We define rewinding operators that invert quantum measurements. Then, we
define complexity classes RwBQP, CBQP, and AdPostBQP as
sets of decision problems solvable by polynomial-size quantum circuits with a
polynomial number of rewinding operators, cloning operators, and adaptive
postselections, respectively. Our main result is that BPPPP⊆RwBQP=CBQP=AdPostBQP⊆PSPACE. As a
byproduct of this result, we show that any problem in PostBQP can be
solved with only postselections of outputs whose probabilities are polynomially
close to one. Under the strongly believed assumption that BQP⊉SZK, or the shortest independent vectors problem cannot be
efficiently solved with quantum computers, we also show that a single rewinding
operator is sufficient to achieve tasks that are intractable for quantum
computation. In addition, we consider rewindable Clifford and instantaneous
quantum polynomial time circuits.Comment: 29 pages, 3 figures, v2: Added Result 3 and improved Result