Covariant Quantum Error-Correcting Codes with Metrological Entanglement Advantage
ORAL
Abstract
We show that a subset of the basis for the irreducible representations of the total $SU(2)$ rotation forms a covariant approximate quantum error-correcting code with transversal $U(1)$ logical gates.
Using only properties of the angular momentum algebra, we obtain bounds on the code inaccuracy against generic noise on any known $d$ sites and against heralded $d$-local erasures, generalizing and improving previous works on the ``thermodynamic code" to general local spin and different irreducible representations.
We demonstrate that this family of codes can host and protect 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.
Using only properties of the angular momentum algebra, we obtain bounds on the code inaccuracy against generic noise on any known $d$ sites and against heralded $d$-local erasures, generalizing and improving previous works on the ``thermodynamic code" to general local spin and different irreducible representations.
We demonstrate that this family of codes can host and protect 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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Publication: arXiv:2409.20561
Presenters
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Cheng-Ju Lin
University of Maryland College Park
Authors
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Cheng-Ju Lin
University of Maryland College Park
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Zi-Wen Liu
Tsinghua University, Yau Mathematical Sciences Center, Tsinghua University
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Victor V Albert
QuICS @ NIST & UMD College Park, University of Maryland College Park
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Alexey V Gorshkov
National Institute of Standards and Technology (NIST), NIST / University of Maryland, College Park, AWS Center for Quantum Computing, JQI, National Institute of Standards and Technology (NIST) & JQI & AWS