Diagnostics of Mixed-State Topological Order and Breakdown of Quantum Memory
By Ruihua Fan, Yimu Bao, E. Altman, Ashvin Vishwanath. PRX Quantum, 2023
144 citations recorded by the source corpus.
Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed states describing corrupted memories. Here we provide an intrinsic characterization of the breakdown of topological quantum memory, which both gives a bound on the performance of decoding algorithms and provides examples of topologically distinct mixed states. We employ three information-theoretical quantities that can be regarded as generalizations of the diagnostics of ground-state topological order, and serve as a definition for topological order in error-corrupted mixed states. We consider the topological contribution to entanglement negativity and two other metrics based on quantum relative entropy and coherent information. In the concrete example of the two-dimensional (2D) Toric code with local bit-flip and phase errors, we map three quantities to observables in 2D classical spin models and analytically show they all undergo a transition at the same error threshold. This threshold is an upper bound on that achieved in any decoding algorithm and is indeed saturated by that in the optimal decoding algorithm for the Toric code. Published by the American Physical Society 2024
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/8955098265e44480eecddd8b0d9f158291f480d2
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In Artificial Intelligence
In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States (2024, unknown): “The summation over the replica index s = 1 , 2 , · · · , t − 1 is kept implicit.”
- Generalized Symmetries in Condensed Matter (2022, unknown): “■ A state very much like the Chamon-Castelnovo state is realized upon subjecting the toric code to enough decoherence (37, 163, 164, 165, 166, 167).”
- Quantum Criticality Under Decoherence or Weak Measurement (2023, background): “Note Added: While finishing up this work, we became aware of an independent related work [96, 97], which should appear on arXiv on the same day as our work.”