352 lines
14 KiB
Plaintext
352 lines
14 KiB
Plaintext
---
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title: QFT (v1.2)
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description: API reference for qiskit.circuit.library.QFT in qiskit v1.2
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in_page_toc_min_heading_level: 1
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python_api_type: class
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python_api_name: qiskit.circuit.library.QFT
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---
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# QFT
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<Class id="qiskit.circuit.library.QFT" isDedicatedPage={true} github="https://github.com/Qiskit/qiskit/tree/stable/1.2/qiskit/circuit/library/basis_change/qft.py#L23-L294" signature="qiskit.circuit.library.QFT(num_qubits=None, approximation_degree=0, do_swaps=True, inverse=False, insert_barriers=False, name=None)" modifiers="class">
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Bases: `BlueprintCircuit`
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Quantum Fourier Transform Circuit.
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The Quantum Fourier Transform (QFT) on $n$ qubits is the operation
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$$
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|j\rangle \mapsto \frac{1}{2^{n/2}} \sum_{k=0}^{2^n - 1} e^{2\pi ijk / 2^n} |k\rangle
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$$
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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.
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For 4 qubits, the circuit that implements this transformation is:
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The inverse QFT can be obtained by calling the `inverse` method on this class. The respective circuit diagram is:
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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).
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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):
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Construct a new QFT circuit.
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**Parameters**
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* **num\_qubits** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)") *| None*) – The number of qubits on which the QFT acts.
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* **approximation\_degree** ([*int*](https://docs.python.org/3/library/functions.html#int "(in Python v3.13)")) – The degree of approximation (0 for no approximation).
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* **do\_swaps** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.13)")) – Whether to include the final swaps in the QFT.
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* **inverse** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.13)")) – If True, the inverse Fourier transform is constructed.
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* **insert\_barriers** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.13)")) – If True, barriers are inserted as visualization improvement.
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* **name** ([*str*](https://docs.python.org/3/library/stdtypes.html#str "(in Python v3.13)") *| None*) – The name of the circuit.
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## Attributes
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### ancillas
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<Attribute id="qiskit.circuit.library.QFT.ancillas">
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A list of `AncillaQubit`s in the order that they were added. You should not mutate this.
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</Attribute>
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### approximation\_degree
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<Attribute id="qiskit.circuit.library.QFT.approximation_degree">
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The approximation degree of the QFT.
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**Returns**
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The currently set approximation degree.
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</Attribute>
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### calibrations
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<Attribute id="qiskit.circuit.library.QFT.calibrations">
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Return calibration dictionary.
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The custom pulse definition of a given gate is of the form `{'gate_name': {(qubits, params): schedule}}`
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</Attribute>
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### clbits
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<Attribute id="qiskit.circuit.library.QFT.clbits">
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A list of `Clbit`s in the order that they were added. You should not mutate this.
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</Attribute>
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### data
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<Attribute id="qiskit.circuit.library.QFT.data">
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The circuit data (instructions and context).
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**Returns**
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a list-like object containing the [`CircuitInstruction`](qiskit.circuit.CircuitInstruction "qiskit.circuit.CircuitInstruction")s for each instruction.
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**Return type**
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QuantumCircuitData
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</Attribute>
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### do\_swaps
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<Attribute id="qiskit.circuit.library.QFT.do_swaps">
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Whether the final swaps of the QFT are applied or not.
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**Returns**
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True, if the final swaps are applied, False if not.
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</Attribute>
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### global\_phase
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<Attribute id="qiskit.circuit.library.QFT.global_phase">
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The global phase of the current circuit scope in radians.
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</Attribute>
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### insert\_barriers
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<Attribute id="qiskit.circuit.library.QFT.insert_barriers">
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Whether barriers are inserted for better visualization or not.
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**Returns**
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True, if barriers are inserted, False if not.
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</Attribute>
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### instances
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<Attribute id="qiskit.circuit.library.QFT.instances" attributeValue="214" />
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### layout
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<Attribute id="qiskit.circuit.library.QFT.layout">
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Return any associated layout information about the circuit
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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.
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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.
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</Attribute>
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### metadata
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<Attribute id="qiskit.circuit.library.QFT.metadata">
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Arbitrary user-defined metadata for the circuit.
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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.
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</Attribute>
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### num\_ancillas
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<Attribute id="qiskit.circuit.library.QFT.num_ancillas">
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Return the number of ancilla qubits.
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</Attribute>
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### num\_captured\_vars
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<Attribute id="qiskit.circuit.library.QFT.num_captured_vars">
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The number of real-time classical variables in the circuit marked as captured from an enclosing scope.
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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.
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</Attribute>
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### num\_clbits
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<Attribute id="qiskit.circuit.library.QFT.num_clbits">
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Return number of classical bits.
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</Attribute>
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### num\_declared\_vars
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<Attribute id="qiskit.circuit.library.QFT.num_declared_vars">
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The number of real-time classical variables in the circuit that are declared by this circuit scope, excluding inputs or captures.
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This is the length of the `iter_declared_vars()` iterable.
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</Attribute>
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### num\_input\_vars
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<Attribute id="qiskit.circuit.library.QFT.num_input_vars">
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The number of real-time classical variables in the circuit marked as circuit inputs.
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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.
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</Attribute>
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### num\_parameters
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<Attribute id="qiskit.circuit.library.QFT.num_parameters">
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The number of parameter objects in the circuit.
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</Attribute>
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### num\_qubits
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<Attribute id="qiskit.circuit.library.QFT.num_qubits">
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The number of qubits in the QFT circuit.
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**Returns**
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The number of qubits in the circuit.
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</Attribute>
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### num\_vars
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<Attribute id="qiskit.circuit.library.QFT.num_vars">
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The number of real-time classical variables in the circuit.
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This is the length of the `iter_vars()` iterable.
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</Attribute>
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### op\_start\_times
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<Attribute id="qiskit.circuit.library.QFT.op_start_times">
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Return a list of operation start times.
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This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.
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**Returns**
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List of integers representing instruction start times. The index corresponds to the index of instruction in `QuantumCircuit.data`.
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**Raises**
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[**AttributeError**](https://docs.python.org/3/library/exceptions.html#AttributeError "(in Python v3.13)") – When circuit is not scheduled.
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</Attribute>
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### parameters
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<Attribute id="qiskit.circuit.library.QFT.parameters">
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The parameters defined in the circuit.
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This attribute returns the [`Parameter`](qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit sorted alphabetically. Note that parameters instantiated with a [`ParameterVector`](qiskit.circuit.ParameterVector "qiskit.circuit.ParameterVector") are still sorted numerically.
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**Examples**
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The snippet below shows that insertion order of parameters does not matter.
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```python
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>>> from qiskit.circuit import QuantumCircuit, Parameter
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>>> a, b, elephant = Parameter("a"), Parameter("b"), Parameter("elephant")
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>>> circuit = QuantumCircuit(1)
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>>> circuit.rx(b, 0)
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>>> circuit.rz(elephant, 0)
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>>> circuit.ry(a, 0)
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>>> circuit.parameters # sorted alphabetically!
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ParameterView([Parameter(a), Parameter(b), Parameter(elephant)])
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```
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Bear in mind that alphabetical sorting might be unintuitive when it comes to numbers. The literal “10” comes before “2” in strict alphabetical sorting.
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```python
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>>> from qiskit.circuit import QuantumCircuit, Parameter
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>>> angles = [Parameter("angle_1"), Parameter("angle_2"), Parameter("angle_10")]
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>>> circuit = QuantumCircuit(1)
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>>> circuit.u(*angles, 0)
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>>> circuit.draw()
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┌─────────────────────────────┐
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q: ┤ U(angle_1,angle_2,angle_10) ├
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└─────────────────────────────┘
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>>> circuit.parameters
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ParameterView([Parameter(angle_1), Parameter(angle_10), Parameter(angle_2)])
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```
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To respect numerical sorting, a [`ParameterVector`](qiskit.circuit.ParameterVector "qiskit.circuit.ParameterVector") can be used.
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```python
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>>> from qiskit.circuit import QuantumCircuit, Parameter, ParameterVector
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>>> x = ParameterVector("x", 12)
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>>> circuit = QuantumCircuit(1)
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>>> for x_i in x:
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... circuit.rx(x_i, 0)
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>>> circuit.parameters
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ParameterView([
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ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
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ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
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..., ParameterVectorElement(x[11])
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])
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```
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**Returns**
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The sorted [`Parameter`](qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit.
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</Attribute>
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### prefix
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<Attribute id="qiskit.circuit.library.QFT.prefix" attributeValue="'circuit'" />
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### qregs
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<Attribute id="qiskit.circuit.library.QFT.qregs" attributeTypeHint="list[QuantumRegister]">
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A list of the `QuantumRegister`s in this circuit. You should not mutate this.
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</Attribute>
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### qubits
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<Attribute id="qiskit.circuit.library.QFT.qubits">
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A list of `Qubit`s in the order that they were added. You should not mutate this.
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</Attribute>
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### name
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<Attribute id="qiskit.circuit.library.QFT.name" attributeTypeHint="str">
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A human-readable name for the circuit.
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</Attribute>
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### cregs
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<Attribute id="qiskit.circuit.library.QFT.cregs" attributeTypeHint="list[ClassicalRegister]">
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A list of the `ClassicalRegister`s in this circuit. You should not mutate this.
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</Attribute>
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### duration
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<Attribute id="qiskit.circuit.library.QFT.duration" attributeTypeHint="int | float | None">
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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").
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</Attribute>
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### unit
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<Attribute id="qiskit.circuit.library.QFT.unit">
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The unit that [`duration`](#qiskit.circuit.library.QFT.duration "qiskit.circuit.library.QFT.duration") is specified in.
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</Attribute>
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## Methods
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### inverse
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<Function id="qiskit.circuit.library.QFT.inverse" github="https://github.com/Qiskit/qiskit/tree/stable/1.2/qiskit/circuit/library/basis_change/qft.py#L205-L233" signature="inverse(annotated=False)">
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Invert this circuit.
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**Parameters**
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**annotated** ([*bool*](https://docs.python.org/3/library/functions.html#bool "(in Python v3.13)")) – 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").
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**Returns**
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The inverted circuit.
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**Return type**
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[*QFT*](#qiskit.circuit.library.QFT "qiskit.circuit.library.basis_change.qft.QFT")
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</Function>
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### is\_inverse
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<Function id="qiskit.circuit.library.QFT.is_inverse" github="https://github.com/Qiskit/qiskit/tree/stable/1.2/qiskit/circuit/library/basis_change/qft.py#L197-L203" signature="is_inverse()">
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Whether the inverse Fourier transform is implemented.
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**Returns**
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True, if the inverse Fourier transform is implemented, False otherwise.
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**Return type**
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[bool](https://docs.python.org/3/library/functions.html#bool "(in Python v3.13)")
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</Function>
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</Class>
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