Explicit error-correction scheme and code distance for bosonic codes with rotational symmetry

Abstract

Bosonic codes with rotational symmetry are currently one of the best performing quantum error correcting codes. Little is known about error propagation and code distance for these rotation codes in contrast with qubit codes and Bosonic codes with translation symmetry. We use a general purpose error basis that is naturally suited to codes with rotation symmetry to compute how errors propagate through gates. This error basis allows us to give an explicit error detection, decoding, and correction scheme for any code with rotation symmetry. We also prove that codes with an $N$-fold rotation symmetry have a distance of $(d_n,d_{\theta })=(N,\pi /N)$ with respect to number and rotation errors.

arXiv commentV2: new figure and small improvements to the text

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Cited by in corpus (3)

• Clifford operations and homological codes for rotors and oscillators
• Letting the tiger out of its cage: bosonic coding without concatenation
• Generalized Code Distance through Rotated Logical States in Quantum Error Correction