Quantum Logarithmic Space and Post-selection

• URL: http://arxiv.org/abs/2105.02681v1
• Date: Thu, 6 May 2021 14:02:01 GMT
• Title: Quantum Logarithmic Space and Post-selection
• Authors: Fran\c{c}ois Le Gall, Harumichi Nishimura, and Abuzer Yakary{\i}lmaz
• Abstract summary: Post-selection is an influential concept introduced to the field of quantum complexity theory by Aaronson (Proceedings of the Royal Society A, 2005) Our main result shows the identity $sf PostBQL=$, i.e., the class of problems that can be solved by a bounded-error (polynomial-time) logarithmic-space quantum algorithm with post-selection ($sf PostBQL$) We also show that $sf$ coincides with the class of problems that can be solved by bounded-error logarithmic-space quantum algorithms that have no time bound.
• Score: 0.4588028371034406
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Post-selection, the power of discarding all runs of a computation in which an undesirable event occurs, is an influential concept introduced to the field of quantum complexity theory by Aaronson (Proceedings of the Royal Society A, 2005). In the present paper, we initiate the study of post-selection for space-bounded quantum complexity classes. Our main result shows the identity $\sf PostBQL=PL$, i.e., the class of problems that can be solved by a bounded-error (polynomial-time) logarithmic-space quantum algorithm with post-selection ($\sf PostBQL$) is equal to the class of problems that can be solved by unbounded-error logarithmic-space classical algorithms ($\sf PL$). This result gives a space-bounded version of the well-known result $\sf PostBQP=PP$ proved by Aaronson for polynomial-time quantum computation. As a by-product, we also show that $\sf PL$ coincides with the class of problems that can be solved by bounded-error logarithmic-space quantum algorithms that have no time bound.

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