Multi-product Hamiltonian Simulation with Explicit Commutator Scaling

Learn about multi-product Hamiltonian simulation through a 25-minute conference talk presented at the 19th Theory of Quantum Computation, Communication and Cryptography Conference (TQC 2024). Explore the rigorous complexity analysis of well-conditioned multi-product formula (MPF), originally proposed by Low, Kliuchnikov, and Wiebe in 2019. Discover how this analysis demonstrates explicit commutator scaling while achieving near-optimal time and precision dependence. Examine practical applications where MPF, based on second-order product formula, achieves polynomial speedup in system size and evolution time, plus exponential speedup in precision compared to traditional product formulas. Compare MPF's performance against post-Trotter methods, understanding how it achieves polynomially better scaling in system size with only poly-logarithmic overhead in evolution time and precision. Presented by researchers Junaid Aftab, Dong An, and Konstantina Trivisa at OIST, Japan, as part of a leading international conference bringing together theoretical quantum information science experts.