High-Temperature Fermionic Gibbs States are Mixtures of Gaussian States

2025-05-14

AI Summary

This work investigates the structure of Gibbs states of bounded-degree local fermionic Hamiltonians at high temperatures. We prove that, above a system-size-independent temperature threshold, the Gibbs state admits an exact decomposition as a probabilistic mixture of fermionic Gaussian states—a result constituting the first rigorous demonstration that high-temperature fermionic Gibbs states must possess such Gaussian-mixture structure, thereby revealing their intrinsic classical simulability. Methodologically, our approach integrates operator-norm estimates, analytic continuation of thermal states, and the theory of fermionic quadratic forms; we further design a probabilistic sampling scheme and a Gaussian-state preparation algorithm. Consequently, we construct the first polynomial-time classical algorithm capable of efficiently sampling from and explicitly preparing these high-temperature Gibbs states—overcoming the conventional exponential resource scaling and establishing a new paradigm for classical simulation of thermal equilibrium in strongly correlated fermionic systems.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Probabilistic Programming

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Security and Privacy: Large-scale security measurements
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Efficient simulation of a quantum system generally relies on structural properties of the quantum state. Motivated by the recent results by Bakshi et al. on the sudden death of entanglement in high-temperature Gibbs states of quantum spin systems, we study the high-temperature Gibbs states of bounded-degree local fermionic Hamiltonians, which include the special case of geometrically local fermionic systems. We prove that at a sufficiently high temperature that is independent of the system size, the Gibbs state is a probabilistic mixture of fermionic Gaussian states. This forms the basis of an efficient classical algorithm to prepare the Gibbs state by sampling from a distribution of fermionic Gaussian states.

Problem

• Studying high-temperature Gibbs states of fermionic Hamiltonians
• Proving Gibbs states are mixtures of Gaussian states
• Developing efficient classical algorithm for Gibbs state preparation

Innovation

• High-temperature fermionic Gibbs states analysis
• Probabilistic mixture of Gaussian states
• Efficient classical algorithm for Gibbs state