2020/05/21 by Jonathan A. Gross · 2 citations
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physrevlett.127.010504
published as Phys. Rev. Lett. 127, 010504 (2021) · 12 pages, 2 figures
arxiv created 2020/05/21 · arxiv updated 2021/07/07
I present a new approach for designing quantum error-correcting codes that guarantees a physically natural implementation of Clifford operations. Inspired by the scheme put forward by Gottesman, Kitaev, and Preskill for encoding a qubit in an oscillator, in which Clifford operations may be performed via Gaussian unitaries, this approach yields new schemes for encoding a qubit in a large spin in which single-qubit Clifford operations may be performed via spatial rotations. I construct all possible examples of such codes, provide universal-gate-set implementations using Hamiltonians that are at most quadratic in angular-momentum operators, and derive criteria for when these codes exactly correct physically relevant noise channels to lowest order, illustrating their performance numerically for specific low-dimensional examples.