σ Σz i<γ σT•SrSSKrSSKJr SSKJr SSKJr S S\ S\ S\ S \4S jjr g) z1Compute the sum of two qubit registers using QFT.ιN)ΪQuantumCircuit)ΪQuantumRegister)ΪQFTGateΪnum_state_qubitsΪkindΪ annotatedΪreturnc σ@•US:Xa [S5eUS:a [S5e[USS9n[USS9nX4/nUS:Xa[SS S9nURU5 [U6nUS :XaUS S O US S WS S -nUS :XaUOUS-n [ U 5n URX¨S S 5 [ U5HHn [ X›- 5H4n [ RS U -- n URXΣU X‹U -)5 M6 MJ URU RUS 9US S 5 U$)uC A circuit that uses QFT to perform in-place addition on two qubit registers. For registers with :math:`n` qubits, the QFT adder can perform addition modulo :math:`2^n` (with ``kind="fixed"``) or ordinary addition by adding a carry qubits (with ``kind="half"``). The fixed adder uses :math:`(3n^2 - n)/2` :class:`.CPhaseGate` operators, with an additional :math:`n` for the half adder. As an example, a non-fixed_point QFT adder circuit that performs addition on two 2-qubit sized registers is as follows: .. parsed-literal:: a_0: ─────────■──────■────────■────────────────────────────────── β”‚ β”‚ β”‚ a_1: ─────────┼──────┼────────┼────────■──────■────────────────── β”Œβ”€β”€β”€β”€β”€β”€β” β”‚ β”‚ β”‚P(Ο€/4) β”‚ β”‚P(Ο€/2) β”Œβ”€β”€β”€β”€β”€β”€β”€β”€β”€β” b_0: ─0 β”œβ”€β”Όβ”€β”€β”€β”€β”€β”€β”Όβ”€β”€β”€β”€β”€β”€β”€β”€β– β”€β”€β”€β”€β”€β”€β”€β”€β”Όβ”€β”€β”€β”€β”€β”€β– β”€β”€β”€β”€β”€β”€β”€β”€0 β”œ β”‚ β”‚ β”‚ β”‚P(Ο€/2) β”‚P(Ο€) β”‚ β”‚ b_1: ─1 Qft β”œβ”€β”Όβ”€β”€β”€β”€β”€β”€β– β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β– β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€1 qft_dg β”œ β”‚ β”‚ β”‚P(Ο€) β”‚ β”‚ cout: ─2 β”œβ”€β– β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€β”€2 β”œ β””β”€β”€β”€β”€β”€β”€β”˜ β””β”€β”€β”€β”€β”€β”€β”€β”€β”€β”˜ Args: num_state_qubits: The number of qubits in either input register for state :math:`|a\rangle` or :math:`|b\rangle`. The two input registers must have the same number of qubits. kind: The kind of adder, can be ``"half"`` for a half adder or ``"fixed"`` for a fixed-sized adder. A half adder contains a carry-out to represent the most-significant bit, but the fixed-sized adder doesn't and hence performs addition modulo ``2 ** num_state_qubits``. annotated: If ``True``, creates appropriate control and inverse operations as ``AnnotatedOperation`` objects. References: [1] T. G. Draper, Addition on a Quantum Computer, 2000. `arXiv:quant-ph/0008033 `_ [2] Ruiz-Perez et al., Quantum arithmetic with the Quantum Fourier Transform, 2017. `arXiv:1411.5949 `_ [3] Vedral et al., Quantum Networks for Elementary Arithmetic Operations, 1995. `arXiv:quant-ph/9511018 `_ Ϊfullz@The DraperQFTAdder only supports 'half' and 'fixed' as ``kind``.ιz(The number of qubits must be at least 1.Ϊa)ΪnameΪbΪhalfΪcoutΪfixedNι)r) Ϊ ValueErrorrΪappendrrΪrangeΪnpΪpiΪcpΪinverse)rrrΪqr_aΪqr_bΪqr_listΪqr_zΪcircuitΪqr_sumΪnum_sumΪqftΪjΪkΪlams Ϊm/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/synthesis/arithmetic/adders/draper_qft_adder.pyΪ adder_qft_d00r's;€πd ˆvƒ~άΠ[Σ\Π\ΰ˜!ΣάΠCΣDΠDδ Π+°#Ρ 6€Dά Π+°#Ρ 6€DΨˆl€Gΰ ˆvƒ~ά˜q vΡ.ˆΨ‰tΤτ˜gΠ&€Gπ ›ˆT‘!‰W¨T±!¨W°tΉA°wΡ->€FΨ"&¨'£/ΡΠ7GΘ!Ρ7K€Gτ 'Σ €CΨ ‡NN3™q˜ Τ"δ Π#Φ $ˆάw‘{Φ#ˆAά—%‘%˜1˜a™4‘.ˆCπ J‰Js ™G V°!©e¨HΡ%5Φ 6σ $ρ%π ‡NN3—;‘;¨;Π3°VΉA°YΤ?ΰ €Nσ)rF) Ϊ__doc__ΪnumpyrΪqiskit.circuit.quantumcircuitrΪqiskit.circuitrΪ#qiskit.circuit.library.basis_changerΪintΪstrΪboolr'©r(r&Ϊr2sGπρ8γε8έ*έ7πBGρUΨπUΨ!$πUΨ:>πUΰφUr(