\hSrSSKrSSKrSSKJr SSKJr SSKJr SSK J r SSK J r SSK Jr SS KJr SS KJr SS KJrJr SS KJr SS KJr SSKJr "SS\5r"SS\5rSrSr Sr!Sr"g)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\rSrSrSrg)OrderFindingExceptionN)__name__ __module__ __qualname____firstlineno____static_attributes__rR/var/www/auris/envauris/lib/python3.13/site-packages/sympy/physics/quantum/shor.pyrrsrrc^\rSrSrSr\S5r\S5r\S5r \S5r Sr Sr g ) CMod zA 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[S5e)Nz%The CMod gate has not been completed.)NotImplementedError)clsargss r _eval_argsCMod._eval_args(s ""IJJrc URS$)z4Size of 1/2 input register. First 1/2 holds output.rlabelselfs rtCMod.t/zz!}rc URS$)z$Base of the controlled mod function.r%r's raCMod.a4r+rc URS$)z1N is the type of modular arithmetic we are doing.r%r's rNCMod.N9r+rc SnSn[UR5HnXCXRU--- nUS-nM [URU-UR-5n[ UR SSUR5n[[UR55HnURXe- S-5 M [U6$)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 r-rr1N) ranger)intr.r2listr!reversedappendr )r(qubitsoptionsnkioutoutarrays r_apply_operator_QubitCMod._apply_operator_Qubit>s  tvvA 6&&1*%% %A FA $&&!)dff$% Aw/0%-(A OOSXN +)hrrN) rrrr__doc__ classmethodr"propertyr)r.r2rArrrrrr s^KK  rrc[R"US- 5S-n[X5S:wa [X5$[X5nUS-S:Xa [ U5 [XS- -S- U5[XS- -S-U54nU$)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. r1r-)random randranger period_findshor)r2r.ranswers rrJrJXs Q!#A AzQAzAA1uz Q1s8a<#T!c(Q,%: ;F Mrc2[X5n[X25nU$)N)continued_fractionratioize)xyr2fractiontotals rgetrrTls!!'H X !E LrcUSU:a[R$[U5S:XaUS$US[USSU5-$)Nrr-)rZerolenrO)r7r2s rrOrOssF Aw{vv  4yA~Aw 7Xd12h* **rc Sn[S[R"[US55-5n[ U5Vs/sHnSPM nnS[ SU-5- nSn[ [ S5USS9Hn[U5U-n U[U 6-nM Xg-R5n [X0U5U -n [U 5n [ U5Hn [X5n M [[X3S-5R5U -SS9n [ U5Hn [XU-5n M [U [5(aU n OA[U [ 5(aU R"Sn OU R"SR"Sn Sn Sn[ [%U 5S- 5Hn XXU--- nU S-n M US:Xa['S U-5e[)USU-U5nU$s snf) 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?r1rr-T) repetition) floatingPointz/Order finder returned 0. Happens with chance %f)r6mathceilrr5rr r7r expandrr r r decompose isinstancerr!rWrrT)r.r2epsilonr)rPstartfactorr:arr qbitArraycircuitr>registerr<rLgs rrIrI{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 G)#rCr\rGsympy.core.mulrsympy.core.singletonr&sympy.functions.elementary.exponentialr(sympy.functions.elementary.miscellaneousrsympy.core.intfuncr sympy.ntheoryrrNsympy.utilities.iterablesr sympy.physics.quantum.gater sympy.physics.quantum.qubitr r sympy.physics.quantum.qapplyr sympy.physics.quantum.qftrsympy.physics.quantum.qexprrrrrJrTrOrIrrrrusc "69#K0+F/)4 L 5 45 p(+2 r