Fast parallel circuits for the quantum Fourier transform — mentioned by Strilanc

Wed, 03 Sep 2025 18:15:04 GMT

Realistic Shor circuits have depth polynomial in n, but you can easily construct ones whose depth is polylogarithmic in n. Just do the multiplications as a binary tree instead of in a linear order, using log depth multiplication circuits, and then do the frequency basis measurement using a low depth QFT [1]. The only part that isn't known to be doable in polylog depth is the classical GCD computation hiding in the classical postprocessing, to find the closest fraction to get the period. The result is that, if you keep adding qubits that can be operated on in parallel, Shor's algorithm…

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Fast parallel circuits for the quantum Fourier transform · HackerPapers discussions

Fast parallel circuits for the quantum Fourier transform — mentioned by Strilanc