Understanding Stabilizer Codes Under Local Decoherence Through A General Statistical Mechanics Mapping

Understanding Stabilizer Codes Under Local Decoherence Through A General Statistical Mechanics Mapping

March 7, 2024 | Anasuya Lyons
This paper presents a general statistical mechanics (SM) mapping that connects information quantities in stabilizer codes under local Pauli decoherence to thermodynamic quantities in classical statistical mechanics models. The mapping allows for the analysis of phase transitions in quantum codes by comparing them to classical finite-temperature transitions. The authors demonstrate that measures such as quantum relative entropy, coherent information, and entanglement negativity map to thermodynamic quantities in the SM model, enabling the characterization of decoding phase transitions. They apply this mapping to the 3D toric code and X-cube model, deriving bounds on their optimal decoding thresholds and gaining insight into their information properties under decoherence. The SM mapping is also shown to act as an "ungauging" map, allowing classical models under decoherence to be gauged back to the original code. The paper also discusses correlated errors and non-CSS stabilizer codes, showing how the mapping can be generalized. The results provide a framework for understanding the behavior of quantum codes under decoherence through the lens of classical statistical mechanics.This paper presents a general statistical mechanics (SM) mapping that connects information quantities in stabilizer codes under local Pauli decoherence to thermodynamic quantities in classical statistical mechanics models. The mapping allows for the analysis of phase transitions in quantum codes by comparing them to classical finite-temperature transitions. The authors demonstrate that measures such as quantum relative entropy, coherent information, and entanglement negativity map to thermodynamic quantities in the SM model, enabling the characterization of decoding phase transitions. They apply this mapping to the 3D toric code and X-cube model, deriving bounds on their optimal decoding thresholds and gaining insight into their information properties under decoherence. The SM mapping is also shown to act as an "ungauging" map, allowing classical models under decoherence to be gauged back to the original code. The paper also discusses correlated errors and non-CSS stabilizer codes, showing how the mapping can be generalized. The results provide a framework for understanding the behavior of quantum codes under decoherence through the lens of classical statistical mechanics.
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