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Recorded 03 October 2023. Christian Mendl of the Technical University of Munich presents "Aspects of quantum simulation of the Fermi-Hubbard model" at IPAM's Quantum Algorithms for Scientific Computation Workshop. Abstract: This talk is concerned with quantum simulation, i.e., approximating the quantum time evolution operator \e−itH . We first derive higher-order error bounds for a general Trotter product formula and apply these bounds to the time evolution operator governed by the Fermi-Hubbard Hamiltonian on one-dimensional and two-dimensional square and triangular lattices. Comparison with the actual Trotter error (evaluated on a small system) indicates that the bounds still overestimate the error. In the second part of the talk, we further improve Trotter methods via the Riemannian trust-region algorithm, used to optimize the gates in quantum circuits with Trotter splitting topologies. For the Ising and Heisenberg models on a one-dimensional lattice, we achieve orders of magnitude accuracy improvements compared to fourth-order splitting methods. The optimized circuits could also be of practical use for the time-evolving block decimation (TEBD) algorithm. (Based on arXiv:2306.10603 and arXiv:2212.07556) Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-i-quantum-algorithms-for-scientific-computation/?tab=schedule

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