create quantum_fourier_transform (TheAlgorithms#6682)

* create quantum_fourier_transform

This is part of the #Hacktoberfest.
I build the quantum fourier transform for N qubits. (n = 3 in the example)
Best,
Kevin

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* Update q_fourier_transform.py

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* Update q_fourier_transform.py

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Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

Author: 3 people

quantum/q_fourier_transform.py

@@ -0,0 +1,97 @@
+"""
+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 type(number_of_qubits) == str:
+        raise TypeError("number of qubits must be a integer.")
+    if not 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)}"
+    )