A Quantum Time-Space Tradeoff for Directed $st$-Connectivity

• URL: http://arxiv.org/abs/2510.08403v1
• Date: Thu, 09 Oct 2025 16:22:04 GMT
• Title: A Quantum Time-Space Tradeoff for Directed $st$-Connectivity
• Authors: Stacey Jeffery, Galina Pass,
• Abstract summary: We show that for any $Sgeq log2(n)$, there is a quantum algorithm for DSTCON using space $S$ and time $Tleq 2frac12log(n)log(n/S)+o(log2(n))$.
• Score: 0.08594140167290097
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Directed $st$-connectivity (DSTCON) is the problem of deciding if there exists a directed path between a pair of distinguished vertices $s$ and $t$ in an input directed graph. This problem appears in many algorithmic applications, and is also a fundamental problem in complexity theory, due to its ${\sf NL}$-completeness. We show that for any $S\geq \log^2(n)$, there is a quantum algorithm for DSTCON using space $S$ and time $T\leq 2^{\frac{1}{2}\log(n)\log(n/S)+o(\log^2(n))}$, which is an (up to quadratic) improvement over the best classical algorithm for any $S=o(\sqrt{n})$. Of the $S$ total space used by our algorithm, only $O(\log^2(n))$ is quantum space - the rest is classical. This effectively means that we can trade off classical space for quantum time.

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