



01494nas a2200181   4500008004100000245004000041210004000081260001400121490000600135520100800141100002101149700002301170700002501193700001701218700001901235700002101254856003701275       2021                        eng d00aQuantum routing with fast reversals0 aQuantum routing with fast reversals  c8/24/20210 v53 a<p>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&asymp;0.034 such that the quantum routing time is at most (1&minus;ϵ)n, whereas any swap-based protocol needs at least time n&minus;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(k2) on paths and at most 2r/3+O(k2) on general graphs with radius r.</p>1 aBapat, Aniruddha1 aChilds, Andrew, M.1 aGorshkov, Alexey, V.1 aKing, Samuel1 aSchoute, Eddie1 aShastri, Hrishee  uhttps://arxiv.org/abs/2103.03264