Quantum Programming 101: Superdense Coding Tutorial

Macauley Coggins

October 30, 2019

Education

What is Superdense coding ?

Superdense coding is a quantum communications protocol that allows a user to send 2 classical bits by sending only 1 qubit.

The protocol

Step 1: Preparing the Bell pair

First a bell pair consisting of 2 qubits is prepared. Where q0 is the senders qubit and q1 is the receivers qubit. To do this q0 is put in to a superposition of states using a hadamard gate.

Then a CNOT operation is performed with q0 being the control and q1 being the target.

Step 2: Encode the information on to q0

Next the sender has to encode the information they want to send on to q0 by applying certain operations to it.

If they want to send 00 then they perform no operation.
If they want to send 01 then they perform a Pauli-X operation where q1s state is flipped.
If they want to send 10 then they apply a Pauli-Z gate.
If they want to send 11 then apply a Pauli-Z gate followed by a Pauli-X gate

Step 3: Receiver decodes the information

Next q0 is sent and the receiver has to decode the qubit. This is done by applying a CNOT where the received q0 is the control and q1 is the target. Then a hadamard gate is applied to q0.

How to run the program

Copy and paste the code below in to a python file
Enter your API token in the IBMQ.enable_account(‘Insert API token here’) part
Save and run

Code

print('\n Superdense Coding')
print('--------------------------\n')

from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit, execute,IBMQ

IBMQ.enable_account('INSERT TOKEN HERE')
provider = IBMQ.get_provider(hub='ibm-q')

q = QuantumRegister(2,'q')
c = ClassicalRegister(2,'c')

backend = provider.get_backend('ibmq_qasm_simulator')
print('Provider: ',backend)

#################### 00 ###########################
circuit = QuantumCircuit(q,c) 

circuit.h(q[0]) # Hadamard gate applied to q0
circuit.cx(q[0],q[1]) # CNOT gate applied
circuit.cx(q[0],q[1]) 
circuit.h(q[0])  

circuit.measure(q,c) # Qubits measured    

job = execute(circuit, backend, shots=10)
                               
print('Executing Job...\n')                  
result = job.result()
counts = result.get_counts(circuit)

print('RESULT: ',counts,'\n')

#################### 01 ###########################
circuit = QuantumCircuit(q,c) 

circuit.h(q[0])
circuit.cx(q[0],q[1])
circuit.x(q[0]) # X-gate applied
circuit.cx(q[0],q[1])
circuit.h(q[0])

circuit.measure(q,c)
       
job = execute(circuit, backend, shots=10)
                               
print('Executing Job...\n')                  
result = job.result()
counts = result.get_counts(circuit)

print('RESULT: ',counts,'\n')

#################### 10 ###########################
circuit = QuantumCircuit(q,c) 

circuit.h(q[0])
circuit.cx(q[0],q[1])
circuit.z(q[0]) # Z-gate applied to q0 
circuit.cx(q[0],q[1])
circuit.h(q[0])

circuit.measure(q,c)
      
job = execute(circuit, backend, shots=10)
                               
print('Executing Job...\n')                  
result = job.result()
counts = result.get_counts(circuit)

print('RESULT: ',counts,'\n')

#################### 11 ###########################
circuit = QuantumCircuit(q,c) 

circuit.h(q[0])
circuit.cx(q[0],q[1])
circuit.z(q[0]) # Z-gate applied 
circuit.x(q[0]) # X-gate applied 
circuit.cx(q[0],q[1])
circuit.h(q[0])

circuit.measure(q,c)

job = execute(circuit, backend, shots=10)
                               
print('Executing Job...\n')                  
result = job.result()
counts = result.get_counts(circuit)

print('RESULT: ',counts,'\n')
print('Press any key to close')
input()

Output

After running the code you will see something like the following printed on the screen :

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Topics

IBM Q, Python, qiskit, Qiskit Aqua, quantum computers

Macauley Coggins

Macauley Coggins is a Software Developer, Researcher, and Managing Director of Quantum Computing UK. He has experience in developing software for IBMs Quantum Computers and has a special interest in developing secure cryptographic systems with quantum hardware.