Quantum Programming 101: Superdense Coding Tutorial
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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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