Perfect completeness for BQP and QMA(2)

Determine whether BQP equals its perfectly complete variant BQP_1 (equivalently, whether BQP equals coRQP) and whether QMA(2) equals its perfectly complete variant QMA_1(2).

Background

The paper proves that QMA has perfect completeness, establishing QMA = QMA_1, and develops a verifier construction based on exact arithmetic and cyclic consistency checks. The authors state that analogous perfect-completeness equalities remain unresolved for BQP and QMA(2).

For BQP, the construction does not directly apply because there is no prover to provide the exact rational quantity used in the cyclic consistency test. For QMA(2), the soundness condition applies only to product states across the two proof registers, which does not provide the operator-norm bound used in the QMA argument.