Lab04_Bell_GHZ_Circuit.ipynb

Kernel: Python 3

Lab 4 Bell Circuit & GHZ Circuit

Prerequisite Ch.2.2 Multiple Qubits and Entangled States

Other relevant materials Circuit Tutorial: Getting Started with Qiskit

Applications Ch.3.11 Quantum Teleportation Ch.3.12 Superdense Coding Ch.3.13 Quantum Key Distribution

# 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')

Part 1: Bell State using Controlled-X gate

Goal

Create Bell state using CNOT or controlled-X gate.

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')'''

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.

Input State	Circuit	QSphere Plot	Histogram	City Plot	Paulivec	Hinton Plot
q0 = 0 q1 = 0
q0 = 1 q1 = 0
q0 = 0 q1 = 1
q0 = 1 q1 = 1

Part 2: Bell States on Real Quantum Device

Goal

Run Bell State circuit on real quantum device.

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

Part 3: 3-Qubit GHZ Circuit

Goal

Create a 3-qubit GHZ circuit and visualize the states.

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')

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.

Input State	Circuit	QSphere Plot	Histogram	City Plot	Paulivec	Hinton Plot
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

Part 4: 5-Qubit GHZ Circuit

Goal

Create a 5-qubit GHZ circuit and visualize the states.

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:

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

Part 5: Real Quantum Device

Goal

Run 5-qubit GHZ circuit on real quantum device.

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'}