Fixed Depth Hamiltonian Simulation via Cartan Decomposition

TL;DR

This paper introduces a Cartan decomposition-based algorithm for quantum Hamiltonian simulation that produces fixed-depth circuits, significantly improving precision and efficiency for certain models compared to traditional methods.

Contribution

The authors present a constructive, Lie algebra-based algorithm for generating fixed-depth quantum circuits for Hamiltonian simulation, applicable to various models and offering enhanced accuracy.

Findings

Produces fixed-depth quantum circuits for Hamiltonian simulation.

Achieves higher precision with fewer gates compared to product formulas.

Provides exact circuits and insights for spin and fermionic models.

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.