Merlinization of complexity classes above BQP

Abstract

We study how complexity classes above BQP, such as postBQP, postBQP 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.

Quantum Technology and Optimization Problems

“…For instance, the amount of instructions required to execute a particular algorithm is one of the main measures of efficiency or practicability on a classical machine, whereas the notion of a discrete computational "step" is hard to define on a quantum annealing device. Interest in quantum computing has also spawned definitions of new complexity classes (e.g., [28,37]), whose relations to traditional complexity classes have been and are still subject to ongoing research [8,31].…”