Merlinization of complexity classes above BQP

TL;DR

This paper explores how adding a quantum or classical witness to certain quantum complexity classes above BQP affects their computational power, revealing equalities with known classes like PSPACE and PP.

Contribution

It introduces the concept of 'Merlinization' for classes above BQP and establishes their equivalences to PSPACE and PP under specific conditions.

Findings

Merlinized postBQP equals PSPACE

Restricted Merlinized postBQP equals PP

Merlinization does not change SBQP class

Abstract

We study how complexity classes above BQP, such as postBQP, ${\rm postBQP}_{\rm FP}$, and SBQP, change if we "Merlinize" them, i.e., if we allow an extra input quantum state (or classical bit string) given by Merlin as witness. Main results are the following three: First, the Merlinized version of postBQP is equal to PSPACE. Second, if the Merlinized postBQP is restricted in such a way that the postselection probability is equal to all witness states, then the class is equal to PP. Finally, the Merlinization does not change the class SBQP.