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We then show that these techniques can significantly reduce the cost of the arithmetic in Regev's factoring algorithm. For example, we find that 4096-bit integers $N$ can be factored in multiplication depth 193, which outperforms the 680 required of previous variants of Regev and the 444 reported by Ekerå and Gärtner for Shor's algorithm. While the space required for Shor's algorithm is considerably less than any variant of Regev's algorithm including ours, and thus Shor likely remains the best candidate for the first quantum factorization of large integers, our results show that implementations of Regev's algorithm are far from fully optimized, and Regev's algorithm may have practical importance in the future. We also believe our pebbling techniques are applicable in quantum cryptanalysis beyond integer factorization, and in quantum circuit compilation more broadly.
From: Seyoon Ragavan [view email]
[v1]
Thu, 9 Oct 2025 16:45:58 UTC (73 KB)
[v2]
Mon, 13 Apr 2026 15:57:43 UTC (97 KB)
[v3]
Fri, 3 Jul 2026 02:58:51 UTC (97 KB)
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