transform is implemented, False otherwise.

Return type

bool

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