再论量子电路模拟量子图灵机
Revisiting the simulation of quantum Turing machines by quantum circuits
摘要：
Yao（1993）证明了量子图灵机和均匀生成的量子电路是多项式等价的计算模型：在长度为$n$的输入上运行的量子图灵机的$t \geq n$步骤可以通过在$t$中具有二次尺寸的均匀生成的量子电路族来模拟，并且可以通过运行在多项式时间的量子图灵机来模拟多项式时间均匀生成的量子电路族。本文重新讨论了量子图灵机的均匀生成量子电路模拟，这是两个模拟任务中更具挑战性的一个，并对Yao采用的模拟方法进行了改进和分析。分析表明，量子图灵机的模拟可以用具有$t$线性深度的量子电路来完成，而不是二次深度的量子电路。并且可以扩展到量子图灵机的变体，例如具有多维带的量子图灵机。我们的分析是基于Arrighi，Nesme和Werner（2011）的方法的扩展，该方法允许因果酉演化的局部化。
英文摘要：
Yao (1993) proved that quantum Turing machines and uniformly generated quantum circuits are polynomially equivalent computational models: $t \geq n$ steps of a quantum Turing machine running on an input of length $n$ can be simulated by a uniformly generated family of quantum circuits with size quadratic in $t$, and a polynomial-time uniformly generated family of quantum circuits can be simulated by a quantum Turing machine running in polynomial time. We revisit the simulation of quantum Turing machines with uniformly generated quantum circuits, which is the more challenging of the two simulation tasks, and present a variation on the simulation method employed by Yao together with an analysis of it. This analysis reveals that the simulation of quantum Turing machines can be performed by quantum circuits having depth linear in $t$, rather than quadratic depth, and can be extended to variants of quantum Turing machines, such as ones having multi-dimensional tapes. Our analysis is based on an extension of a method of Arrighi, Nesme, and Werner (2011) that allows for the localization of causal unitary evolutions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
