General limit to thermodynamic annealing performance

Abstract

Annealing has proven highly successful in finding minima in a cost landscape. Yet, depending on the landscape, systems often converge towards local minima rather than global ones. In this Letter, we analyse the conditions for which annealing is approximately successful in finite time. We connect annealing to stochastic thermodynamics to derive a general bound on the distance between the system state at the end of the annealing and the ground state of the landscape. This distance depends on the amount of state updates of the system and the accumulation of non-equilibrium energy, two protocol and energy landscape dependent quantities which we show are in a trade-off relation. We describe how to bound the two quantities both analytically and physically. This offers a general approach to assess the performance of annealing from accessible parameters, both for simulated and physical implementations.

arXiv comment6 pages, 3 figures

References in corpus (21)

• A nonequilibrium equality for free energy differences
• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Parallel Tempering: Theory, Applications, and New Perspectives
• Fundamental limitations for quantum and nano thermodynamics
• The thermodynamic meaning of negative entropy
• Second law and Landauer principle far from equilibrium
• The Three Faces of the Second Law: I. Master Equation Formulation
• Thermalizing Quantum Machines: Dissipation and Entanglement
• Truly work-like work extraction
• Speed Limit for Classical Stochastic Processes
• Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
• The work value of information
• An introduction to Monte Carlo methods
• Minimum entropy production, detailed balance and Wasserstein distance for continuous-time Markov processes
• Universal Bound on Energy Cost of Bit Reset in Finite Time
• Macroscopic non-equilibrium thermodynamics in dynamic calorimetry
• Guaranteed energy-efficient bit reset in finite time
• Bound on annealing performance from stochastic thermodynamics, with application to simulated annealing

Cited by in corpus (1)

• Bound on annealing performance from stochastic thermodynamics, with application to simulated annealing