gdZddlZddlZddlmZddlmZddlmZddl m Z ddl m Z ddl mZdd lmZdd lmZdd lmZmZdd lmZdd lmZddlmZGddeZGddeZdZdZ dZ!dZ"dS)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) QuantumErrorceZdZdS)OrderFindingExceptionN)__name__ __module__ __qualname__V/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/physics/quantum/shor.pyrrsDrrcpeZdZdZedZedZedZedZ dZ dS)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 td)Nz%The CMod gate has not been completed.)NotImplementedError)clsargss r _eval_argszCMod._eval_args(s ""IJJJrc|jdS)z4Size of 1/2 input register. First 1/2 holds output.rlabelselfs rtzCMod.t/z!}rc|jdS)z$Base of the controlled mod function.r r"s razCMod.a4r%rc|jdS)z1N is the type of modular arithmetic we are doing.r r"s rNzCMod.N9r%rc d}d}t|jD]}||||j|zzz }|dz}t|j|z|jz}t |jdd|j}tt|jD]}|||z dzt|S)z This directly calculates the controlled mod of the second half of the register and puts it in the second This will look pretty when we get Tensor Symbolically working r'rr*N) ranger$intr(r+listrreversedappendr )r#qubitsoptionsnkioutoutarrays r_apply_operator_QubitzCMod._apply_operator_Qubit>s  tv  A 6$&1*%% %A FAA$&!)df$%% Aww/00%--(( , ,A OOSAXN + + + +hrN) rrr__doc__ classmethodrpropertyr$r(r+r9rrrrr sKK[K XXX     rrc6tj|dz dz}t||dkrt||St||}|dzdkrt |t||dz zdz |t||dz zdz|f}|S)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. r*r')random randranger period_findshor)r+r(ranswers rrArAXs Q!#A AqzzQAqzzAqA1uzz Q1qs8a<##T!ac(Q,%:%: ;F MrcFt||}t||}|S)N)continued_fractionratioize)xyr+fractiontotals rgetrrKls%!!Q''H Xq ! !E Lrc|d|kr tjSt|dkr|dS|dt|dd|zS)Nrr')rZerolenrF)r/r+s rrFrFssO Aw{{v  4yyA~~Aw 7Xd122h** **rc 4d}tdtjt|dz}dt |D}dt d|zz }d}t t d|dD] }t||z}|t|z}!||z } t|||| z} t| } t |D]} t| | } tt||dz| zd} t |D]} t| | |z} t| tr| } n;t| t r| jd } n| jd jd } d} d} t t%| dz D]} | | | | |zzz } | dz} | dkrt'd |zt)| d|z|}|S) a0Finds 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?r*cg|]}dS)rr).0rGs r zperiod_find..s ! ! !1Q ! ! !rr'rT) repetition) floatingPointz/Order finder returned 0. Happens with chance %f)r.mathceilrr-rr r/r expandrr r r decompose isinstancerrrNrrK)r(r+epsilonr$startfactorr2arr qbitArraycircuitr6registerr4rCgs rr@r@{s8G AdiAq "" "##A ! !a ! ! !E tAqDzz\F F%((A$777,,II% %++f}$$&&G1ammG#GWooG 1XX66)'155SAaC[[**,,W4DIIIG 1XX::)'1q599'5!!- GS ! !-<#<#(, A F 3x==? # #!HQUO## F {{# = GII I VQT1A Hr)#r:rVr>sympy.core.mulrsympy.core.singletonr&sympy.functions.elementary.exponentialr(sympy.functions.elementary.miscellaneousrsympy.core.intfuncr sympy.ntheoryrrEsympy.utilities.iterablesr sympy.physics.quantum.gater sympy.physics.quantum.qubitr r sympy.physics.quantum.qapplyr sympy.physics.quantum.qftrsympy.physics.quantum.qexprrrrrArKrFr@rrrros """"""666666999999######KKKKKK000000++++++FFFFFFFF//////))))))444444     L   5 5 5 5 5 45 5 5 p(+++2 2 2 2 2 r