SpaceBounded Unitary Quantum Computation with Postselection
Abstract
Spacebounded 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 spacebounded computation changes by allowing intermediate measurement. In the bounded error case, Fefferman and Remscrim [STOC 2021, pp.13431356] and Girish, Raz and Zhan~[ICALP 2021, pp.73:173:20] recently provided the breakthrough results that the power does not change. This paper shows that a similar result holds for spacebounded quantum computation with postselection. Namely, it is proved possible to eliminate intermediate postselections and measurements in the spacebounded quantum computation in the boundederror setting. Our result strengthens the recent result by Le Gall, Nishimura and Yakaryilmaz~[TQC 2021, pp.10:110:17] that logarithmicspace boundederror quantum computation with intermediate postselections and measurements is equivalent in computational power to logarithmicspace unboundederror probabilistic computation. As an application, it is shown that boundederror spacebounded oneclean qubit computation (DQC1) with postselection is equivalent in computational power to unboundederror spacebounded probabilistic computation, and the computational supremacy of the boundederror spacebounded DQC1 is interpreted in complexitytheoretic terms.
 Publication:

arXiv eprints
 Pub Date:
 June 2022
 arXiv:
 arXiv:2206.15122
 Bibcode:
 2022arXiv220615122T
 Keywords:

 Quantum Physics;
 Computer Science  Computational Complexity;
 68Q12;
 68Q15;
 F.1.2;
 F.1.3
 EPrint:
 Full version of the MFCS 2022 paper. Typos fixed. Some minor clarifications and corrections