--- title: QFT (v2.0) description: API reference for qiskit.circuit.library.QFT in qiskit v2.0 source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/2.0/qiskit.circuit.library.QFT --- # QFT *class* `qiskit.circuit.library.QFT(num_qubits=None, approximation_degree=0, do_swaps=True, inverse=False, insert_barriers=False, name=None)` [GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.0/qiskit/circuit/library/basis_change/qft.py#L23-L279) 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: ![Diagram illustrating the previously described circuit.](https://eu-de.quantum.cloud.ibm.com/docs/images/api/qiskit/2.0/qiskit-circuit-library-QFT-1.avif) 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.](https://eu-de.quantum.cloud.ibm.com/docs/images/api/qiskit/2.0/qiskit-circuit-library-QFT-2.avif) 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): ![Diagram illustrating the previously described circuit.](https://eu-de.quantum.cloud.ibm.com/docs/images/api/qiskit/2.0/qiskit-circuit-library-QFT-3.avif) 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*](https://docs.python.org/3/library/functions.html#int) *| None*) – The number of qubits on which the QFT acts. - **approximation\_degree** ([*int*](https://docs.python.org/3/library/functions.html#int)) – The degree of approximation (0 for no approximation). - **do\_swaps** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – Whether to include the final swaps in the QFT. - **inverse** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – If True, the inverse Fourier transform is constructed. - **insert\_barriers** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – If True, barriers are inserted as visualization improvement. - **name** ([*str*](https://docs.python.org/3/library/stdtypes.html#str) *| None*) – The name of the circuit. ## Attributes ### ancillas A list of `AncillaQubit`s 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. ### clbits A list of `Clbit`s in the order that they were added. You should not mutate this. **Example** ```python from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit qr1 = QuantumRegister(2) qr2 = QuantumRegister(1) cr1 = ClassicalRegister(2) cr2 = ClassicalRegister(1) qc = QuantumCircuit(qr1, qr2, cr1, cr2) print("List the qubits in this circuit:", qc.qubits) print("List the classical bits in this circuit:", qc.clbits) ``` ```text List the qubits in this circuit: [Qubit(QuantumRegister(2, 'q0'), 0), Qubit(QuantumRegister(2, 'q0'), 1), Qubit(QuantumRegister(1, 'q1'), 0)] List the classical bits in this circuit: [Clbit(ClassicalRegister(2, 'c0'), 0), Clbit(ClassicalRegister(2, 'c0'), 1), Clbit(ClassicalRegister(1, 'c1'), 0)] ``` ### cregs A list of `Clbit`s 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 [`CircuitInstruction`](/docs/api/qiskit/2.0/qiskit.circuit.CircuitInstruction "qiskit.circuit.CircuitInstruction")s 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`](#qiskit.circuit.library.QFT.unit "qiskit.circuit.library.QFT.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 3.0.0. ### global\_phase The global phase of the current circuit scope in radians. **Example** ```python from qiskit import QuantumCircuit circuit = QuantumCircuit(2) circuit.h(0) circuit.cx(0, 1) print(circuit.global_phase) ``` ```text 0.0 ``` ```python from numpy import pi circuit.global_phase = pi/4 print(circuit.global_phase) ``` ```text 0.7853981633974483 ``` ### insert\_barriers Whether barriers are inserted for better visualization or not. **Returns** True, if barriers are inserted, False if not. ### instances Default value: `223` ### layout Return any associated layout information about the circuit. This attribute contains an optional [`TranspileLayout`](/docs/api/qiskit/2.0/qiskit.transpiler.TranspileLayout "qiskit.transpiler.TranspileLayout") object. This is typically set on the output from [`transpile()`](/docs/api/qiskit/2.0/compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") or [`PassManager.run()`](/docs/api/qiskit/2.0/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()`](/docs/api/qiskit/2.0/compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") function: an initial layout that permutes the qubits based on the selected physical qubits on the [`Target`](/docs/api/qiskit/2.0/qiskit.transpiler.Target "qiskit.transpiler.Target"), and a final layout, which is an output permutation caused by [`SwapGate`](/docs/api/qiskit/2.0/qiskit.circuit.library.SwapGate "qiskit.circuit.library.SwapGate")s inserted during routing. **Example** ```python from qiskit import QuantumCircuit from qiskit.providers.fake_provider import GenericBackendV2 from qiskit.transpiler import generate_preset_pass_manager # Create circuit to test transpiler on qc = QuantumCircuit(3, 3) qc.h(0) qc.cx(0, 1) qc.swap(1, 2) qc.cx(0, 1) # Add measurements to the circuit qc.measure([0, 1, 2], [0, 1, 2]) # Specify the QPU to target backend = GenericBackendV2(3) # Transpile the circuit pass_manager = generate_preset_pass_manager( optimization_level=1, backend=backend ) transpiled = pass_manager.run(qc) # Print the layout after transpilation print(transpiled.layout.routing_permutation()) ``` ```text [0, 1, 2] ``` ### metadata Arbitrary user-defined dictionary of 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. **Example** ```python from qiskit import QuantumCircuit qc = QuantumCircuit(2, 2, metadata={'experiment_type': 'Bell state experiment'}) print(qc.metadata) ``` ```text {'experiment_type': 'Bell state experiment'} ``` ### num\_ancillas Return the number of ancilla qubits. **Example** ```python from qiskit import QuantumCircuit, QuantumRegister, AncillaRegister # Create a 2-qubit quantum circuit reg = QuantumRegister(2) qc = QuantumCircuit(reg) # Create an ancilla register with 1 qubit anc = AncillaRegister(1) qc.add_register(anc) # Add the ancilla register to the circuit print("Number of ancilla qubits:", qc.num_ancillas) ``` ```text Number of ancilla qubits: 1 ``` ### num\_captured\_stretches The number of stretches in the circuit marked as captured from an enclosing scope. This is the length of the `iter_captured_stretches()` 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. ### 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. ### num\_clbits Return number of classical bits. **Example** ```python from qiskit import QuantumCircuit # Create a new circuit with two qubits and one classical bit qc = QuantumCircuit(2, 1) print("Number of classical bits:", qc.num_clbits) ``` ```text Number of classical bits: 1 ``` ### num\_declared\_stretches The number of stretches in the circuit that are declared by this circuit scope, excluding captures. This is the length of the `iter_declared_stretches()` iterable. ### 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\_identifiers The number of real-time classical variables and stretches in the circuit. This is equal to [`num_vars()`](#qiskit.circuit.library.QFT.num_vars "qiskit.circuit.library.QFT.num_vars") + [`num_stretches()`](#qiskit.circuit.library.QFT.num_stretches "qiskit.circuit.library.QFT.num_stretches"). ### 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. ### 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\_stretches The number of stretches in the circuit. This is the length of the `iter_stretches()` iterable. ### 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. > **Note** > > This attribute computes the estimate starting time of the operations in the scheduled circuit and only works for simple circuits that have no control flow or other classical feed-forward operations. This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit. **Example** ```python from qiskit import QuantumCircuit from qiskit.providers.fake_provider import GenericBackendV2 from qiskit.transpiler import generate_preset_pass_manager qc = QuantumCircuit(2) qc.h(0) qc.cx(0, 1) qc.measure_all() # Print the original circuit print("Original circuit:") print(qc) # Transpile the circuit with a specific basis gates list and print the resulting circuit backend = GenericBackendV2(2, basis_gates=['u1', 'u2', 'u3', 'cx']) pm = generate_preset_pass_manager( optimization_level=1, backend=backend, scheduling_method="alap" ) transpiled_qc = pm.run(qc) print("Transpiled circuit with basis gates ['u1', 'u2', 'u3', 'cx']:") print(transpiled_qc) # Print the start times of each instruction in the transpiled circuit print("Start times of instructions in the transpiled circuit:") for instruction, start_time in zip(transpiled_qc.data, transpiled_qc.op_start_times): print(f"{instruction.operation.name}: {start_time}") ``` ```text Original circuit: ┌───┐ ░ ┌─┐ q_0: ┤ H ├──■───░─┤M├─── └───┘┌─┴─┐ ░ └╥┘┌─┐ q_1: ─────┤ X ├─░──╫─┤M├ └───┘ ░ ║ └╥┘ meas: 2/══════════════╩══╩═ 0 1 Transpiled circuit with basis gates ['u1', 'u2', 'u3', 'cx']: ┌─────────┐ ░ ┌─────────────────┐┌─┐ q_0 -> 0 ───┤ U2(0,π) ├──────■───░─┤ Delay(1255[dt]) ├┤M├ ┌──┴─────────┴───┐┌─┴─┐ ░ └───────┬─┬───────┘└╥┘ q_1 -> 1 ┤ Delay(196[dt]) ├┤ X ├─░─────────┤M├─────────╫─ └────────────────┘└───┘ ░ └╥┘ ║ meas: 2/═══════════════════════════════════╩══════════╩═ 1 0 Start times of instructions in the transpiled circuit: u2: 0 delay: 0 cx: 196 barrier: 2098 delay: 2098 measure: 3353 measure: 2098 ``` **Returns** List of integers representing instruction estimated start times. The index corresponds to the index of instruction in `QuantumCircuit.data`. **Raises** [**AttributeError**](https://docs.python.org/3/library/exceptions.html#AttributeError) – When circuit is not scheduled. ### parameters The parameters defined in the circuit. This attribute returns the [`Parameter`](/docs/api/qiskit/2.0/qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit sorted alphabetically. Note that parameters instantiated with a [`ParameterVector`](/docs/api/qiskit/2.0/qiskit.circuit.ParameterVector "qiskit.circuit.ParameterVector") are still sorted numerically. **Examples** The snippet below shows that insertion order of parameters does not matter. ```python >>> 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. ```python >>> 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`](/docs/api/qiskit/2.0/qiskit.circuit.ParameterVector "qiskit.circuit.ParameterVector") can be used. ```python >>> 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`](/docs/api/qiskit/2.0/qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit. ### prefix Default value: `'circuit'` ### qregs A list of the quantum registers associated with the circuit. ### qubits A list of `Qubit`s in the order that they were added. You should not mutate this. ### unit The unit that [`duration`](#qiskit.circuit.library.QFT.duration "qiskit.circuit.library.QFT.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 3.0.0. ### name Type: `str` A human-readable name for the circuit. **Example** ```python from qiskit import QuantumCircuit qc = QuantumCircuit(2, 2, name="my_circuit") print(qc.name) ``` ```text my_circuit ``` ## Methods ### inverse `inverse(annotated=False)` [GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.0/qiskit/circuit/library/basis_change/qft.py#L216-L244) Invert this circuit. **Parameters** **annotated** ([*bool*](https://docs.python.org/3/library/functions.html#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`](#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") ### is\_inverse `is_inverse()` [GitHub](https://github.com/Qiskit/qiskit/tree/stable/2.0/qiskit/circuit/library/basis_change/qft.py#L208-L214) 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)