aiqbench analysis
This research establishes a unified algebraic-geometric framework to certify partial self-correction in 3D stabilizer codes, offering a computable criterion for passive quantum memory protection at finite temperatures. By linking local stabilizer structures to recoverability under Davies dynamics, the study provides a systematic method for designing quantum memories with super-Arrhenius lifetimes using polynomial-time decoders.
Universally Certifying Partially Self-Correcting Quantum Memories in 3D Translation-Invariant Stabilizer Codes
arXiv:2611.06469v1 Announce Type: new Abstract: Achieving passive protection of quantum information at finite temperature is a central problem at the intersection of quantum information and quantum many-body physics. Yet a general, computable criterion for determining self-correcting behavior directly from the form of local interactions remains elusive. Here we develop a unified algebraic-geometric framework for certifying partial self-correction in three-dimensional translation-invariant local stabilizer codes, encompassing the cubic code as a special case. From the algebraic curves defined by the codes' defining polynomials, we construct valuation matrices on the boundaries of their normalized projective closures and derive a computable rank criterion. Together with a polynomial-time decoder, this criterion guarantees super-Arrhenius memory lifetimes for code families satisfying it under the specified local Davies dynamics. We apply the framework to certify several classes of partially self-correcting quantum memories, including nearest-neighbor models with stabilizer weight as low as six and long memory lifetimes at modest system sizes. These results establish an algebraic-geometric connection between local stabilizer structure and the recoverability of quantum information at finite temperature, providing a systematic approach to certifying and designing passive quantum memories.
Abstract:Achieving passive protection of quantum information at finite temperature is a central problem at the intersection of quantum information and quantum many-body physics. Yet a general, computable criterion for determining self-correcting behavior directly from the form of local interactions remains elusive. Here we develop a unified algebraic-geometric framework for certifying partial self-correction in three-dimensional translation-invariant local stabilizer codes, encompassing the cubic code as a special case. From the algebraic curves defined by the codes' defining polynomials, we construct valuation matrices on the boundaries of their normalized projective closures and derive a computable rank criterion. Together with a polynomial-time decoder, this criterion guarantees super-Arrhenius memory lifetimes for code families satisfying it under the specified local Davies dynamics. We apply the framework to certify several classes of partially self-correcting quantum memories, including nearest-neighbor models with stabilizer weight as low as six and long memory lifetimes at modest system sizes. These results establish an algebraic-geometric connection between local stabilizer structure and the recoverability of quantum information at finite temperature, providing a systematic approach to certifying and designing passive quantum memories.
arXiv:2611.06469 [quant-ph]
(or arXiv:2611.06469v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2611.06469 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 268 words