#### Q Fourier Transform

M
K
```"""
Build the quantum fourier transform (qft) for a desire
number of quantum bits using Qiskit framework. This
experiment run in IBM Q simulator with 10000 shots.
This circuit can be use as a building block to design
the Shor's algorithm in quantum computing. As well as,
quantum phase estimation among others.
.
References:
https://en.wikipedia.org/wiki/Quantum_Fourier_transform
https://qiskit.org/textbook/ch-algorithms/quantum-fourier-transform.html
"""

import math

import numpy as np
import qiskit
from qiskit import Aer, ClassicalRegister, QuantumCircuit, QuantumRegister, execute

def quantum_fourier_transform(number_of_qubits: int = 3) -> qiskit.result.counts.Counts:
"""
# >>> quantum_fourier_transform(2)
# {'00': 2500, '01': 2500, '11': 2500, '10': 2500}
# quantum circuit for number_of_qubits = 3:
┌───┐
qr_0: ──────■──────────────────────■───────┤ H ├─X─
│                ┌───┐ │P(π/2) └───┘ │
qr_1: ──────┼────────■───────┤ H ├─■─────────────┼─
┌───┐ │P(π/4)  │P(π/2) └───┘               │
qr_2: ┤ H ├─■────────■───────────────────────────X─
└───┘
cr: 3/═════════════════════════════════════════════
Args:
n : number of qubits
Returns:
qiskit.result.counts.Counts: distribute counts.

>>> quantum_fourier_transform(2)
{'00': 2500, '01': 2500, '10': 2500, '11': 2500}
>>> quantum_fourier_transform(-1)
Traceback (most recent call last):
...
ValueError: number of qubits must be > 0.
>>> quantum_fourier_transform('a')
Traceback (most recent call last):
...
TypeError: number of qubits must be a integer.
>>> quantum_fourier_transform(100)
Traceback (most recent call last):
...
ValueError: number of qubits too large to simulate(>10).
>>> quantum_fourier_transform(0.5)
Traceback (most recent call last):
...
ValueError: number of qubits must be exact integer.
"""
if isinstance(number_of_qubits, str):
raise TypeError("number of qubits must be a integer.")
if number_of_qubits <= 0:
raise ValueError("number of qubits must be > 0.")
if math.floor(number_of_qubits) != number_of_qubits:
raise ValueError("number of qubits must be exact integer.")
if number_of_qubits > 10:
raise ValueError("number of qubits too large to simulate(>10).")

qr = QuantumRegister(number_of_qubits, "qr")
cr = ClassicalRegister(number_of_qubits, "cr")

quantum_circuit = QuantumCircuit(qr, cr)

counter = number_of_qubits

for i in range(counter):

quantum_circuit.h(number_of_qubits - i - 1)
counter -= 1
for j in range(counter):
quantum_circuit.cp(np.pi / 2 ** (counter - j), j, counter)

for k in range(number_of_qubits // 2):
quantum_circuit.swap(k, number_of_qubits - k - 1)

# measure all the qubits
quantum_circuit.measure(qr, cr)
# simulate with 10000 shots
backend = Aer.get_backend("qasm_simulator")
job = execute(quantum_circuit, backend, shots=10000)

return job.result().get_counts(quantum_circuit)

if __name__ == "__main__":
print(
f"Total count for quantum fourier transform state is: \
{quantum_fourier_transform(3)}"
)
```