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DOE OSTI · 3376347

Covariant Quantum Error-Correcting Codes with Metrological Entanglement Advantage

Lin, Cheng-Ju [National Inst. of Standards and Technology (NIST), Boulder, CO (United States); Univ. of Maryland, College Park, MD (United States). Joint Center for Quantum Information and Computer Science; Univ. of Maryland, College Park, MD (United States). Joint Quantum Inst.] (ORCID:0000000178980211)·Liu, Zi-Wen [Tsinghua Univ., Beijing (China); Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)] (ORCID:0000000234029763)·Albert, Victor V. [Univ. of Maryland, College Park, MD (United States). Joint Center for Quantum Information and Computer Science] (ORCID:0000000203359508)·Gorshkov, Alexey V. [Univ. of Maryland, College Park, MD (United States). Joint Center for Quantum Information and Computer Science; Univ. of Maryland, College Park, MD (United States). Joint Quantum Inst.] (ORCID:0000000305093421)
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Abstract

Here, 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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Lin, Cheng-Ju [National Inst. of Standards and Technology (NIST), Boulder, CO (United States); Univ. of Maryland, College Park, MD (United States). Joint Center for Quantum Information and Computer Science; Univ. of Maryland, College Park, MD (United States). Joint Quantum Inst.] (ORCID:0000000178980211), Liu, Zi-Wen [Tsinghua Univ., Beijing (China); Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)] (ORCID:0000000234029763), Albert, Victor V. [Univ. of Maryland, College Park, MD (United States). Joint Center for Quantum Information and Computer Science] (ORCID:0000000203359508), Gorshkov, Alexey V. [Univ. of Maryland, College Park, MD (United States). Joint Center for Quantum Information and Computer Science; Univ. of Maryland, College Park, MD (United States). Joint Quantum Inst.] (ORCID:0000000305093421). 2025-09-10. Covariant Quantum Error-Correcting Codes with Metrological Entanglement Advantage. https://doi.org/10.1103/dttc-ksdn

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