Práctica 1

%matplotlib inline #from IPython.display import display import matplotlib.pyplot as plt import numpy as np from numpy.linalg import eig from qutip import * plt.rcParams["figure.figsize"] = (12,9)

# Define the Phv measurement operator: MOpz= sigmaz() MOpx= sigmax() MOpy= sigmay()

ψ = ((2-1j)*basis(2,0)+(1-3j)*basis(2,1)).unit() ψ2=(basis(2,0)+basis(2,1)).unit() ψ3=basis(2,0)

def GenerateLabResults(N): state=((np.random.random()+1j*np.random.random())*basis(2,0)+(np.random.random())*basis(2,1)).unit() oper=[0.5*sigmax(), 0.5*sigmay(), 0.5*sigmaz()] data=[] for k in oper: eigenv1 = k.eigenstates()[1][0] eigenv2 = k.eigenstates()[1][1] allowed_results = k.eigenstates()[0] probability_amps = [qo.full()[0][0] for qo in [eigenv1.dag()*state, eigenv2.dag()*state]] pvals = [abs(pa.conjugate()*pa) for pa in probability_amps] dataK=np.random.choice(allowed_results,size=N, p=pvals) data.append(dataK) return data

datax,datay,dataz=GenerateLabResults(1000000) sx=datax.mean() sy=datay.mean() sz=dataz.mean()

print("Variance: ",datax.var()) print("Mean: ",datax.mean()) print(sx)

print("Variance: ",datay.var()) print("Mean: ",datay.mean())

print("Variance: ",dataz.var()) print("Mean: ",dataz.mean())

plt.hist(np.real(datax))

plt.hist(np.real(datay))

plt.hist(np.real(dataz))

from qutip.ipynbtools import version_table version_table()

alpha=np.sqrt(1/2+sz) beta=np.sqrt(1/2-sz) phicos=np.arccos(sx/(alpha*beta)) phisen=-np.arcsin(sy/(alpha*beta)) print("α =",alpha) print("β =",beta)

print("Φ =", phicos) print("Φ =", phisen)

Npoints=1000000 #datax #datay #dataz #para ver la tendencia vamos a calcular la media de los ppuntos para los primeros putnos Nmedidas=500 divisionsize=10 nresults=np.linspace(divisionsize, Nmedidas*divisionsize, Nmedidas) #calculo de la media de x Meanx=datax.mean() Varx=datax.var() dispmeanx=np.zeros(Nmedidas) for i in range(500): Nmean=int(nresults[i]) #second dispmeanx[i]=np.abs(datax[:Nmean].mean()-Meanx) #plt.ylin[0,0.03] plt.plot(nresults, dispmeanx, label='$X_n-\\mu_x$') #plt.plot(nresults, np.sqrt(Varx/nresults), label='$\sqrt{Var(x)/n}$') # me he quedado aqui, me faltan leyendas y ejes plt.xlabel('Numero de medidas') plt.ylabel('Error expected value') plt.legend(bbox_to_anchor=(1.05, 1), loc='upper left', borderaxespad=0.) #No es buena medida del error porque no conozco mu y me sale distinto en cada medida que hago

Npoints=1000000 Nmedidas=500 divisionsize=10 nresults=np.linspace(divisionsize, Nmedidas*divisionsize, Nmedidas) #calculo de la media de x Meanx=datax.mean() Varx=datax.var() dispmeanx=np.zeros(Nmedidas) errorx=np.zeros(Nmedidas) for i in range(len(nresults)): Nmean=int(nresults[i]) #second dispmeanx[i]=np.abs(datax[:Nmean].mean()-Meanx) Numeropaquetes=int(Npoints/Nmean) avmeanx=np.zeros(Numeropaquetes) for j in range(Numeropaquetes): avmeanx[j]=datax[j*Nmean:(j+1)*Nmean].mean() errorx[i]=np.sqrt(avmeanx.var()) plt.ylim(0,0.03) plt.plot(nresults, dispmeanx, label='$X_n-\\mu_x$') plt.plot(nresults,errorx,label='$Var(\overline{X}_n)$') plt.xlabel('Numero de medidas') plt.ylabel('Error expected value') plt.legend(bbox_to_anchor=(1.05, 1), loc='upper left', borderaxespad=0.)

Npoints=1000000 Nmedidas=500 divisionsize=10 nresults=np.linspace(divisionsize, Nmedidas*divisionsize, Nmedidas) #calculo de la media de x Meanx=datax.mean() Varx=datax.var() dispmeanx=np.zeros(Nmedidas) errorx=np.zeros(Nmedidas) for i in range(len(nresults)): Nmean=int(nresults[i]) #second dispmeanx[i]=np.abs(datax[:Nmean].mean()-Meanx) Numeropaquetes=int(Npoints/Nmean) avmeanx=np.zeros(Numeropaquetes) for j in range(Numeropaquetes): avmeanx[j]=datax[j*Nmean:(j+1)*Nmean].mean() errorx[i]=np.sqrt(avmeanx.var()) plt.ylim(0,0.03) plt.plot(nresults, dispmeanx, label='$X_n-\\mu_x$') plt.plot(nresults,errorx,label='$Var(\overline{X}_n)$') plt.plot(nresults,np.sqrt(Varx/nresults), label='$\sqrt{Var(\overline{X_N})/N)}$') plt.xlabel('Numero de medidas') plt.ylabel('Error expected value') plt.legend(bbox_to_anchor=(1.05, 1), loc='upper left', borderaxespad=0.)

#Función que devuelve el vector obtenido tras aplicar un operador sobre un vector. def vmedio(A,v): return expect(A,v) #Función que devuelve la incertidumbre asociada a un cierto operador ΔA def delta(A,v): return np.sqrt(np.abs(variance(A,v))) #Definición de los operadores y estados que nos da el enunciado Psi1=basis(2,1) Psi2=(0.236-0.471j)*basis(2,0)+(0.471-0.707j)*basis(2,0) Psi3=np.sqrt(1/2)*(basis(2,0)-basis(2,1)) A=sigmax() B=sigmay() Conm=-1j*(A*B-B*A) #Definición de una función que devuelve true si se verifica la desigualdad o false en caso contrario #en función de los operadores y estados que se le quiera transmitir. def comprobacion(deltaA,deltaB,Psi): if (deltaA*deltaB>=np.abs(1/2*vmedio(Conm,Psi))): return True else: return False print(comprobacion(delta(A,Psi1),delta(B,Psi1),Psi1)) print(comprobacion(delta(A,Psi2),delta(B,Psi2),Psi2)) print(comprobacion(delta(A,Psi3),delta(B,Psi3),Psi3))

plus=basis(2,0) print("ψ=",plus) print("Autovalor=",vmedio(sigmaz(),plus)) print("Δσz=",delta(sigmaz(),plus))