z i 1SrSSKJr SSKJr SSKJrJrJr SSK J r SSK J r Sr S rS r"S S \ 5r"S S\5rg)z(Polynomially controlled Pauli-rotations.) annotations)product)QuantumRegisterQuantumCircuitGate) CircuitError)FunctionalPauliRotationscSU4SUS4S0nSn[SUS-S-5H!nX U- S--U-nU=XX- 4'XU- U4'M# U$)zReturn a dictionary of binomial coefficients Based-on/forked from sympy's binomial_coefficients() function [#] .. [#] https://github.com/sympy/sympy/blob/sympy-1.5.1/sympy/ntheory/multinomial.py rr )range)ndatatempks v/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/circuit/library/arithmetic/polynomial_pauli_rotations.py_binomial_coefficientsrspFA1vq !D D 1a1fqj !A "q(*..X!eQh" Kc ## USU-:dUS:Xa*[X5nUR5H up4X44v M g[X5n0nUR5Hup4XE[[SU55'M UnU/S/US- --n[U5n[[SU55nXrU4v U(aSn OUn XS- :a|Xin U (aSXi'XS'U S:aXiS-==S- ss'Sn OU S- n Xi==S- ss'US==S-ss'[U5n[[SU55nXrU4v XS- :aM{gg7f)zReturn an iterator of multinomial coefficients Based-on/forked from sympy's multinomial_coefficients_iterator() function [#] .. [#] https://github.com/sympy/sympy/blob/sympy-1.5.1/sympy/ntheory/multinomial.py r r Nr)_multinomial_coefficientsitemstuplefilter) mr coefficientskeyvaluecoefficients_dictrtemp_abjtemp_js r_large_coefficients_iterr#*sY 1q5yAF06 &,,.JC, /16 &,,.JC:?eF4$56 7/( saSAE]"t &v& 'A'' AAa%iWF QzU q Q1  GqLG4[FfT6*+A?+ +!a%is D;E?EcU(d U(a0$SS0$US:Xa [U5$USU-:aUS:a[[X55$U(aSnOUnU/S/US- --n[U5S0nX S- :aX2nU(aSX2'XSS'US:aX2S-==S- ss'SnSnSnO$US- nUS-nU[U5nX2==S- ss'[ X`5H6nX8(dMX8==S-ss'Xt[U5- nX8==S- ss'M8 US==S-ss'Xu-XS- -U[U5'X S- :aMU$)zReturn an iterator of multinomial coefficients Based-on/forked from sympy's multinomial_coefficients() function [#] .. [#] https://github.com/sympy/sympy/blob/sympy-1.5.1/sympy/ntheory/multinomial.py r r r)rdictr#rr ) rrr!rresr"startvrs rrrXsg IAwAv%a((AEza!e,Q233   3!A D ; C !e) DGG A: QK1 KAEA FAEEE$K A GqLGuAww1 t%%1  ! Q1 JAQK8E$K+ !e), Jrc^\rSrSrSrS S U4Sjjjr\S Sj5r\RSSj5r\SSj5r Sr SSSjjr U4S jr S r U=r$)PolynomialPauliRotationsaA circuit implementing polynomial Pauli rotations. For a polynomial :math:`p(x)`, a basis state :math:`|i\rangle` and a target qubit :math:`|0\rangle` this operator acts as: .. math:: |i\rangle |0\rangle \mapsto \cos\left(\frac{p(i)}{2}\right) |i\rangle |0\rangle + \sin\left(\frac{p(i)}{2}\right) |i\rangle |1\rangle Let n be the number of qubits representing the state, d the degree of p(x) and q_i the qubits, where q_0 is the least significant qubit. Then for .. math:: x = \sum_{i=0}^{n-1} 2^i q_i, we can write .. math:: p(x) = \sum_{j=0}^{j=d} c_j x^j where :math:`c` are the input coefficients, ``coeffs``. cF>U=(d SS/Ul[TU] XUS9 g)a1 Args: num_state_qubits: The number of qubits representing the state. coeffs: The coefficients of the polynomial. ``coeffs[i]`` is the coefficient of the i-th power of x. Defaults to linear: [0, 1]. basis: The type of Pauli rotation ('X', 'Y', 'Z'). name: The name of the circuit. rr )num_state_qubitsbasisnameN)_coeffssuper__init__)selfr.coeffsr/r0 __class__s rr3!PolynomialPauliRotations.__init__s* '!Q  *:dSrcUR$)aThe coefficients of the polynomial. ``coeffs[i]`` is the coefficient of the i-th power of the function input :math:`x`, that means that the rotation angles are based on the coefficients value, following the formula .. math:: c_j x^j , j=0, ..., d where :math:`d` is the degree of the polynomial :math:`p(x)` and :math:`c` are the coefficients ``coeffs``. Returns: The coefficients of the polynomial. )r1r4s rr5PolynomialPauliRotations.coeffss$||rc0UR5 Xlg)zSet the coefficients of the polynomial. ``coeffs[i]`` is the coefficient of the i-th power of x. Args: The coefficients of the polynomial. N) _invalidater1)r4r5s rr5r:s  rcVUR(a[UR5S- $g)zReturn the degree of the polynomial, equals to the number of coefficients minus 1. Returns: The degree of the polynomial. If the coefficients have not been set, return 0. r r)r5lenr9s rdegreePolynomialPauliRotations.degrees" ;;t{{#a' 'rcRUb[USS9n[SSS9nX#/Ulg/Ulg)zReset the registers.Nstate)r0r target)rqregs)r4r.qr_state qr_targets r_reset_registers)PolynomialPauliRotations._reset_registerss2  '&'7gFH'9I".DJDJrcSnURcSnU(a [S5eURURS-:a%SnU(a[SURS-S35eU$)z,Check if the current configuration is valid.TFz&The number of qubits has not been set.r z0Not enough qubits in the circuit, need at least .)r.AttributeError num_qubitsr)r4raise_on_failurevalids r_check_configuration-PolynomialPauliRotations._check_configurationsu  (E$%MNN ??T22Q6 6E"F,,q014  rc>UR(ag[TU] 5 [URUR UR 5nURXR5 g)z(If not already built, build the circuit.N) _is_builtr2_buildPolynomialPauliRotationsGater.r5r/appendqubits)r4gater6s rrSPolynomialPauliRotations._buildsF >>  +D,A,A4;;PTPZPZ[ D++&r)r1rD)NNYpoly) r.z int | Noner5list[float] | Noner/strr0r\returnNone)r] list[float])r5r_r]r^)r]int)T)rMboolr]ra)__name__ __module__ __qualname____firstlineno____doc__r3propertyr5setterr?rGrOrS__static_attributes__ __classcell__r6s@rr+r+s8(,%) T$T#T T  T  TT*& ]]   &''rr+c\^\rSrSrSrSSU4SjjjrSrS SjrSrU=r $) rTi a~A gate implementing polynomial Pauli rotations. For a polynomial :math:`p(x)`, a basis state :math:`|i\rangle` and a target qubit :math:`|0\rangle` this operator acts as: .. math:: |i\rangle |0\rangle \mapsto \cos\left(\frac{p(i)}{2}\right) |i\rangle |0\rangle + \sin\left(\frac{p(i)}{2}\right) |i\rangle |1\rangle Let n be the number of qubits representing the state, d the degree of p(x) and q_i the qubits, where q_0 is the least significant qubit. Then for .. math:: x = \sum_{i=0}^{n-1} 2^i q_i, we can write .. math:: p(x) = \sum_{j=0}^{j=d} c_j x^j where :math:`c` are the input coefficients, ``coeffs``. cz>U=(d SS/UlUR5Ul[TU]SUS-/US9 g)a~Prepare an approximation to a state with amplitudes specified by a polynomial. Args: num_state_qubits: The number of qubits representing the state. coeffs: The coefficients of the polynomial. ``coeffs[i]`` is the coefficient of the i-th power of x. Defaults to linear: [0, 1]. basis: The type of Pauli rotation ('X', 'Y', 'Z'). label: A label for the gate. rr PolyPauli)labelN)r5lowerr/r2r3)r4r.r5r/ror6s rr3%PolynomialPauliRotationsGate.__init__%s> &A [[]  &6&:BeLrc[UR5nURSURS- nURSnUR5nURS:Xa UR UR SU5 OOURS:Xa URUR SU5 OURUR SU5 UGH&n/n[U5H"upxXWS:dMURX'5 M$ [U5S:abURS:XaURXEXc5 MlURS:XaURXEXc5 MURXEXc5 M[U5S:XdMURS:XaURXEUSU5 MURS:XaUR!XEUSU5 GMUR#XEUSU5 GM) Xlg)Nr xry)rrLrV_get_rotation_coefficientsr/rxr5ryrz enumeraterUr>mcrxmcrymcrzcrxcrycrz definition) r4circuitrErFrotation_coeffsc qr_controli_s r_define$PolynomialPauliRotationsGate._define9s 1>>"7DOOa$78NN2& 99; ::  JJt{{1~y 1 ZZ3  JJt{{1~y 1 JJt{{1~y 1 AJ!! 4!8%%hk2% :"::$LL!3ZKZZ3&LL!3ZKLL!3ZKZA%::$KK 2JqM9MZZ3&KK 2JqM9MKK 2JqM9M+!."rcURS- n[UR5S- n[[ SS/US95n/nUH$nS[ U5s=:aU::dMO MXE/- nM& UVs0sHofS_M nn[ URSS5HqupUS- n[X5R5HJupSnSn [ U 5H!upUS:aUS- nU SX---n MUS - nM# Xv==X-U -- ss'ML Ms U$s snf) zCompute the coefficient of each monomial. Returns: A dictionary with pairs ``{control_state: rotation angle}`` where ``control_state`` is a tuple of ``0`` or ``1`` bits. r r)repeatgNr%)r r )r) rLr>r5listrsumrzrr)r4r.r?all_combinationsvalid_combinations combination control_staterrcoeffcomb num_combspowerr!qubits rrv7PolynomialPauliRotationsGate._get_rotation_coefficients`s: ??Q.T[[!A%A7G HI+K3{#-v--"m3",DVVCU-#-CUV"$++ab/2HA FA$==M#Q#W#W#Y13  )$HAqy%- qy!11%- !0 .%2Ce2KK.$Z 3")Ws- D )r/r5r)NrYN) r.r`r5r[r/r\roz str | Noner]r^)r]zdict[tuple[int, ...], float]) rbrcrdrerfr3rrvrirjrks@rrTrT sd:&* MM#M M  M  MM(%"N$$rrTN)rf __future__r itertoolsrqiskit.circuitrrrqiskit.circuit.exceptionsrfunctional_pauli_rotationsr rr#rr+rTr%rrrsK/"@@2@  +,\+\A'7A'Hz4zr