eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2022-08-22
81:1
81:15
10.4230/LIPIcs.MFCS.2022.81
article
Space-Bounded Unitary Quantum Computation with Postselection
Tani, Seiichiro
1
2
https://orcid.org/0000-0002-6041-1704
NTT Communication Science Laboratories, NTT Corporation, Japan
International Research Frontiers Initiative (IRFI), Tokyo Institute of Technology, Japan
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol241-mfcs2022/LIPIcs.MFCS.2022.81/LIPIcs.MFCS.2022.81.pdf
quantum complexity theory
space-bounded computation
postselection