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Quantum Error Correction Fault Tolerance

A Polylogarithmic-Depth Quantum Multiplier

arXiv
Authors: Fred Sun, Anton Borissov

Year

2026

Paper ID

48603

Status

Preprint

Abstract Read

~2 min

Abstract Words

98

Citations

0

Abstract

We present a quantum algorithm for multiplying two n-bit integers with overall circuit depth and T-depth both bounded by O\(log2 n\), while using O\(n2\) 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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  • This paper contributes to the Quantum Error Correction & Fault Tolerance research area in the Quantum Articles archive.
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  • 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.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2604.09847 [2] arXiv https://arxiv.org/abs/2604.09847 [3] Publisher https://arxiv.org/abs/2604.09847

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Current Paper #48603 #68397 Optimizing Parallel Execution o...

External citation index: OpenAlex citation signal • updated 2026-06-11 03:07:23

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