Fixed Depth Hamiltonian Simulation via Cartan Decomposition
Abstract
Simulating quantum dynamics on classical computers is challenging for large systems due to the significant memory requirements. Simulation on quantum computers is a promising alternative, but fully optimizing quantum circuits to minimize limited quantum resources remains an open problem. We tackle this problem presenting a constructive algorithm, based on Cartan decomposition of the Lie algebra generated by the Hamiltonian, that generates quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model, where a O(n^2)-gate circuits naturally emerge. Compared to product formulas with significantly larger gate counts, our algorithm drastically improves simulation precision. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
Keywords
Cite
@article{arxiv.2104.00728,
title = {Fixed Depth Hamiltonian Simulation via Cartan Decomposition},
author = {Efekan Kökcü and Thomas Steckmann and Yan Wang and J. K. Freericks and Eugene F. Dumitrescu and Alexander F. Kemper},
journal= {arXiv preprint arXiv:2104.00728},
year = {2022}
}