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 epsilon approximate to 0.034 such that the quantum routing time is at most (1 - epsilon)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(k(2)) on paths and at most 2r/3 + O(k(2)) on general graphs with radius r.

Publication Details
Publication Type
Journal Article
Year of Publication
2021
Volume
5
DOI
10.22331/q-2021-08-31-533
Journal
Quantum
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