U Zʹj@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__rrY/var/www/html/bwave/python/venv/lib/python3.8/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 cCs tddS)Nz%The CMod gate has not been completed.)NotImplementedError)clsargsrrr _eval_args(szCMod._eval_argscCs |jdS)z4Size of 1/2 input register. First 1/2 holds output.rlabelselfrrrt/szCMod.tcCs |jdS)z$Base of the controlled mod function.rrrrra4szCMod.acCs |jdS)z1N is the type of modular arithmetic we are doing.rrrrrN9szCMod.NcKsd}d}t|jD]"}||||j|7}|d9}qt|j||j}t|jdd|j}tt|jD]}|||?d@qpt |S)z This directly calculates the controlled mod of the second half of the register and puts it in the second This will look pretty when we get Tensor Symbolically working rrr!N) rangerintr r"listrreversedappendr )rqubitsoptionsnkioutZoutarrayrrr_apply_operator_Qubit>s zCMod._apply_operator_QubitN) rrr__doc__ classmethodrpropertyrr r"r.rrrrr s    rcCsxt|dd}t||dkr*t||St||}|ddkrHt|t||dd|t||dd|f}|S)aThis function implements Shor's factoring algorithm on the Integer N The algorithm starts by picking a random number (a) and seeing if it is coprime with N. If it is not, then the gcd of the two numbers is a factor and we are done. Otherwise, it begins the period_finding subroutine which finds the period of a in modulo N arithmetic. This period, if even, can be used to calculate factors by taking a**(r/2)-1 and a**(r/2)+1. These values are returned. r!r)random randranger period_findshor)r"r ranswerrrrr5Xs    ,r5cCst||}t||}|S)N)continued_fractionratioize)xyr"Zfractiontotalrrrgetrls  r=cCs@|d|krtjSt|dkr&|dS|dt|dd|S)Nrr)rZZerolenr9)r%r"rrrr9ss   r9cCsd}tdtt|d}ddt|D}dtd|}d}ttd|ddD]}t||}|t|}qT|| } t |||| } t | } t|D]} t | | } qt t ||d| dd } t|D]} t | | |} qt| tr| } n(t| tr| jd } n| jd jd } d} d} tt| dD]"} | | | | |7} | d>} q8| dkrrtd |t| d||}|S) a0Finds the period of a in modulo N arithmetic This is quantum part of Shor's algorithm. It takes two registers, puts first in superposition of states with Hadamards so: ``|k>|0>`` with k being all possible choices. It then does a controlled mod and a QFT to determine the order of a. g?r!cSsg|]}dqS)rr).0r:rrr szperiod_find..rrT)Z repetition)Z floatingPointz/Order finder returned 0. Happens with chance %f)r$mathceilrr#rrr%r expandrr r r Z decompose isinstancerrr>rr=)r r"epsilonrstartfactorr(ZarrZ qbitArrayZcircuitr,registerr*r7grrrr4{s@          r4)#r/rBr2Zsympy.core.mulrZsympy.core.singletonrZ&sympy.functions.elementary.exponentialrZ(sympy.functions.elementary.miscellaneousrZsympy.core.intfuncrZ sympy.ntheoryrr8Zsympy.utilities.iterablesrZsympy.physics.quantum.gater Zsympy.physics.quantum.qubitr r Zsympy.physics.quantum.qapplyr Zsympy.physics.quantum.qftr Zsympy.physics.quantum.qexprrrrr5r=r9r4rrrrs(            8