1. Code, python3.7:

import numpy as np import math import matplotlib.pyplot as plt import time import colorsys import cmath size=1000  def run_classical_randwalk(itersteps,initsim_mat):     simmat=initsim_mat     for iterstep in range(itersteps):         newsimmat=np.zeros((2*size+1,2), dtype=complex)         for matindex in range(2*size+1):             to_right=0.5*simmat[matindex][0]             to_left=0.5*simmat[matindex][0]             if(matindex-1>=0):                 newsimmat[matindex-1][0]+=to_left             if(matindex+1<=2*size):                 newsimmat[matindex+1][0]+=to_right         simmat=newsimmat      psisquared=np.zeros(2*size+1)     for matindex in range(2*size+1):         psisquared[matindex]+=abs(newsimmat[matindex][0])      average_x=0     min_x=0     max_x=0     datastartflag=0     for matindex in range(2*size+1):         if(datastartflag==0):             min_x=matindex         if(psisquared[matindex]>0):             datastartflag=1             max_x=matindex         average_x+=psisquared[matindex]*(matindex-(size+1))     print(f"validdatarange {max_x-min_x}")     return(range(min_x-(size+1),max_x-size,2),psisquared[min_x:max_x+1:2],average_x)  def run_quantum_randwalk(itersteps,initsim_mat):     simmat=initsim_mat     for iterstep in range(itersteps):         newsimmat=np.zeros((2*size+1,2), dtype=complex)         for matindex in range(2*size+1):             hadamard_spinup=1/math.sqrt(2)*(simmat[matindex][0]+simmat[matindex][1])             hadamard_spindown=1/math.sqrt(2)*(simmat[matindex][0]-simmat[matindex][1])             if(matindex-1>=0):                 newsimmat[matindex-1][1]+=hadamard_spindown             if(matindex+1<=2*size):                 newsimmat[matindex+1][0]+=hadamard_spinup         simmat=newsimmat      psisquared=np.zeros(2*size+1)     for matindex in range(2*size+1):         psisquared[matindex]+=abs(newsimmat[matindex][0])**2+abs(newsimmat[matindex][1])**2      average_x=0     min_x=0     max_x=0     datastartflag=0     for matindex in range(2*size+1):         if(datastartflag==0):             min_x=matindex         if(psisquared[matindex]>0):             datastartflag=1             max_x=matindex         average_x+=psisquared[matindex]*(matindex-(size+1))     print(f"validdatarange {max_x-min_x}")     return(range(min_x-(size+1),max_x-size,2),psisquared[min_x:max_x+1:2],average_x)  simmat=np.zeros((2*size+1,2), dtype=complex) #(-size, ....,-1,0,1, size) #first index spin up, second index spin down simmat[size+1][0]=1.0 simmat[size+1][1]=0.0#1.0#1.0j  fig=plt.figure() plt.xlabel("position") plt.ylabel("probability of occurence") q_list_return_50=run_quantum_randwalk(50,simmat) c_list_return_50=run_classical_randwalk(50,simmat) plt.plot(q_list_return_50[0],q_list_return_50[1],color="#e67300") plt.plot(c_list_return_50[0],c_list_return_50[1],color="#0000a0") xlim=plt.gca().get_xlim() ylim=plt.gca().get_ylim() plt.vlines(q_list_return_50[2],*ylim,color="#e67300",alpha=.7) plt.vlines(c_list_return_50[2],*ylim,color="#0000a0",alpha=.7) print(fig.axes) plt.gca().spines['top'].set_visible(False) plt.gca().spines['right'].set_visible(False) plt.gca().grid(color='grey', linestyle='-', linewidth=0.25, alpha=0.5) plt.show() fig.savefig("One_dimensional_quantum_random_walk.svg") 

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