2025/01/23 by Joseph Peetz, Prineha Narang, Peetz, Joseph +1 · 2 citations
Mathematics · #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2501.13922
openalex publication_date 2025/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the stochastic Zassenhaus expansions (SZEs), a class of ancilla-free quantum algorithms for Hamiltonian simulation. These algorithms map nested Zassenhaus formulas onto quantum gates and then employ randomized sampling to minimize circuit depths. Unlike Suzuki-Trotter product formulas, which grow exponentially long with approximation order, the nested commutator structures of SZEs enable high-order formulas for many systems of interest. For a 10-qubit transverse-field Ising model, we construct an 11th-order SZE with 42x fewer CNOTs than the standard 10th-order product formula. Further, we empirically demonstrate regimes where SZEs reduce simulation errors by many orders of magnitude compared to leading algorithms.