Description

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
Circuit diagram showing the Superdense coding protocol

1.2. Step 1 Step 2-
3. Step 3
4. Step 4
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-Z operation where q1s state is flipped.
• If they want to send 10 then they apply a Pauli-X 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
1. Copy and paste the code below in to a python file
2. Enter your API token in the IBMQ.enable_account(‘Insert API token here’) part
3. Save and run
Code
print(‘ Superdense Coding’) print(‘————————- ‘) from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit, execute,IBMQ from qiskit.tools.monitor import job_monitor
IBMQ.enable_account(‘ENTER API TOKEN’) 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… ‘) job_monitor(job) counts = job.result().get_counts() print(‘RESULT: ‘,counts,’ ‘) #################### 10 ########################### 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… ‘) job_monitor(job) counts = job.result().get_counts() print(‘RESULT: ‘,counts,’ ‘) #################### 01 ########################### 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… ‘) job_monitor(job) counts = job.result().get_counts() print(‘RESULT: ‘,counts,’ ‘) #################### 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… ‘) job_monitor(job) counts = job.result().get_counts() print(‘RESULT: ‘,counts,’ ‘) print(‘Press any key to close’) input()
Output
After running the code you will see something like the following printed on the screen :

My output:-