Quantum and Classical Algorithms for Weakly Interacting Fermions at Finite Temperature

Learn about quantum and classical computational approaches for analyzing weakly interacting fermionic systems at finite temperatures in this 47-minute conference presentation. Explore how weakly interacting fermions represent prototypical quantum systems that, while considered practically solvable, remain beyond exact diagonalization capabilities and have historically driven the development of perturbative methods for quantum many-body systems, including diagrammatic quantum Monte Carlo techniques. Discover a quantum algorithm based on Lindbladians designed to compute finite-temperature properties of these fermionic systems, followed by examination of a classical algorithm that employs cluster expansion and belief propagation methods for calculating the log partition function. Gain insights into recent advances in developing algorithms with provable runtime guarantees for these quantum systems, moving beyond empirical numerical approaches that have dominated the field. Understand the theoretical foundations and practical implications of both quantum and classical computational strategies for tackling these fundamental quantum many-body problems.