具有快速反转的量子路由
Quantum routing with fast reversals
摘要：
我们提出了在相互作用约束下实现量子比特任意排列的方法。我们的协议利用以前的方法快速反转量子位沿路径的顺序.给定最近邻相互作用的长度$n$的路径上，我们证明了存在一个常数$ε\approx 0.034$，使得量子路由时间最多为$(1-ε)n$，而任何基于交换的协议需要至少时间$n-1$ .这代表了第一个已知的量子优势交换为基础的路由方法，也给出了改进的量子路由时间的现实架构，如网格。此外，我们表明，我们的算法接近量子路由时间的$2n/3$的期望均匀随机排列，而交换为基础的协议需要时间$n$渐近。此外，我们考虑路由$k \le n$量子比特的稀疏排列，并给出量子路由时间在路径上最多为$n/3 + O(k^2)$，在半径为$r$的一般图上最多为$2r/3 + O(k^2)$的算法。
英文摘要：
We present methods for implementing arbitrary permutations of qubits under interaction constraints. Our protocols make use of previous methods for rapidly reversing the order of qubits along a path. Given nearest-neighbor interactions on a path of length $n$, we show that there exists a constant $ε\approx 0.034$ such that the quantum routing time is at most $(1-ε)n$, whereas any swap-based protocol needs at least time $n-1$. This represents the first known quantum advantage over swap-based routing methods and also gives improved quantum routing times for realistic architectures such as grids. Furthermore, we show that our algorithm approaches a quantum routing time of $2n/3$ in expectation for uniformly random permutations, whereas swap-based protocols require time $n$ asymptotically. Additionally, we consider sparse permutations that route $k \le n$ qubits and give algorithms with quantum routing time at most $n/3 + O(k^2)$ on paths and at most $2r/3 + O(k^2)$ on general graphs with radius $r$.
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