FA-91158 / Quantum circuit simulation / Member archive

Inverse QFT reverses the gates but keeps phase signs · case 03

The inverse QFT applied to |j> is not the conjugate spectrum; round trips do not return to the input.

Member previewVariant 3 · 3 implementations · 7 checks per implementation

Case contract

Input [n, j, inverse]. Build the textbook QFT on n qubits (qubit 0 = LSB): for q from n-1 down to 0 apply H(q) then CP(pi / 2**(q-k)) between q and each k < q (k descending), then swap q with n-1-q for q < n//2; the inverse is the reversed sequence with negated phases. Apply it to |j> and return the amplitudes as [re, im] rounded to 6 decimals (QFT|j> = sum_k e^{2 pi i jk/N}|k>/sqrt N).

Why this case matters

QFT circuits are the core of phase estimation and arithmetic; decomposition slips produce bit-reversed or dephased spectra.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
regression: qft n=3 j=6 inverse	`[[0.353553, 0.0], [0.0, -0.353553], [-0.353553, 0.0], [0.0, 0.353553], [0.353553, 0.0], [0.0, -0.353553], [-0.353553, 0.0], [0.0, 0.353553]]`	`[[0.353553, 0.0], [0.0, 0.353553], [-0.353553, 0.0], [0.0, -0.353553], [0.353553, 0.0], [0.0, 0.353553], [-0.353553, 0.0], [0.0, -0.353553]]`	Failed

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