Redirecting to original paper in 30 seconds...
Click below to go immediately or wait for automatic redirect
📄 Abstract
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.
Key Contributions
This paper proves that Gibbs states of classical and commuting-Pauli Hamiltonians are stable under weak local decoherence, meaning their effect can be locally reversed. This implies thermally stable quantum memories have a non-zero threshold against decoherence near critical temperatures, and conceptually links to efficient local denoisers in diffusion models.
Business Value
Fundamental insights for building robust quantum memories and potentially inspires new approaches in generative AI by highlighting the stability of generative processes under noise.