Hamiltonian Simulation via Stochastic Zassenhaus Expansions

Joseph Peetz; Prineha Narang

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arXiv · 2501.13922

Hamiltonian Simulation via Stochastic Zassenhaus Expansions

Joseph Peetz·Prineha Narang

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Abstract

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.

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Joseph Peetz, Prineha Narang. 2025-01-23. Hamiltonian Simulation via Stochastic Zassenhaus Expansions. https://arxiv.org/abs/2501.13922

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