+ iRt^RIt^RIt^RIHt^RIHt^RIHt^RI H t ^RI H t ^RI Ht^RIHt^R IHt^R IHtHt^R IHt^R IHt^R IHt!RR]4t!RR]4tRtRt Rt!Rt"R#)zShor's algorithm and helper functions. Todo: * Get the CMod gate working again using the new Gate API. * Fix everything. * Update docstrings and reformat. N)Mul)S)log)sqrt)igcd)continued_fraction_periodic) variations)Gate)Qubitmeasure_partial_oneshot)qapply)QFT) QuantumErrorc]tRt^tRtR#)OrderFindingExceptionN)__name__ __module__ __qualname____firstlineno____static_attributes__rX/var/www/html/photoedit/myenv/lib/python3.14/site-packages/sympy/physics/quantum/shor.pyrrsrrcja]tRt^ toRt]R4t]R4t]R4t ]R4t Rt Rt Vt R#) CModzA controlled mod gate. This is black box controlled Mod function for use by shor's algorithm. TODO: implement a decompose property that returns how to do this in terms of elementary gates c\R4h)z%The CMod gate has not been completed.)NotImplementedError)clsargss&&r _eval_argsCMod._eval_args(s ""IJJrc (VP^,#)z4Size of 1/2 input register. First 1/2 holds output.labelselfs&rtCMod.t/zz!}rc (VP^,#)z$Base of the controlled mod function.r"r$s&raCMod.a4r(rc (VP^,#)z1N is the type of modular arithmetic we are doing.r"r$s&rNCMod.N9r(rc ^p^p\VP4F2pWCWPV,,,, pV^,pK4 \VPV,VP,4p\ VP ^,RVP4p\\VP44F!pVPWe, ^,4K# \V!#)z This directly calculates the controlled mod of the second half of the register and puts it in the second This will look pretty when we get Tensor Symbolically working N) ranger&intr*r-listrreversedappendr )r%qubitsoptionsnkioutoutarrays&&, r_apply_operator_QubitCMod._apply_operator_Qubit>s  tvvA 6&&1*%% %A FA $&&!)dff$% Aw/0%-(A OOSXN +)hrrN)rrrr__doc__ classmethodrpropertyr&r*r-r<r__classdictcell__) __classdict__s@rrr sfKK   rrcL\P!V^, 4^,p\W4^8wd \W4#\W4pV^,^8Xd \ V4\W^, ,^, V4\W^, ,^,V43pV#)aThis function implements Shor's factoring algorithm on the Integer N The algorithm starts by picking a random number (a) and seeing if it is coprime with N. If it is not, then the gcd of the two numbers is a factor and we are done. Otherwise, it begins the period_finding subroutine which finds the period of a in modulo N arithmetic. This period, if even, can be used to calculate factors by taking a**(r/2)-1 and a**(r/2)+1. These values are returned. )random randranger period_findshor)r-r*ranswers& rrGrGXs Q!#A AzQAzAA1uz Q1s8a<#T!c(Q,%: ;F Mrc2\W4p\W24pV#)N)continued_fractionratioize)xyr-fractiontotals&&& rgetrrQls!!'H X !E LrcV^,V8d\P#\V4^8Xd V^,#V^,\VR,V4,#):NN)rZerolenrL)r2r-s&&rrLrLssD Aw{vv  4yA~Aw 7Xd2h* **rc jRp\^\P!\V^44,4p\ V4Uu.uFp^NK pp^\ ^V,4, p^p\ \ ^4VRR7F%p\V4V,p V\V !,pK' Wg,P4p \W0V4V ,p \V 4p \ V4Fp \W4p K \\W3^,4P4V ,RR7p \ V4Fp \WV,4p K \V \4'dT p MN\V \ 4'dV P"R,p M$V P"R,P"R,p ^p ^p\ \%V 4^, 4F(p WWV,,,, pV ^,p K* V^8Xd\'RV,4h\)V^V,V4pV#uupi)aFinds the period of a in modulo N arithmetic This is quantum part of Shor's algorithm. It takes two registers, puts first in superposition of states with Hadamards so: ``|k>|0>`` with k being all possible choices. It then does a controlled mod and a QFT to determine the order of a. g?T) repetition) floatingPointz/Order finder returned 0. Happens with chance %f)r1mathceilrr0rrr2r expandrr r r decompose isinstancerrrVrrQ)r*r-epsilonr&rMstartfactorr5arr qbitArraycircuitr9registerr7rIgs&& rrFrF{sG AdiiAq " "#Aa !1QE ! tAqDz\F F%(A$7I% %++8}$$&G1mG#GWoG 1X)'5SaC[**,W4DIG 1X)'q59'5!! GS ! !<<#<<#((, A F 3x=? #HUO## F${# = GI I VQT1A HM "s H0)#r>r[rDsympy.core.mulrsympy.core.singletonr&sympy.functions.elementary.exponentialr(sympy.functions.elementary.miscellaneousrsympy.core.intfuncr sympy.ntheoryrrKsympy.utilities.iterablesrsympy.physics.quantum.gater sympy.physics.quantum.qubitr r sympy.physics.quantum.qapplyr sympy.physics.quantum.qftr sympy.physics.quantum.qexprrrrrGrQrLrFrrrrtsc "69#K0+F/)4 L 5 45 p(+2 r