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arXiv · 2604.09847

A Polylogarithmic-Depth Quantum Multiplier

Fred Sun·Anton Borissov
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Abstract

We present a quantum algorithm for multiplying two $n$-bit integers with overall circuit depth and $T$-depth both bounded by $O(\log^{2} n)$, while using $O(n^{2})$ gates and ancillary qubits. Our construction generates partial products via indicator-controlled copying and adds them using a binary adder tree, enabling parallel accumulation with logarithmic depth overhead per level. To the best of our knowledge, our design has the lowest $T$-depth among all multiplication algorithms using the Clifford + $T$ model. By optimizing both circuit depth and $T$-depth, our construction advances the practical feasibility of large-scale fault-tolerant quantum algorithms.

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Fred Sun, Anton Borissov. 2026-04-10. A Polylogarithmic-Depth Quantum Multiplier. https://arxiv.org/abs/2604.09847

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