Encoding a qubit in a spin

Abstract

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.

12 pages, 2 figures

References in corpus (3)

• Minimal qudit code for a qubit in the phase-damping channel
• Cubic phase gates are not suitable for non-Clifford operations on GKP states
• Breaking classical Lie groups to finite subgroups - an automated approach

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