ó ¡¼™\c@ sddZddlmZmZddlmZmZmZmZm Z m Z m Z ddl m Z ddlmZddlmZddlmZmZddlmZdd lmZdd lmZmZmZmZmZmZm Z m!Z!d d d dgZ"d efd„ƒYZ#e#Z$defd„ƒYZ%d e%fd„ƒYZ&d e%fd„ƒYZ'dS(stAn implementation of qubits and gates acting on them. Todo: * Update docstrings. * Update tests. * Implement apply using decompose. * Implement represent using decompose or something smarter. For this to work we first have to implement represent for SWAP. * Decide if we want upper index to be inclusive in the constructor. * Fix the printing of Rk gates in plotting. iÿÿÿÿ(tprint_functiontdivision(tExprtMatrixtexptItpitIntegertSymbol(trange(tsqrt(tqapply(t QuantumErrortQExpr(teye(tmatrix_tensor_product(tGatet HadamardGatetSwapGatet OneQubitGatetCGatet PhaseGatetTGatetZGatetQFTtIQFTtRkGatetRkcB skeZdZdZdZd„Zed„ƒZed„ƒZ ed„ƒZ ed„ƒZ dd „Z RS( s This is the R_k gate of the QTF.uRkuRcG s²t|ƒdkr%td|ƒ‚n|d}|d}|dkrOt|ƒS|dkret|ƒS|dkr{t|ƒS|j|ƒ}tj||Œ}|j|ƒ|_ |S(Nis)Rk gates only take two arguments, got: %riii( tlenR RRRt _eval_argsRt__new__t_eval_hilbert_spacet hilbert_space(tclstargsttargettktinst((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyR.s        cC s tj|ƒS(N(R R(R!R"((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyRCscC s |jdS(Ni(tlabel(tself((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyR$IscC s |jd S(Ni(R&(R'((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyttargetsMscC sd|jt|jƒfS(Ns$%s_%s$(tgate_name_latextstrR$(R'((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pytgate_name_plotQstsympycC sa|dkrMtddgdttdƒtttdƒ|jƒggƒStd|ƒ‚dS(NR,iiis#Invalid format for the R_k gate: %r(RRRRRR$tNotImplementedError(R'tformat((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pytget_target_matrixUs A( t__name__t __module__t__doc__t gate_nameR)Rt classmethodRtpropertyR$R(R+R/(((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyR)s tFouriercB skeZdZed„ƒZd„Zd„Zed„ƒZed„ƒZ ed„ƒZ ed„ƒZ RS(s@Superclass of Quantum Fourier and Inverse Quantum Fourier Gates.cC sUt|ƒdkr%td|ƒ‚n|d|dkrHtdƒ‚ntj|ƒS(Nis*QFT/IQFT only takes two arguments, got: %riis!Start must be smaller than finish(RR RR(R'R"((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyRbs cK s|jd|S(N(t_represent_ZGatetNone(R'toptions((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyt_represent_default_basislsc K s'|jddƒ}|dkr-tdƒ‚n||jkrOtd|ƒ‚n|j}|j}gt|ƒD];}gt|ƒD]"}||||t|ƒ^q^qn}t|ƒ} |jddkrñt t d|jdƒ| ƒ} n|j|kr#t | t d||jƒƒ} n| S(s: Represents the (I)QFT In the Z Basis tnqubitsis.The number of qubits must be given as nqubits.s2The number of qubits %r is too small for the gate.i( tgetR t min_qubitstsizetomegaR R RR&RR( R'tbasisR9R;R>R?tjtitarrayFTtmatrixFT((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyR7os$    K # cC st|jd|jdƒS(Nii(R R&(R'((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyR(ŒscC s |jdS(Ni(R&(R'((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyR=scC sd|jd|jdS(s"Size is the size of the QFT matrixiii(R&(R'((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyR>”scC s tdƒS(NR?(R(R'((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyR?™s( R0R1R2R4RR:R7R5R(R=R>R?(((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyR6_s  cB sDeZdZdZdZd„Zd„Zd„Zed„ƒZ RS(s&The forward quantum Fourier transform.uQFTcC sÕ|jd}|jd}d}xptt||ƒƒD]Y}t|ƒ|}x@t||ƒD].}t||dt||dƒƒ|}q]Wq6Wx;t||dƒD]%}t||||dƒ|}q¨W|S(s%Decomposes QFT into elementary gates.iii(R&treversedR RRRR(R'tstarttfinishtcircuittlevelRB((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyt decompose¤s  0#cK st|jƒ|ƒS(N(R RJ(R'tqubitsR9((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyt_apply_operator_Qubit±scC s t|jŒS(N(RR"(R'((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyt _eval_inverse´scC stdtt|jƒS(Ni(RRRR>(R'((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyR?·s( R0R1R2R3R)RJRLRMR5R?(((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyRžs  cB s;eZdZdZdZd„Zd„Zed„ƒZRS(s&The inverse quantum Fourier transform.uIQFTu {QFT^{-1}}cC sÖ|jd}|jd}d}x;t||dƒD]%}t||||dƒ|}q5Wxqt||ƒD]`}xGtt||ƒƒD]/}t||dt|| dƒƒ|}q‹Wt|ƒ|}qnW|S(s&Decomposes IQFT into elementary gates.iii(R"R RRERRR(R'RFRGRHRBRI((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyRJÂs  #-cC s t|jŒS(N(RR"(R'((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyRMÏscC stdtt|jƒS(Niþÿÿÿ(RRRR>(R'((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyR?Òs( R0R1R2R3R)RJRMR5R?(((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyR¼s  N((R2t __future__RRR,RRRRRRRtsympy.core.compatibilityR tsympy.functionsR tsympy.physics.quantum.qapplyR tsympy.physics.quantum.qexprR R tsympy.matricesRt#sympy.physics.quantum.tensorproductRtsympy.physics.quantum.gateRRRRRRRRt__all__RRR6RR(((s8lib/python2.7/site-packages/sympy/physics/quantum/qft.pyt s$4: 3?