QFT¶
- class QFT(num_qubits=None, approximation_degree=0, do_swaps=True, inverse=False, insert_barriers=False, name=None)[source]¶
Bases:
qiskit.circuit.library.blueprintcircuit.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:
The inverse QFT can be obtained by calling the
inverse
method on this class. The respective circuit diagram is: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 smallestapproximation_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):Construct a new QFT circuit.
- Parameters
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
Invert this circuit.
Whether the inverse Fourier transform is implemented.
Attributes
- ancillas¶
Returns a list of ancilla bits in the order that the registers were added.
- Return type
List
[AncillaQubit
]
- approximation_degree¶
The approximation degree of the QFT.
- Return type
int
- 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}}
- Return type
dict
- clbits¶
Returns a list of classical bits in the order that the registers were added.
- Return type
List
[Clbit
]
- data¶
- do_swaps¶
Whether the final swaps of the QFT are applied or not.
- Return type
bool
- Returns
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.
- Return type
Union
[ParameterExpression
,float
]
- header = 'OPENQASM 2.0;'¶
- insert_barriers¶
Whether barriers are inserted for better visualization or not.
- Return type
bool
- Returns
True, if barriers are inserted, False if not.
- instances = 9¶
- 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.- Return type
dict
- num_ancillas¶
Return the number of ancilla qubits.
- Return type
int
- num_clbits¶
Return number of classical bits.
- Return type
int
- num_parameters¶
- Return type
int
- num_qubits¶
The number of qubits in the QFT circuit.
- Return type
int
- Returns
The number of qubits in the circuit.
- parameters¶
- Return type
ParameterView
- prefix = 'circuit'¶
- qregs¶
A list of the quantum registers associated with the circuit.