Bosonic quantum Fourier codes

• URL: http://arxiv.org/abs/2505.16618v1
• Date: Thu, 22 May 2025 12:51:22 GMT
• Title: Bosonic quantum Fourier codes
• Authors: Anthony Leverrier,
• Abstract summary: We show an approach where information is encoded in an irreducible representation of a finite subgroup of $U(2)$ through an inverse quantum Fourier transform.<n>The resulting two-mode Fourier cat code displays good error correction properties and admits an experimentally-friendly universal gate set.
• Score: 2.9914612342004503
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: While 2-level systems, aka qubits, are a natural choice to perform a logical quantum computation, the situation is less clear at the physical level. Encoding information in higher-dimensional physical systems can indeed provide a first level of redundancy and error correction that simplifies the overall fault-tolerant architecture. A challenge then is to ensure universal control over the encoded qubits. Here, we explore an approach where information is encoded in an irreducible representation of a finite subgroup of $U(2)$ through an inverse quantum Fourier transform. We illustrate this idea by applying it to the real Pauli group $\langle X, Z\rangle$ in the bosonic setting. The resulting two-mode Fourier cat code displays good error correction properties and admits an experimentally-friendly universal gate set that we discuss in detail.

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