Quantum and classical algorithms for weakly interaction fermions at finite temperature
Yu Tong
Duke University
Mathematics
Weakly interacting fermions are prototypical quantum systems that are considered solvable in practice yet are beyond exact diagonalizability. They have motivated the development of perturbative methods for quantum many-body systems, including the diagrammatic quantum Monte Carlo method. Despite the empirical success in studying these quantum systems numerically, algorithms with provable runtime guarantees have only recently been discovered. I will present a quantum algorithm based on Lindbladians to compute the finite-temperature properties of weakly interacting fermions, followed by a later classical algorithm based on cluster expansion and belief propagation for computing the log partition function.
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