Title | Quantum routing with fast reversals |

Publication Type | Journal Article |

Year of Publication | 2021 |

Authors | Bapat, A, Childs, AM, Gorshkov, AV, King, S, Schoute, E, Shastri, H |

Date Published | 3/4/2021 |

Abstract | 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≈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≤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. |

URL | https://arxiv.org/abs/2103.03264 |