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A Quantum Time-Space Tradeoff for Directed st-Connectivity

Authors Stacey Jeffery , Galina Pass

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LIPIcs.ICALP.2026.117.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum complexity theory
Keywords
  • Quantum algorithms
  • time-space tradeoffs
  • directed st-connectivity
  • switching networks
  • space-bounded computation

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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 NL-completeness. We show that for any S ≥ log²(n), there is a quantum algorithm for dstcon using space S and time T ≤ 2^{1/2 log(n) log(n/S) + o(log²(n))}, which is an (up to quadratic) improvement over the best classical algorithm for any S = o(√n). Of the S total space used by our algorithm, only O(log²(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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Stacey Jeffery and Galina Pass. A Quantum Time-Space Tradeoff for Directed st-Connectivity. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 117:1-117:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.117

Author Details

Stacey Jeffery
  • CWI, QuSoft, Amsterdam, The Netherlands
  • University of Amsterdam, The Netherlands
Galina Pass
  • QuSoft, Amsterdam, The Netherlands
  • University of Amsterdam, The Netherlands

Funding

This work is co-funded by the European Union (ERC, ASC-Q, 101040624); the project Divide & Quantum (with project number 1389.20.241) of the research programme NWA-ORC, which is (partly) financed by the Dutch Research Council (NWO); and the Dutch National Growth Fund (NGF), as part of the Quantum Delta NL programme. SJ is a CIFAR Fellow in the Quantum Information Science Program.

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