ó ¡¼™\c@ sJdZddlmZmZddlZddlZddlmZmZddlm Z m Z ddl m Z ddl mZddlmZdd lmZdd lmZdd lmZmZdd lmZdd lmZddlmZdefd„ƒYZdefd„ƒYZ d„Z!d„Z"d„Z#d„Z$dS(sêShor's algorithm and helper functions. Todo: * Get the CMod gate working again using the new Gate API. * Fix everything. * Update docstrings and reformat. * Remove print statements. We may want to think about a better API for this. iÿÿÿÿ(tprint_functiontdivisionN(tMultS(tlogtsqrt(tigcd(trange(tcontinued_fraction_periodic(t variations(tGate(tQubittmeasure_partial_oneshot(tqapply(tQFT(t QuantumErrortOrderFindingExceptioncB seZRS((t__name__t __module__(((s9lib/python2.7/site-packages/sympy/physics/quantum/shor.pyRstCModcB sSeZdZed„ƒZed„ƒZed„ƒZed„ƒZd„Z RS(sÌA controlled mod gate. This is black box controlled Mod function for use by shor's algorithm. TODO implement a decompose property that returns how to do this in terms of elementary gates cC stdƒ‚dS(Ns%The CMod gate has not been completed.(tNotImplementedError(tclstargs((s9lib/python2.7/site-packages/sympy/physics/quantum/shor.pyt _eval_args)scC s |jdS(s4Size of 1/2 input register. First 1/2 holds output.i(tlabel(tself((s9lib/python2.7/site-packages/sympy/physics/quantum/shor.pytt0scC s |jdS(s$Base of the controlled mod function.i(R(R((s9lib/python2.7/site-packages/sympy/physics/quantum/shor.pyta5scC s |jdS(s1N is the type of modular arithmetic we are doing.i(R(R((s9lib/python2.7/site-packages/sympy/physics/quantum/shor.pytN:scK s¼d}d}x:t|jƒD])}||||j|}|d}qWt|j||jƒ}t|jd|j ƒ}x2tt|jƒƒD]}|j||?d@ƒq“Wt |ŒS(sÔ 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 iii( RRtintRRtlistRtreversedtappendR (Rtqubitstoptionstntktitouttoutarray((s9lib/python2.7/site-packages/sympy/physics/quantum/shor.pyt_apply_operator_Qubit?s( RRt__doc__t classmethodRtpropertyRRRR((((s9lib/python2.7/site-packages/sympy/physics/quantum/shor.pyR!s cC sÚtj|dƒd}t||ƒdkrCtdƒt||ƒStd|ƒtd|ƒt||ƒ}td|ƒ|ddkr tdƒt|ƒnt||dd|ƒt||dd|ƒf}|S(sâThis 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 isn't, 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. iisgot lucky with randsa= sN= sr= sr is not even, begin again(trandomt randrangeRtprintt period_findtshor(RRtrtanswer((s9lib/python2.7/site-packages/sympy/physics/quantum/shor.pyR0Ys        6cC s"t||ƒ}t||ƒ}|S(N(tcontinued_fractiontratioize(txtyRtfractionttotal((s9lib/python2.7/site-packages/sympy/physics/quantum/shor.pytgetrrscC sJ|d|krtjSt|ƒdkr1|dS|dt|d|ƒS(Nii(RtZerotlenR4(RR((s9lib/python2.7/site-packages/sympy/physics/quantum/shor.pyR4ys cC sYd}tdtjt|dƒƒƒ}gt|ƒD] }d^q5}dtd|ƒ}d}x=ttdƒ|dtƒD] }||} |t| Œ}q}W||j ƒ} t |||ƒ| } t | ƒ} t dƒx#t|ƒD]} t | | ƒ} qêWt dƒt t||dƒjƒ| dtƒ} t d ƒx't|ƒD]} t | | |ƒ} qMWt | ƒt| tƒrŒ| } n3t| tƒr«| jd } n| jd jd } t | ƒd} d}x>tt| ƒdƒD]&} || | | |7}| d>} qìW|dkr5td |ƒ‚nt|d||ƒ}t |ƒ|S( s/Finds 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. gà?iiit repetitionscontrolled Mod'ds measured 1t floatingPointsQFT'diÿÿÿÿs/Order finder returned 0. Happens with chance %f(RtmathtceilRRRR tTrueR texpandRR R.R Rt decomposet isinstanceRRR;RR9(RRtepsilonRR5tstarttfactorR!tarrt qbitArraytcircuitR%tregisterR#R2tg((s9lib/python2.7/site-packages/sympy/physics/quantum/shor.pyR/sJ""    )      (%R)t __future__RRR>R,tsympyRRRRtsympy.core.numbersRtsympy.core.compatibilityRt sympy.ntheoryRR3tsympy.utilities.iterablesR tsympy.physics.quantum.gateR tsympy.physics.quantum.qubitR R tsympy.physics.quantum.qapplyR tsympy.physics.quantum.qftRtsympy.physics.quantum.qexprRRRR0R9R4R/(((s9lib/python2.7/site-packages/sympy/physics/quantum/shor.pyt s(  8