z iH*tSrSSKJr SSKrSSKJrJrJr SSK J r SSK J r "SS \ 5r "S S \5rg) zMDefine a Quantum Fourier Transform circuit (QFT) and a native gate (QFTGate).) annotationsN)QuantumRegisterCircuitInstructionGate)deprecate_func)BlueprintCircuitc^\rSrSrSr\"SSSS9SSU4Sjjj5r\SU4Sjj5r\RSS j5r\SS j5r \ RSS j5r \SS j5r \ RSS j5r \SSj5r \ RSSj5r SSjr SSSjjrSS SjjrS!U4SjjrSrU=r$)"QFTaQuantum Fourier Transform Circuit. The Quantum Fourier Transform (QFT) on :math:`n` qubits is the operation .. math:: |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: .. plot:: :alt: Diagram illustrating the previously described circuit. from qiskit.circuit.library import QFT from qiskit.visualization.library import _generate_circuit_library_visualization circuit = QFT(4) _generate_circuit_library_visualization(circuit) The inverse QFT can be obtained by calling the ``inverse`` method on this class. The respective circuit diagram is: .. plot:: :alt: Diagram illustrating the previously described circuit. from qiskit.circuit.library import QFT from qiskit.visualization.library import _generate_circuit_library_visualization circuit = QFT(4).inverse() _generate_circuit_library_visualization(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): .. plot:: :alt: Diagram illustrating the previously described circuit. from qiskit.circuit.library import QFT from qiskit.visualization.library import _generate_circuit_library_visualization circuit = QFT(5, approximation_degree=2) _generate_circuit_library_visualization(circuit) z2.1)zxUse qiskit.circuit.library.QFTGate or qiskit.synthesis.qft.synth_qft_full instead, for access to all previous arguments.z in Qiskit 3.0)sinceadditional_msgremoval_timelinecx>Uc U(aSOSn[TU]US9 X lX0lXPlX@lXlg)a Args: num_qubits: The number of qubits on which the QFT acts. approximation_degree: The degree of approximation (0 for no approximation). do_swaps: Whether to include the final swaps in the QFT. inverse: If True, the inverse Fourier transform is constructed. insert_barriers: If True, barriers are inserted as visualization improvement. name: The name of the circuit. NIQFTr name)super__init___approximation_degree _do_swaps_insert_barriers_inverse num_qubits)selfrapproximation_degreedo_swapsinverseinsert_barriersr __class__s a/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/circuit/library/basis_change/qft.pyr QFT.__init__Ns>4 <$6%D d#%9"! / $c>[TU]$)z\The number of qubits in the QFT circuit. Returns: The number of qubits in the circuit. )rr)rr s r!rQFT.num_qubitsrsw!!r#cXR:wa3UR5 /UlUbUS:a[USS9/Ulgggg)zSet the number of qubits. Note that this changes the registers of the circuit. Args: num_qubits: The new number of qubits. Nrqr)r _invalidateqregsr)rrs r!rr%}sK  (    DJ%*q.-jsCD +9% )r#cUR$)z[The approximation degree of the QFT. Returns: The currently set approximation degree. )rrs r!rQFT.approximation_degrees)))r#crUS:a [S5eXR:waUR5 Xlgg)zSet the approximation degree of the QFT. Args: approximation_degree: The new approximation degree. Raises: ValueError: If the approximation degree is smaller than 0. rz.Approximation degree cannot be smaller than 0.N) ValueErrorrr()rrs r!rr,s; ! #MN N #=#= =    )= & >r#cUR$)z{Whether barriers are inserted for better visualization or not. Returns: True, if barriers are inserted, False if not. )rr+s r!rQFT.insert_barrierss$$$r#cPXR:waUR5 Xlgg)zSpecify whether barriers are inserted for better visualization or not. Args: insert_barriers: If True, barriers are inserted, if False not. N)rr()rrs r!rr0s' 33 3    $3 ! 4r#cUR$)zyWhether the final swaps of the QFT are applied or not. Returns: True, if the final swaps are applied, False if not. )rr+s r!r QFT.do_swapss~~r#cPXR:waUR5 Xlgg)zSpecify whether to do the final swaps of the QFT circuit or not. Args: do_swaps: If True, the final swaps are applied, if False not. N)rr()rrs r!rr3s$ ~~ %    %N &r#cUR$)zWhether the inverse Fourier transform is implemented. Returns: True, if the inverse Fourier transform is implemented, False otherwise. )rr+s r! is_inverseQFT.is_inverses }}r#cURS;aUR(aSOSnOURS-nURUS9nURSRR 5nX$lURR 5 UR[XCR/55 UR(+UlU$)a-Invert this circuit. Args: annotated: indicates whether the inverse gate can be implemented as an annotated gate. The value of this argument is ignored as the inverse of a QFT is an IQFT which is just another instance of :class:`.QFT`. Returns: The inverted circuit. )r rr r_dgrr) rrcopydata operationrclear_appendrqubits)r annotatedrinvertediqfts r!r QFT.inverses 99 ' MM5vD99u$D99$9'yy|%%--/  +D//2FG $ -r#cLSnURcSnU(a [S5eU$)z,Check if the current configuration is valid.TFz&The number of qubits has not been set.)rAttributeError)rraise_on_failurevalids r!_check_configurationQFT._check_configurations* ?? "E$%MNN r#c >UR(ag[TU] 5 URnUS:XagSSKJn U"UUR URURURURS9nUR(aUR5OUR5nURX@RSS9 g)z(If not already built, build the circuit.Nrsynth_qft_full)rrrrrT)r?inplace) _is_builtr_buildrqiskit.synthesis.qftrLrrrrrrto_instructionto_gatecomposer?)rrrLcircuitwrappedr s r!rO QFT._builds >>  __ ? 7 ^^ 11!%!;!;MM  /3.B.B'((*HY W[[$ ?r#)rrrrrr))NrTFFN)rz int | NonerintrboolrrXrrXrz str | NonereturnNone)rYrW)rrWrYrZ)rrWrYrZ)rYrX)rrXrYrZ)rrXrYrZ)F)r@rXrYz'QFT')T)rFrXrYrX)rYrZ)__name__ __module__ __qualname____firstlineno____doc__rrpropertyrsetterrrrr6rrHrO__static_attributes__ __classcell__r s@r!r r sZ4l ) "&$% %%%"% %  %  %% %%8"" E E**  >!> %%44__&&<@@r#r cH^\rSrSrSrSU4Sjjr\S4SjrSrSr U=r $) QFTGateizQuantum Fourier Transform Gate. The Quantum Fourier Transform (QFT) on :math:`n` qubits is the operation .. math:: |j\rangle \mapsto \frac{1}{2^{n/2}} \sum_{k=0}^{2^n - 1} e^{2\pi ijk / 2^n} |k\rangle c$>[TU]SU/S9 g)zC Args: num_qubits: The number of qubits on which the QFT acts. qft)rrparamsN)rr)rrr s r!rQFTGate.__init__$s e 2Fr#NcUSLa [S5eURn[R"SU-5n[R"XD5n[R "S[R -U-SU--US9SUS- --$)z%Return a numpy array for the QFTGate.Fz9unable to avoid copy while creating an array as requestedry@g?)dtype)r.rnparangeouterexppi)rrlr:nnumsros r! __array__QFTGate.__array__.sr 5=XY Y OOyyA$vvb255j5(CF35ASQQRU^TTr#c:SSKJn U"URS9Ulg)zGProvide a specific decomposition of the QFTGate into a quantum circuit.rrK)rN)rPrLr definition)rrLs r!_defineQFTGate._define7s7(DOODr#)rw)rrW) r[r\r]r^r_rcomplexrtrxrbrcrds@r!rfrfs0GG&DUEEr#rf)r_ __future__rnumpyrmqiskit.circuit.quantumcircuitrrrqiskit.utils.deprecationrblueprintcircuitr r rfr#r!rs=T"SS3/@ @D"Ed"Er#