Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection

Explore a 24-minute conference talk from the 18th Theory of Quantum Computation Conference (TQC 2023) that delves into the theoretical foundations of rewindable quantum computation and its relationship to cloning operations. Learn about newly defined rewinding operators that can invert quantum measurements, and discover how they relate to complexity classes RwBQP, CBQP, and AdPostBQP. Understand the groundbreaking proof that BPP^PP is contained within these equivalent complexity classes, which are themselves contained within PSPACE. Examine how a single rewinding operator can accomplish tasks beyond the capabilities of standard quantum computation, particularly under the assumption that BQP does not contain SZK. Gain insights into the applications of these concepts to Clifford and instantaneous quantum polynomial time circuits, while exploring how problems in PostBQP can be solved using postselections with probabilities close to one.