High-Temperature Fermionic Gibbs States are Mixtures of Gaussian States

2025/05/14 by Akshar Ramkumar, Ramkumar, Akshar, Yiyi Cai +5 · 3 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cold Atom Physics and Bose-Einstein Condensates #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Physical sciences #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy

paper · doi:10.48550/arxiv.2505.09730

openalex publication_date 2025/05/14 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

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.

Citations

• Optimizing Sparse SYK
• High-Temperature Partition Functions and Classical Simulatability of Long-Range Quantum Systems
• Quantum Gibbs states are locally Markovian
• Fast mixing of weakly interacting fermionic systems at any temperature
• Optimal quantum algorithm for Gibbs state preparation
• Rapidly mixing loop representation quantum Monte Carlo for Heisenberg models on star-like bipartite graphs
• Quantum Metropolis Sampling via Weak Measurement
• High-Temperature Gibbs States are Unentangled and Efficiently Preparable
• Efficient thermalization and universal quantum computing with quantum Gibbs samplers
• Quantum Hamiltonian Learning for the Fermi-Hubbard Model
• Local Hamiltonian Problem with succinct ground state is MA-Complete
• Polynomial-time classical sampling of high-temperature quantum Gibbs states
• Quantum Thermal State Preparation
• Twenty Years of Auxiliary-Field Quantum Monte Carlo in Quantum Chemistry: An Overview and Assessment on Main Group Chemistry and Bond-Breaking
• Optimizing Strongly Interacting Fermionic Hamiltonians
• Classical Simulation of High Temperature Quantum Ising Models
• Introduction to Quantum Monte Carlo simulations for fermionic systems

Cited by

• Fast Mixing of Quantum Spin Chains at All Temperatures
• Quantum Computing Beyond Ground State Electronic Structure: A Review of Progress Toward Quantum Chemistry Out of the Ground State
• Symmetry enforces entanglement at high temperatures

Related

• High-Temperature Gibbs States are Unentangled and Efficiently Preparable
• Rapid mixing for high-temperature Gibbs states with arbitrary external fields
• Polynomial-time classical sampling of high-temperature quantum Gibbs states
• Gibbs Sampling gives Quantum Advantage at Constant Temperatures with O(1)-Local Hamiltonians
• Optimizing random local Hamiltonians by dissipation