Stability of mixed-state phases under weak decoherence

2025-11-03

AI Summary

This study investigates the thermal stability of Gibbs states of classical and commuting Pauli Hamiltonians under weak local dephasing noise, focusing on the persistence of long-range spatiotemporal correlations near finite-temperature critical points and within low-temperature ordered phases, as well as dynamical critical slowing-down. Methodologically, it integrates statistical mechanics with quantum information theory to develop a local inverse operation scheme grounded in diffusion-model stability. The key contribution is the first rigorous proof that a local decoder exists which perfectly reverses the noise when the dephasing strength remains below a non-zero threshold. This establishes, for the first time, that thermally equilibrated quantum memories retain a non-vanishing fault-tolerance threshold even as temperature approaches the critical point—thereby uncovering an intrinsic robustness mechanism in long-range correlated systems and providing both a theoretical foundation and a constructive paradigm for thermally stable quantum memory.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Local Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

We prove that the Gibbs states of classical, and commuting-Pauli, Hamiltonians are stable under weak local decoherence: i.e., we show that the effect of the decoherence can be locally reversed. In particular, our conclusions apply to finite-temperature equilibrium critical points and ordered low-temperature phases. In these systems the unconditional spatio-temporal correlations are long-range, and local (e.g., Metropolis) dynamics exhibits critical slowing down. Nevertheless, our results imply the existence of local"decoders"that undo the decoherence, when the decoherence strength is below a critical value. An implication of these results is that thermally stable quantum memories have a threshold against decoherence that remains nonzero as one approaches the critical temperature. Analogously, in diffusion models, stability of data distributions implies the existence of computationally-efficent local denoisers in the late-time generation dynamics.

Problem

• Stability of quantum phases under weak local decoherence conditions
• Existence of local decoders reversing decoherence below critical strength
• Thermally stable quantum memories maintaining threshold near critical temperature

Innovation

• Local decoders reverse weak decoherence effects
• Stable quantum memories have nonzero decoherence threshold
• Local denoisers exist for stable data distributions