Lab04_Bell_GHZ_Circuit.ipynb

Kernel: Python 3

ラボ4 ベル回路とGHZ回路

前提条件
Ch.2.2 複数の量子ビットともつれ状態

その他の関連資料
回路チュートリアル：Qiskit入門

アプリケーション
Ch.3.11 量子テレポーテーション
Ch.3.12 超高密度符号化
Ch.3.13 量子鍵配送

# Importing standard Qiskit libraries
from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit
from qiskit import Aer, assemble
from qiskit.visualization import plot_histogram, plot_bloch_multivector, plot_state_qsphere, plot_state_city, plot_state_paulivec, plot_state_hinton

# Ignore warnings
import warnings
warnings.filterwarnings('ignore')

# Define backend
sim = Aer.get_backend('aer_simulator')

パート1：制御Xゲートを使用したベル状態

ゴール

CNOT、すなわち制御Xゲートを使用してベル状態を作成します。

def createBellStates(inp1, inp2):
    qc = QuantumCircuit(2)
    qc.reset(range(2))

    if inp1=='1':
        qc.x(0)
    if inp2=='1':
        qc.x(1)

    qc.barrier()

    qc.h(0)
    qc.cx(0,1)

    qc.save_statevector()
    qobj = assemble(qc)
    result = sim.run(qobj).result()
    state = result.get_statevector()

    return qc, state, result

print('Note: Since these qubits are in entangled state, their state cannot be written as two separate qubit states. This also means that we lose information when we try to plot our state on separate Bloch spheres as seen below.\n')

inp1 = 0
inp2 = 1

qc, state, result = createBellStates(inp1, inp2)

display(plot_bloch_multivector(state))

# Uncomment below code in order to explore other states
#for inp2 in ['0', '1']:
    #for inp1 in ['0', '1']:
        #qc, state, result = createBellStates(inp1, inp2)
        
        #print('For inputs',inp2,inp1,'Representation of Entangled States are:')
        
        # Uncomment any of the below functions to visualize the resulting quantum states
        
        # Draw the quantum circuit
        #display(qc.draw())

        # Plot states on QSphere
        #display(plot_state_qsphere(state))

        # Plot states on Bloch Multivector
        #display(plot_bloch_multivector(state))

        # Plot histogram
        #display(plot_histogram(result.get_counts()))
        
        # Plot state matrix like a city
        #display(plot_state_city(state))

        # Represent state matix using Pauli operators as the basis
        #display(plot_state_paulivec(state))

        # Plot state matrix as Hinton representation
        #display(plot_state_hinton(state))
        
        #print('\n')'''

注記：これらの量子ビットはエンタングル状態にあるため、それらの状態を2つの別個の量子ビット状態として書き込むことはできません。これは、以下に示すように、状態を別々のブロッホ球にプロットしようとすると情報が失われることも意味します。

入力状態	回路	QSphereプロット	ヒストグラム	シティプロット	パウリベクトル	ヒントンプロット
q0 = 0 q1 = 0
q0 = 1 q1 = 0
q0 = 0 q1 = 1
q0 = 1 q1 = 1

パート2：実機の量子デバイスでのベル状態

ゴール

実機の量子デバイスでベル状態回路を実行します。

from qiskit import IBMQ, execute
from qiskit.providers.ibmq import least_busy
from qiskit.tools import job_monitor

# Loading your IBM Quantum account(s)
provider = IBMQ.load_account()
backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= 2
                                    and not x.configuration().simulator
                                    and x.status().operational==True))

def createBSRealDevice(inp1, inp2):
    qr = QuantumRegister(2)
    cr = ClassicalRegister(2)
    qc = QuantumCircuit(qr, cr)
    qc.reset(range(2))

    if inp1 == 1:
        qc.x(0)
    if inp2 == 1:
        qc.x(1)

    qc.barrier()

    qc.h(0)
    qc.cx(0,1)
    
    qc.measure(qr, cr)

    job = execute(qc, backend=backend, shots=100)
    job_monitor(job)
    result = job.result()

    return qc, result

inp1 = 0
inp2 = 0
       
print('For inputs',inp2,inp1,'Representation of Entangled States are,')
        
#first results
qc, first_result = createBSRealDevice(inp1, inp2)
first_counts = first_result.get_counts()

# Draw the quantum circuit
display(qc.draw())

For inputs 0 0 Representation of Entangled States are,
Job Status: job has successfully run

#second results
qc, second_result = createBSRealDevice(inp1, inp2)
second_counts = second_result.get_counts()


# Plot results on histogram with legend
legend = ['First execution', 'Second execution']
plot_histogram([first_counts, second_counts], legend=legend)

Job Status: job has successfully run

パート3：3量子ビットGHZ回路

ゴール

3量子ビットのGHZ回路を作成し、状態を可視化します。

def ghzCircuit(inp1, inp2, inp3):
    
    qc = QuantumCircuit(3)
    qc.reset(range(3))
    
    if inp1 == 1:
        qc.x(0)
    if inp2 == 1:
        qc.x(1)
    if inp3 == 1:
        qc.x(2)
    
    qc.barrier()
    
    qc.h(0)
    qc.cx(0,1)
    qc.cx(0,2)
    
    qc.save_statevector()
    qobj = assemble(qc)
    result = sim.run(qobj).result()
    state = result.get_statevector()

    return qc, state, result

print('Note: Since these qubits are in entangled state, their state cannot be written as two separate qubit states. This also means that we lose information when we try to plot our state on separate Bloch spheres as seen below.\n')

inp1 = 0
inp2 = 1
inp3 = 1

qc, state, result = ghzCircuit(inp1, inp2, inp3)

display(plot_bloch_multivector(state))

# Uncomment below code in order to explore other states
#for inp3 in ['0','1']:
    #for inp2 in ['0','1']:
        #for inp1 in ['0','1']:
            #qc, state, result = ghzCircuit(inp1, inp2, inp3)

            #print('For inputs',inp3,inp2,inp1,'Representation of GHZ States are:')

            # Uncomment any of the below functions to visualize the resulting quantum states

            # Draw the quantum circuit
            #display(qc.draw())

            # Plot states on QSphere
            #display(plot_state_qsphere(state))

            # Plot states on Bloch Multivector
            #display(plot_bloch_multivector(state))

            # Plot histogram
            #display(plot_histogram(result.get_counts()))

            # Plot state matrix like a city
            #display(plot_state_city(state))

            # Represent state matix using Pauli operators as the basis
            #display(plot_state_paulivec(state))

            # Plot state matrix as Hinton representation
            #display(plot_state_hinton(state))

            #print('\n')

注記：これらの量子ビットはエンタングル状態にあるため、それらの状態を2つの別個の量子ビット状態として書き込むことはできません。これは、以下に示すように、状態を別々のブロッホ球にプロットしようとすると情報が失われることも意味します。

入力状態	回路	QSphereプロット	ヒストグラム	シティプロット	パウリベクトル	ヒントンプロット
q0 = 0; q1 = 0; q2 = 0
q0 = 1; q1 = 0; q2 = 0
q0 = 0; q1 = 1; q2 = 0
q0 = 1; q1 = 1; q2 = 0
q0 = 0; q1 = 0; q2 = 1
q0 = 1; q1 = 0; q2 = 1
q0 = 0; q1 = 1; q2 = 1
q0 = 1; q1 = 1; q2 = 1

パート4：5量子ビットGHZ回路

ゴール

5量子ビットのGHZ回路を作成し、状態を視覚化します。

def ghz5QCircuit(inp1, inp2, inp3, inp4, inp5):
    
    qc = QuantumCircuit(5)
    #qc.reset(range(5))
    
    if inp1 == 1:
        qc.x(0)
    if inp2 == 1:
        qc.x(1)
    if inp3 == 1:
        qc.x(2)
    if inp4 == 1:
        qc.x(3)
    if inp5 == 1:
        qc.x(4)
    
    qc.barrier()
    
    qc.h(0)
    qc.cx(0,1)
    qc.cx(0,2)
    qc.cx(0,3)
    qc.cx(0,4)
    
    qc.save_statevector()
    qobj = assemble(qc)
    result = sim.run(qobj).result()
    state = result.get_statevector()

    return qc, state, result

# Explore GHZ States for input 00010. Note: the input has been stated in little-endian format.
inp1 = 0
inp2 = 1
inp3 = 0
inp4 = 0
inp5 = 0

qc, state, result = ghz5QCircuit(inp1, inp2, inp3, inp4, inp5)

print('For inputs',inp5,inp4,inp3,inp2,inp1,'Representation of GHZ States are:')
display(plot_state_qsphere(state))
print('\n')

For inputs 0 0 0 1 0 Representation of GHZ States are:

# Explore GHZ States for input 11001. Note: the input has been stated in little-endian format.
inp1 = 1
inp2 = 0
inp3 = 0
inp4 = 1
inp5 = 1

qc, state, result = ghz5QCircuit(inp1, inp2, inp3, inp4, inp5)

print('For inputs',inp5,inp4,inp3,inp2,inp1,'Representation of GHZ States are:')
display(plot_state_qsphere(state))
print('\n')

# Explore GHZ States for input 01010. Note: the input has been stated in little-endian format.
inp1 = 0
inp2 = 1
inp3 = 0
inp4 = 1
inp5 = 0

qc, state, result = ghz5QCircuit(inp1, inp2, inp3, inp4, inp5)

print('For inputs',inp5,inp4,inp3,inp2,inp1,'Representation of GHZ States are:')
display(plot_state_qsphere(state))
print('\n')

# Uncomment below code in order to explore other states
#for inp5 in ['0','1']:
    #for inp4 in ['0','1']:
        #for inp3 in ['0','1']:
            #for inp2 in ['0','1']:
                #for inp1 in ['0','1']:
                    #qc, state, result = ghz5QCircuit(inp1, inp2, inp3, inp4, inp5)

                    #print('For inputs',inp5,inp4,inp3,inp2,inp1,'Representation of GHZ States are:')

                    # Uncomment any of the below functions to visualize the resulting quantum states

                    # Draw the quantum circuit
                    #display(qc.draw())

                    # Plot states on QSphere
                    #display(plot_state_qsphere(state))

                    # Plot states on Bloch Multivector
                    #display(plot_bloch_multivector(state))

                    # Plot histogram
                    #display(plot_histogram(result.get_counts()))

                    # Plot state matrix like a city
                    #display(plot_state_city(state))

                    # Represent state matix using Pauli operators as the basis
                    #display(plot_state_paulivec(state))

                    # Plot state matrix as Hinton representation
                    #display(plot_state_hinton(state))

                    #print('\n')

For inputs 1 1 0 0 1 Representation of GHZ States are:

パート5：実機の量子デバイス

ゴール

実機の量子デバイスで5量子ビットGHZ回路を実行します。

backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= 5
                                    and not x.configuration().simulator
                                    and x.status().operational==True))

def create5QGHZRealDevice(inp1, inp2, inp3, inp4, inp5):
    qr = QuantumRegister(5)
    cr = ClassicalRegister(5)
    qc = QuantumCircuit(qr, cr)
    qc.reset(range(5))

    if inp1=='1':
        qc.x(0)
    if inp2=='1':
        qc.x(1)
    if inp3=='1':
        qc.x(1)
    if inp4=='1':
        qc.x(1)
    if inp5=='1':
        qc.x(1)

    qc.barrier()

    qc.h(0)
    qc.cx(0,1)
    qc.cx(0,2)
    qc.cx(0,3)
    qc.cx(0,4)
    
    qc.measure(qr, cr)

    job = execute(qc, backend=backend, shots=1000)
    job_monitor(job)
    result = job.result()

    return qc, result

inp1 = 0
inp2 = 0
inp3 = 0
inp4 = 0
inp5 = 0

#first results
qc, first_result = create5QGHZRealDevice(inp1, inp2, inp3, inp4, inp5)
first_counts = first_result.get_counts()

# Draw the quantum circuit
display(qc.draw())

Job Status: job has successfully run

#second results
qc, second_result = create5QGHZRealDevice(inp1, inp2, inp3, inp4, inp5)
second_counts = second_result.get_counts()

print('For inputs',inp5,inp4,inp3,inp2,inp1,'Representation of GHZ circuit states are,')

# Plot results on histogram with legend
legend = ['First execution', 'Second execution']
plot_histogram([first_counts, second_counts], legend=legend)

Job Status: job has successfully run
For inputs 0 0 0 0 0 Representation of GHZ circuit states are,

import qiskit
qiskit.__qiskit_version__

{'qiskit-terra': '0.19.1', 'qiskit-aer': '0.9.1', 'qiskit-ignis': '0.7.0', 'qiskit-ibmq-provider': '0.18.2', 'qiskit-aqua': None, 'qiskit': '0.33.1', 'qiskit-nature': '0.3.0', 'qiskit-finance': '0.3.0', 'qiskit-optimization': '0.2.3', 'qiskit-machine-learning': '0.3.0'}