z ihSrSSKJr SSKrSSKrSSKJr SSSjjrSr g) z& Circuit synthesis for a QFT circuit. ) annotationsN)QuantumCircuitc >[X- S- 5 [U5n[[U55HnUR U5 [ SU[ SX U- S- - 5- 5n[[Xx- U55H-n [ RSX- --n URXU 5 M/ U(dMUR5 M U(a,[US-5Hn URXU - S- 5 M U(aUR5nUbXVl U$)aConstruct a circuit for the Quantum Fourier Transform using all-to-all connectivity. .. note:: With the default value of ``do_swaps = True``, this synthesis algorithm creates a circuit that faithfully implements the QFT operation. This circuit contains a sequence of swap gates at the end, corresponding to reversing the order of its output qubits. In some applications this reversal permutation can be avoided. Setting ``do_swaps = False`` creates a circuit without this reversal permutation, at the expense that this circuit implements the "QFT-with-reversal" instead of QFT. Alternatively, the :class:`~.ElidePermutations` transpiler pass is able to remove these swap gates. Args: num_qubits: The number of qubits on which the Quantum Fourier Transform acts. do_swaps: Whether to synthesize the "QFT" or the "QFT-with-reversal" operation. approximation_degree: The degree of approximation (0 for no approximation). It is possible to implement the QFT approximately by ignoring controlled-phase rotations with the angle 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. insert_barriers: If ``True``, barriers are inserted for improved visualization. inverse: If ``True``, the inverse Quantum Fourier Transform is constructed. name: The name of the circuit. Returns: A circuit implementing the QFT operation. rg@) _warn_if_precision_lossrreversedrangehmaxnppicpbarrierswapinversename) num_qubitsdo_swapsapproximation_degreeinsert_barriersrrcircuitjnum_entanglementsklamis a/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/synthesis/qft/qft_decompose_full.pysynth_qft_fullrsHJ=ABZ(G eJ' ( ! 1s1.BSTnWXFX.Y'Z#Z[% 5q9:A%%315>*C JJsq ! ; ? OO )zQ'A LLNQ. /(//#  NcU[R"[5R*:a[R "SUS3[ SS9 gg)a>Issue a warning if constructing the circuit will lose precision. If we need an angle smaller than ``pi * 2**-1022``, we start to lose precision by going into the subnormal numbers. We won't lose _all_ precision until an exponent of about 1075, but beyond 1022 we're using fractional bits to represent leading zeros. z8precision loss in QFT. The rotation needed to represent zI entanglements is smaller than the smallest normal floating-point number.)category stacklevelN)r finfofloatminexpwarningswarnRuntimeWarning)max_num_entanglementss rrrXsN 6 666  11F0GHJ J$  7r )TrFFN)rintrboolrr,rr-rr-rz str | Nonereturnr) __doc__ __future__rr(numpyr qiskit.circuit.quantumcircuitrrrr rr4sv#8  !! ???? ?  ?  ??D r