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Quantum Time-Space Tradeoffs for Exponential Dynamic Programming

Authors Susanna Caroppo , Jevgēnijs Vihrovs , Dārta Zajakina , Aleksejs Zajakins

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Subject Classification

ACM Subject Classification
  • Theory of computation → Dynamic programming
  • Theory of computation → Divide and conquer
  • Theory of computation → Quantum complexity theory
Keywords
  • Quantum Algorithms
  • Time-Space Tradeoffs
  • NP-Hard Problems
  • Dynamic Programming
  • Divide & Conquer

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Abstract

We investigate the quantum algorithms for dynamic programming by Ambainis et al. (SODA'19). While giving provable complexity speedups and applicable to a variety of NP-hard problems, these algorithms have a notable drawback: they require a large amount of Quantum Random Access Memory (QRAM), which potentially could be very challenging to implement in a physical quantum computer. In this work, we study how the space complexity can be improved by trading it for time, while still retaining a speedup over the classical algorithms. We show novel quantum time-space tradeoffs by combining different classical approaches with quantum techniques. For instance, we show that the Travelling Salesman Problem can be solved quantumly in Õ(1.859ⁿ) time and Õ(1.315ⁿ) QRAM space.

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Susanna Caroppo, Jevgēnijs Vihrovs, Dārta Zajakina, and Aleksejs Zajakins. Quantum Time-Space Tradeoffs for Exponential Dynamic Programming. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 37:1-37:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.37

Author Details

Susanna Caroppo
  • Roma Tre University, Department of Engineering, Rome, Italy
Jevgēnijs Vihrovs
  • Faculty of Science and Technology, University of Latvia, Riga, Latvia
Dārta Zajakina
  • Faculty of Science and Technology, University of Latvia, Riga, Latvia
Aleksejs Zajakins
  • Faculty of Science and Technology, University of Latvia, Riga, Latvia

Funding

  • Vihrovs, Jevgēnijs: Supported by the 1.1.1.9 Research application No 1.1.1.9/LZP/2/25/206 of the Activity "Post-doctoral Research" "Practical applications and limitations of quantum search".

References

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