#### Superdense Coding

M
K
```"""
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)}")
```