Hamiltonian Simulation via Stochastic Zassenhaus Expansions

TL;DR

The paper presents stochastic Zassenhaus expansions (SZEs), a novel quantum algorithm for Hamiltonian simulation that reduces circuit depth and error by employing randomized sampling of high-order formulas.

Contribution

Introduces SZEs, a new class of ancilla-free quantum algorithms that use randomized sampling of nested Zassenhaus formulas for efficient Hamiltonian simulation.

Findings

An 11th-order SZE for a 10-qubit model uses 42x fewer CNOTs than standard methods.

Empirical results show SZEs can significantly reduce simulation errors.

SZEs outperform existing algorithms in specific regimes.

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.