Covariant Quantum Error-Correcting Codes with Metrological Entanglement Advantage

• URL: http://arxiv.org/abs/2409.20561v2
• Date: Wed, 24 Sep 2025 14:50:29 GMT
• Title: Covariant Quantum Error-Correcting Codes with Metrological Entanglement Advantage
• Authors: Cheng-Ju Lin, Zi-Wen Liu, Victor V. Albert, Alexey V. Gorshkov,
• Abstract summary: We show that a subset of the basis for the irreducible representations of a tensor-product SU(2) forms an approximate quantum error-correcting code with U(1) logical gates.<n>We demonstrate that this family of codes protects a probe state with quantum information surpassing the standard quantum limit when the sensing parameter couples to the generator of the U(1) logical gate.
• Score: 1.6018724979340826
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show that a subset of the basis for the irreducible representations of a tensor-product SU(2) rotation forms a covariant approximate quantum error-correcting code with transversal U(1) logical gates. Generalizing previous work on ``thermodynamic codes" to general local spin and different irreducible representations using only properties of the angular momentum algebra, we obtain bounds on the code inaccuracy under generic noise on any known $d$ sites, under independent and identically distributed noise, and under heralded $d$-local erasures. We demonstrate that this family of codes protects a probe state with quantum Fisher information surpassing the standard quantum limit when the sensing parameter couples to the generator of the U(1) logical gate.

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