"""

Build the superdense coding protocol. This quantum

circuit can send two classical bits using one quantum

bit. This circuit is designed using the Qiskit

framework. This experiment run in IBM Q simulator

with 1000 shots.

.

References:

https://qiskit.org/textbook/ch-algorithms/superdense-coding.html

https://en.wikipedia.org/wiki/Superdense_coding

"""

import math

import qiskit

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

def superdense_coding(bit_1: int = 1, bit_2: int = 1) -> qiskit.result.counts.Counts:

"""

The input refer to the classical message

that you wants to send. {'00','01','10','11'}

result for default values: {11: 1000}

┌───┐ ┌───┐

qr_0: ─────┤ X ├──────────┤ X ├─────

┌───┐└─┬─┘┌───┐┌───┐└─┬─┘┌───┐

qr_1: ┤ H ├──■──┤ X ├┤ Z ├──■──┤ H ├

└───┘ └───┘└───┘ └───┘

cr: 2/══════════════════════════════

Args:

bit_1: bit 1 of classical information to send.

bit_2: bit 2 of classical information to send.

Returns:

qiskit.result.counts.Counts: counts of send state.

>>> superdense_coding(0,0)

{'00': 1000}

>>> superdense_coding(0,1)

{'01': 1000}

>>> superdense_coding(-1,0)

Traceback (most recent call last):

...

ValueError: inputs must be positive.

>>> superdense_coding(1,'j')

Traceback (most recent call last):

...

TypeError: inputs must be integers.

>>> superdense_coding(1,0.5)

Traceback (most recent call last):

...

ValueError: inputs must be exact integers.

>>> superdense_coding(2,1)

Traceback (most recent call last):

...

ValueError: inputs must be less or equal to 1.

"""

if isinstance(bit_1, str) or isinstance(bit_2, str):

raise TypeError("inputs must be integers.")

if (bit_1 < 0) or (bit_2 < 0):

raise ValueError("inputs must be positive.")

if (math.floor(bit_1) != bit_1) or (math.floor(bit_2) != bit_2):

raise ValueError("inputs must be exact integers.")

if (bit_1 > 1) or (bit_2 > 1):

raise ValueError("inputs must be less or equal to 1.")

# build registers

qr = QuantumRegister(2, "qr")

cr = ClassicalRegister(2, "cr")

quantum_circuit = QuantumCircuit(qr, cr)

# entanglement the qubits

quantum_circuit.h(1)

quantum_circuit.cx(1, 0)

# send the information

c_information = str(bit_1) + str(bit_2)

if c_information == "11":

quantum_circuit.x(1)

quantum_circuit.z(1)

elif c_information == "10":

quantum_circuit.z(1)

elif c_information == "01":

quantum_circuit.x(1)

else:

quantum_circuit.i(1)

# unentangled the circuit

quantum_circuit.cx(1, 0)

quantum_circuit.h(1)

# measure the circuit

quantum_circuit.measure(qr, cr)

backend = Aer.get_backend("aer_simulator")

job = execute(quantum_circuit, backend, shots=1000)

return job.result().get_counts(quantum_circuit)

if __name__ == "__main__":

print(f"Counts for classical state send: {superdense_coding(1,1)}")