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Space-Bounded Unitary Quantum Computation with Postselection

Author Seiichiro Tani

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ACM Subject Classification
  • Theory of computation → Quantum computation theory
Keywords
  • quantum complexity theory
  • space-bounded computation
  • postselection

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Abstract

Space-bounded computation has been a central topic in classical and quantum complexity theory. In the quantum case, every elementary gate must be unitary. This restriction makes it unclear whether the power of space-bounded computation changes by allowing intermediate measurement. In the bounded error case, Fefferman and Remscrim [STOC 2021, pp.1343-1356] and Girish, Raz and Zhan [ICALP 2021, pp.73:1-73:20] recently provided the break-through results that the power does not change. This paper shows that a similar result holds for space-bounded quantum computation with postselection. Namely, it is proved possible to eliminate intermediate postselections and measurements in the space-bounded quantum computation in the bounded-error setting. Our result strengthens the recent result by Le Gall, Nishimura and Yakaryilmaz [TQC 2021, pp.10:1-10:17] that logarithmic-space bounded-error quantum computation with intermediate postselections and measurements is equivalent in computational power to logarithmic-space unbounded-error probabilistic computation. As an application, it is shown that bounded-error space-bounded one-clean qubit computation (DQC1) with postselection is equivalent in computational power to unbounded-error space-bounded probabilistic computation, and the computational supremacy of the bounded-error space-bounded DQC1 is interpreted in complexity-theoretic terms.

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Seiichiro Tani. Space-Bounded Unitary Quantum Computation with Postselection. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 81:1-81:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.MFCS.2022.81

Author Details

Seiichiro Tani
  • NTT Communication Science Laboratories, NTT Corporation, Japan
  • International Research Frontiers Initiative (IRFI), Tokyo Institute of Technology, Japan

Funding

This work was partially supported by JSPS KAKENHI Grant Number JP20H05966 and JP22H00522.

Acknowledgements

I am grateful to anonymous referees of MFCS 2022 for their valuable comments.

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