Quantum Computation Relative to Oracles

Abstract

The study of the power and limitations of quantum computation remains a major challenge in complexity theory. Key questions revolve around the quantum complexity classes EQP, BQP, NQP, and their derivatives. This paper presents new relativized worlds in which (i) co-RP is not a subset of NQE, (ii) P=BQP and UP=EXP, (iii) P=EQP and RP=EXP, and (iv) EQP is not a subset of the union of Sigma{p}{2} and Pi{p}{2}. We also show a partial answer to the question of whether Almost-BQP=BQP