A Note on Quantum Divide and Conquer for Minimal String Rotation

• URL: http://arxiv.org/abs/2210.09149v2
• Date: Thu, 20 Feb 2025 02:04:15 GMT
• Title: A Note on Quantum Divide and Conquer for Minimal String Rotation
• Authors: Qisheng Wang,
• Abstract summary: Lexicographically minimal string rotation is a fundamental problem in string processing. Near-optimal quantum algorithms have been proposed for solving this problem. We show that its quantum query complexity is $sqrtn cdot 2O(sqrtlog n)$, improving the prior result.
• Score: 3.1157817010763136
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• Abstract: Lexicographically minimal string rotation is a fundamental problem in string processing that has recently garnered significant attention in quantum computing. Near-optimal quantum algorithms have been proposed for solving this problem, utilizing a divide-and-conquer structure. In this note, we show that its quantum query complexity is $\sqrt{n} \cdot 2^{O(\sqrt{\log n})}$, improving the prior result of $\sqrt{n} \cdot 2^{(\log n)^{1/2+\varepsilon}}$ due to Akmal and Jin (SODA 2022). Notably, this improvement is quasi-polylogarithmic, which is achieved by only logarithmic level-wise optimization using fault-tolerant quantum minimum finding.

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