o GZh@sdZddlZddlZddlmZddlmZddlmZddl m Z ddl m Z ddl mZdd lmZdd lmZdd lmZmZdd lmZdd lmZddlmZGdddeZGdddeZddZddZ ddZ!ddZ"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) QuantumErrorc@s eZdZdS)OrderFindingExceptionN)__name__ __module__ __qualname__rrI/var/www/auris/lib/python3.10/site-packages/sympy/physics/quantum/shor.pyrsrc@sHeZdZdZeddZeddZeddZedd Z d d Z d S) 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 cCstd)Nz%The CMod gate has not been completed.)NotImplementedError)clsargsrrr _eval_args(szCMod._eval_argscC |jdS)z4Size of 1/2 input register. First 1/2 holds output.rlabelselfrrrt/ zCMod.tcCr)z$Base of the controlled mod function.rrrrra4r zCMod.acCr)z1N is the type of modular arithmetic we are doing.rrrrrN9r zCMod.NcKsd}d}t|jD]}||||j|7}|d9}q t|j||j}t|jdd|j}tt|jD] }|||?d@q8t |S)z This directly calculates the controlled mod of the second half of the register and puts it in the second This will look pretty when we get Tensor Symbolically working r!rr#N) rangerintr"r$listrreversedappendr )rqubitsoptionsnkioutZoutarrayrrr_apply_operator_Qubit>s zCMod._apply_operator_QubitN) rrr__doc__ classmethodrpropertyrr"r$r0rrrrr s     rcCsxt|dd}t||dkrt||St||}|ddkr$t|t||dd|t||dd|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$r"ranswerrrrr7Xs    ,r7cCst||}t||}|S)N)continued_fractionratioize)xyr$fractiontotalrrrgetrls  r@cCs@|d|kr tjSt|dkr|dS|dt|dd|S)Nrr!)rZZerolenr;)r'r$rrrr;ss  r;cCsd}tdtt|d}ddt|D}dtd|}d}ttd|ddD]}t||}|t|}q*|| } t |||| } t | } t|D]} t | | } qOt t ||d| dd } t|D] } t | | |} qjt| tr|| } nt| tr| jd } n| jd jd } d} d} tt| dD]} | | | | |7} | d>} q| dkrtd |t| d||}|S) a0Finds the period of a in modulo N arithmetic This is quantum part of Shor's algorithm. It takes two registers, puts first in superposition of states with Hadamards so: ``|k>|0>`` with k being all possible choices. It then does a controlled mod and a QFT to determine the order of a. g?r#cSsg|]}dqS)rr).0r<rrr szperiod_find..r!rT)Z repetition)Z floatingPointz/Order finder returned 0. Happens with chance %f)r&mathceilrr%rrr'r expandrr r r Z decompose isinstancerrrArr@)r"r$epsilonrstartfactorr*ZarrZ qbitArrayZcircuitr.registerr,r9grrrr6{s@         r6)#r1rEr4Zsympy.core.mulrZsympy.core.singletonrZ&sympy.functions.elementary.exponentialrZ(sympy.functions.elementary.miscellaneousrZsympy.core.intfuncrZ sympy.ntheoryrr:Zsympy.utilities.iterablesrZsympy.physics.quantum.gater Zsympy.physics.quantum.qubitr r Zsympy.physics.quantum.qapplyr Zsympy.physics.quantum.qftr Zsympy.physics.quantum.qexprrrrr7r@r;r6rrrrs*            8