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Quantum Fourier Transform circuit builder -- the textbook cascade of H and
controlled-phase gates, plus the trailing qubit-order swap, returned as a
gate-tuple list ready for run_circuit. A standard building block (phase
estimation, Shor's algorithm, arithmetic circuits) that every general-
purpose SDK ships (Qiskit's `QFT`, Cirq's `cirq.QuantumFourierTransformGate`).
"""
import numpy as np
__all__ = ['qft']
def _invert_op(op):
"""H and SWAP are self-inverse; CP(theta)^-1 = CP(-theta)."""
if op[0] == 'cp':
gate, ctrl, tgt, angle = op
return (gate, ctrl, tgt, -angle)
return op
def qft(n_qubits, inverse=False, do_swaps=True):
"""
Build the Quantum Fourier Transform circuit on n_qubits.
Parameters
----------
n_qubits : int
Number of qubits, must be >= 1.
inverse : bool
Build the inverse QFT instead (same gate set, reversed order,
negated phase angles).
do_swaps : bool
Include the trailing qubit-reversal swaps that put the output in
the same qubit order as the input. The H/CP cascade alone
produces the Fourier-transformed amplitudes in bit-reversed
qubit order; set this to False only if the caller will account
for that reversal itself (e.g. chaining straight into another
subroutine that expects it).
Returns
-------
list[tuple]
Examples
--------
>>> import dense_evolution as de
>>> sim = de.DenseSVSimulator(3)
>>> sim.run_circuit(de.qft(3))
>>> sim.get_probabilities() # uniform: QFT|000> = equal superposition
"""
if n_qubits < 1:
raise ValueError(f"qft needs at least 1 qubit, got {n_qubits}")
ops = []
for j in range(n_qubits):
ops.append(('h', j))
for k in range(j + 1, n_qubits):
angle = np.pi / (2 ** (k - j))
ops.append(('cp', k, j, angle))
if do_swaps:
for i in range(n_qubits // 2):
ops.append(('swap', i, n_qubits - 1 - i))
if inverse:
ops = [_invert_op(op) for op in reversed(ops)]
return ops
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