quantum.q_fourier_transform

Build the quantum Fourier transform (QFT) for a desired number of qubits using the Qiskit framework.

This circuit can be used as a building block to design Shor’s algorithm in quantum computing, as well as quantum phase estimation, among others.

The circuit is simulated with Qiskit’s built-in, pure-Python BasicSimulator (no compiled qiskit-aer backend required), so it runs anywhere Qiskit itself installs.

References: https://en.wikipedia.org/wiki/Quantum_Fourier_transform https://quantum.cloud.ibm.com/docs/en/api/qiskit/qiskit.circuit.library.QFT

Functions

quantum_fourier_transform(→ qiskit.result.counts.Counts)

Build and simulate the quantum Fourier transform applied to the all-zero

Module Contents

quantum.q_fourier_transform.quantum_fourier_transform(number_of_qubits: int = 3) → qiskit.result.counts.Counts

Build and simulate the quantum Fourier transform applied to the all-zero state |0...0>. The QFT maps |0...0> to a uniform superposition, so every computational-basis outcome is (up to shot noise) equally likely.

# 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:

number_of_qubits : number of qubits

Returns:

qiskit.result.counts.Counts: measurement counts over 10,000 shots.

The simulation is seeded, so the set of observed outcomes is reproducible:

>>> counts = quantum_fourier_transform(2)
>>> sorted(counts)
['00', '01', '10', '11']
>>> sum(counts.values())
10000
>>> 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 an exact integer.

>>> result = quantum_fourier_transform(2)
>>> 2350<=result['10']<=2600
True
>>> 2350<=result['00']<=2600
True
>>> 2350<=result['11']<=2600
True
>>> 2350<=result['01']<=2600
True
>>> res = quantum_fourier_transform(3)
>>> 1150<=res['000']<=1350 and 1150<=res['001']<=1350
True
>>> 1150<=res['010']<=1350 and 1150<=res['100']<=1350
True
>>> 1150<=res['101']<=1350 and 1150<=res['110']<=1350
True
>>> 1150<=res['011']<=1350 and 1150<=res['111']<=1350
True