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Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection

Authors Ryo Hiromasa, Akihiro Mizutani, Yuki Takeuchi, Seiichiro Tani

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Author Details

Ryo Hiromasa
  • Information Technology R&D Center, Mitsubishi Electric Corporation, Kamakura, Japan
Akihiro Mizutani
  • Information Technology R&D Center, Mitsubishi Electric Corporation, Kamakura, Japan
Yuki Takeuchi
  • NTT Communication Science Laboratories, NTT Corporation, Atsugi, Japan
Seiichiro Tani
  • NTT Communication Science Laboratories, NTT Corporation, Atsugi, Japan
  • International Research Frontiers Initiative (IRFI), Tokyo Institute of Technology, Japan

Funding

  • Mizutani, Akihiro: Supported by JST, ACT-X Grant Number JPMJAX210O, Japan.
  • Takeuchi, Yuki: Supported by MEXT Quantum Leap Flagship Program (MEXT Q-LEAP) Grant Number JPMXS0118067394 and JPMXS0120319794 and JST [Moonshot R&D – MILLENNIA Program] Grant Number JPMJMS2061.
  • Tani, Seiichiro: Supported by the Grant-in-Aid for Transformative Research Areas No.JP20H05966 of JSPS, JST [Moonshot R&D - MILLENNIA Program] Grant Number JPMJMS2061, and the Grant-in-Aid for Scientific Research (A) No.JP22H00522 of JSPS.

Acknowledgements

We thank Yasuhiro Takahashi and Yusuke Aikawa for helpful discussions. We also thank Tomoyuki Morimae for fruitful discussions and pointing out Refs. [Aaronson et al., 2014; Aaronson et al., 2016] to us.

Cite AsGet BibTex

Ryo Hiromasa, Akihiro Mizutani, Yuki Takeuchi, and Seiichiro Tani. Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 9:1-9:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.TQC.2023.9

Abstract

We define rewinding operators that invert quantum measurements. Then, we define complexity classes RwBQP, CBQP, and AdPostBQP as sets of decision problems solvable by polynomial-size quantum circuits with a polynomial number of rewinding operators, cloning operators, and adaptive postselections, respectively. Our main result is that BPP^PP ⊆ RwBQP = CBQP = AdPostBQP ⊆ PSPACE. As a byproduct of this result, we show that any problem in PostBQP can be solved with only postselections of outputs whose probabilities are polynomially close to one. Under the strongly believed assumption that BQP ⊉ SZK, or the shortest independent vectors problem cannot be efficiently solved with quantum computers, we also show that a single rewinding operator is sufficient to achieve tasks that are intractable for quantum computation. In addition, we consider rewindable Clifford and instantaneous quantum polynomial time circuits.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum complexity theory
Keywords
  • Quantum computing
  • Postselection
  • Lattice problems

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