286 lines
11 KiB
Plaintext
286 lines
11 KiB
Plaintext
---
|
||
title: QFT
|
||
description: API reference for qiskit.circuit.library.QFT
|
||
in_page_toc_min_heading_level: 1
|
||
python_api_type: class
|
||
python_api_name: qiskit.circuit.library.QFT
|
||
---
|
||
|
||
# QFT
|
||
|
||
<Class id="qiskit.circuit.library.QFT" isDedicatedPage={true} github="https://github.com/Qiskit/qiskit/tree/stable/1.1/qiskit/circuit/library/basis_change/qft.py#L24-L295" signature="qiskit.circuit.library.QFT(num_qubits=None, approximation_degree=0, do_swaps=True, inverse=False, insert_barriers=False, name=None)" modifiers="class">
|
||
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:
|
||
|
||
|
||
|
||
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](https://arxiv.org/abs/quant-ph/9601018) or [https://arxiv.org/abs/quant-ph/0403071](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):
|
||
|
||
|
||
|
||
Construct a new QFT circuit.
|
||
|
||
**Parameters**
|
||
|
||
* **num\_qubits** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.12)") *| None*) – The number of qubits on which the QFT acts.
|
||
* **approximation\_degree** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.12)")) – The degree of approximation (0 for no approximation).
|
||
* **do\_swaps** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.12)")) – Whether to include the final swaps in the QFT.
|
||
* **inverse** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.12)")) – If True, the inverse Fourier transform is constructed.
|
||
* **insert\_barriers** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.12)")) – If True, barriers are inserted as visualization improvement.
|
||
* **name** ([*str*](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.12)") *| None*) – The name of the circuit.
|
||
|
||
## Attributes
|
||
|
||
### ancillas
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.ancillas">
|
||
A list of `AncillaQubit`s in the order that they were added. You should not mutate this.
|
||
</Attribute>
|
||
|
||
### approximation\_degree
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.approximation_degree">
|
||
The approximation degree of the QFT.
|
||
|
||
**Returns**
|
||
|
||
The currently set approximation degree.
|
||
</Attribute>
|
||
|
||
### calibrations
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.calibrations">
|
||
Return calibration dictionary.
|
||
|
||
The custom pulse definition of a given gate is of the form `{'gate_name': {(qubits, params): schedule}}`
|
||
</Attribute>
|
||
|
||
### clbits
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.clbits">
|
||
A list of `Clbit`s in the order that they were added. You should not mutate this.
|
||
</Attribute>
|
||
|
||
### data
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.data" />
|
||
|
||
### do\_swaps
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.do_swaps">
|
||
Whether the final swaps of the QFT are applied or not.
|
||
|
||
**Returns**
|
||
|
||
True, if the final swaps are applied, False if not.
|
||
</Attribute>
|
||
|
||
### global\_phase
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.global_phase">
|
||
The global phase of the current circuit scope in radians.
|
||
</Attribute>
|
||
|
||
### insert\_barriers
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.insert_barriers">
|
||
Whether barriers are inserted for better visualization or not.
|
||
|
||
**Returns**
|
||
|
||
True, if barriers are inserted, False if not.
|
||
</Attribute>
|
||
|
||
### instances
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.instances" attributeValue="214" />
|
||
|
||
### layout
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.layout">
|
||
Return any associated layout information about the circuit
|
||
|
||
This attribute contains an optional [`TranspileLayout`](qiskit.transpiler.TranspileLayout "qiskit.transpiler.TranspileLayout") object. This is typically set on the output from [`transpile()`](compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") or [`PassManager.run()`](qiskit.transpiler.PassManager#run "qiskit.transpiler.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()`](compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") function, an initial layout which permutes the qubits based on the selected physical qubits on the [`Target`](qiskit.transpiler.Target "qiskit.transpiler.Target"), and a final layout which is an output permutation caused by [`SwapGate`](qiskit.circuit.library.SwapGate "qiskit.circuit.library.SwapGate")s inserted during routing.
|
||
</Attribute>
|
||
|
||
### metadata
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.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.
|
||
</Attribute>
|
||
|
||
### num\_ancillas
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.num_ancillas">
|
||
Return the number of ancilla qubits.
|
||
</Attribute>
|
||
|
||
### num\_captured\_vars
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.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`](#qiskit.circuit.library.QFT.num_input_vars "qiskit.circuit.library.QFT.num_input_vars") must be zero.
|
||
</Attribute>
|
||
|
||
### num\_clbits
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.num_clbits">
|
||
Return number of classical bits.
|
||
</Attribute>
|
||
|
||
### num\_declared\_vars
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.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.
|
||
</Attribute>
|
||
|
||
### num\_input\_vars
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.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`](#qiskit.circuit.library.QFT.num_captured_vars "qiskit.circuit.library.QFT.num_captured_vars") must be zero.
|
||
</Attribute>
|
||
|
||
### num\_parameters
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.num_parameters" />
|
||
|
||
### num\_qubits
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.num_qubits">
|
||
The number of qubits in the QFT circuit.
|
||
|
||
**Returns**
|
||
|
||
The number of qubits in the circuit.
|
||
</Attribute>
|
||
|
||
### num\_vars
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.num_vars">
|
||
The number of real-time classical variables in the circuit.
|
||
|
||
This is the length of the `iter_vars()` iterable.
|
||
</Attribute>
|
||
|
||
### op\_start\_times
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.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**](https://docs.python.org/3/library/exceptions.html#AttributeError "(in Python v3.12)") – When circuit is not scheduled.
|
||
</Attribute>
|
||
|
||
### parameters
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.parameters" />
|
||
|
||
### prefix
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.prefix" attributeValue="'circuit'" />
|
||
|
||
### qregs
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.qregs" attributeTypeHint="list[QuantumRegister]">
|
||
A list of the `QuantumRegister`s in this circuit. You should not mutate this.
|
||
</Attribute>
|
||
|
||
### qubits
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.qubits">
|
||
A list of `Qubit`s in the order that they were added. You should not mutate this.
|
||
</Attribute>
|
||
|
||
### name
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.name" attributeTypeHint="str">
|
||
A human-readable name for the circuit.
|
||
</Attribute>
|
||
|
||
### cregs
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.cregs" attributeTypeHint="list[ClassicalRegister]">
|
||
A list of the `ClassicalRegister`s in this circuit. You should not mutate this.
|
||
</Attribute>
|
||
|
||
### duration
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.duration" attributeTypeHint="int | float | None">
|
||
The total duration of the circuit, set by a scheduling transpiler pass. Its unit is specified by [`unit`](#qiskit.circuit.library.QFT.unit "qiskit.circuit.library.QFT.unit").
|
||
</Attribute>
|
||
|
||
### unit
|
||
|
||
<Attribute id="qiskit.circuit.library.QFT.unit">
|
||
The unit that [`duration`](#qiskit.circuit.library.QFT.duration "qiskit.circuit.library.QFT.duration") is specified in.
|
||
</Attribute>
|
||
|
||
## Methods
|
||
|
||
### inverse
|
||
|
||
<Function id="qiskit.circuit.library.QFT.inverse" github="https://github.com/Qiskit/qiskit/tree/stable/1.1/qiskit/circuit/library/basis_change/qft.py#L206-L234" signature="inverse(annotated=False)">
|
||
Invert this circuit.
|
||
|
||
**Parameters**
|
||
|
||
**annotated** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.12)")) – 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`](#qiskit.circuit.library.QFT "qiskit.circuit.library.QFT").
|
||
|
||
**Returns**
|
||
|
||
The inverted circuit.
|
||
|
||
**Return type**
|
||
|
||
[*QFT*](#qiskit.circuit.library.QFT "qiskit.circuit.library.basis_change.qft.QFT")
|
||
</Function>
|
||
|
||
### is\_inverse
|
||
|
||
<Function id="qiskit.circuit.library.QFT.is_inverse" github="https://github.com/Qiskit/qiskit/tree/stable/1.1/qiskit/circuit/library/basis_change/qft.py#L198-L204" signature="is_inverse()">
|
||
Whether the inverse Fourier transform is implemented.
|
||
|
||
**Returns**
|
||
|
||
True, if the inverse Fourier transform is implemented, False otherwise.
|
||
|
||
**Return type**
|
||
|
||
[bool](https://docs.python.org/3/library/functions.html#bool "(in Python v3.12)")
|
||
</Function>
|
||
</Class>
|
||
|