Related papers: Quantum error-correcting codes with a covariant encoding

Quantum error-correcting codes with a covariant encoding

URL: http://arxiv.org/abs/2306.11621v4
Date: Wed, 24 Jul 2024 17:51:34 GMT
Title: Quantum error-correcting codes with a covariant encoding
Authors: Aurélie Denys, Anthony Leverrier,
Abstract summary: Given some group $G$ of logical gates, what are the quantum encodings for which these logical gates can be implemented by simple physical operations? We study this question by constructing a general form of such encoding maps. For bosonic encodings, we show how to obtain the GKP and cat qudit encodings by considering the appropriate groups, and essentially the simplest physical implementations.
Score: 2.532202013576547
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Given some group $G$ of logical gates, for instance the Clifford group, what are the quantum encodings for which these logical gates can be implemented by simple physical operations, described by some physical representation of $G$? We study this question by constructing a general form of such encoding maps. For instance, we recover that the $[[5,1,3]]$ and Steane codes admit transversal implementations of the binary tetrahedral and binary octahedral groups, respectively. For bosonic encodings, we show how to obtain the GKP and cat qudit encodings by considering the appropriate groups, and essentially the simplest physical implementations. We further illustrate this approach by introducing a 2-mode bosonic code defined from a constellation of 48 coherent states, for which all single-qubit Clifford gates correspond to passive Gaussian unitaries.

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