We define rewinding operators that invert quantum measurements. Then, we define complexity classes ${\sf RwBQP}$, ${\sf CBQP}$, and ${\sf AdPostBQP}$ 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 ${\sf BPP}^{\sf PP}\subseteq{\sf RwBQP}={\sf CBQP}={\sf AdPostBQP}\subseteq{\sf PSPACE}$. As a byproduct of this result, we show that any problem in ${\sf PostBQP}$ can be solved with only postselections of outputs whose probabilities are polynomially close to one. Under the strongly believed assumption that ${\sf BQP}\nsupseteq{\sf SZK}$, 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.
翻译:我们定义了反向量量度测量的倒缩操作器。 然后, 我们定义了 $ $ sf RwBQP $, $ sf CBQP $, $sf CBQP $, 和 $sf AdPostBQP $ 。 作为这一结果的副产品, 我们显示, $_sf PostBP 大小的量子电路中的任何问题只能通过多倍数的回缩操作器、 克隆操作器和适应性后选的结果来解决。 我们的主要结果是, 我们坚信, $sf BQP ⁇ ssubseteq@sf RwBQP QQsf CBQP QP ⁇ sf AdPZPZPQQQQP QP QP 和 $。 或最短独立的矢量的矢量矢量矢量矢量器问题无法以有效解决。 作为这一结果的一个副产品, $sf PostBQQaldealalalmax 的计算, 我们也认为, Qalimalimalimal dealationalizal deal decal 。