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This research establishes a new upper bound of O(q log q) for exact quantum Fourier transform (QFT) circuits by leveraging efficient integer multiplication algorithms. The approach significantly reduces gate counts and workspace requirements compared to previous methods, directly linking classical computational complexity advances to quantum circuit optimization. If OpenAI's recent claims on integer multiplication hold true, this framework could further lower QFT complexity below the current O(q log q) threshold.
Multiplying integers now speeds up quantum Fourier transforms
A new approach leveraging integer multiplication could reduce the gate count for the crucial quantum Fourier transform (QFT) from O(q^2) to O(q log q).
Chandrima Kayal of Université Paris Cité, CNRS, and colleagues have established a new upper bound of O(q( log q)) gates for an exact quantum Fourier transform (QFT) circuit. This improves upon the O(q( log q)^2( log log q)) gate count achieved by Cleve and Watrous in 2000. The work demonstrates that further gains are possible; if OpenAI’s recent claims regarding integer multiplication hold true, a QFT circuit with fewer than O(q( log q)) gates may be achievable. Researchers also refined the best known gate count for approximating the QFT over Z/(2^qZ) to O(q( log log(q/ε))^α) gates,…
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