Fixed Depth Hamiltonian Simulation via Cartan Decomposition

• Published in: arXiv.org
• Main Authors: Kökcü, Efekan, Steckmann, Thomas, Wang, Yan, Freericks, J K, Dumitrescu, Eugene F, Kemper, Alexander F
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 29.06.2022
• Subjects: Algorithms; Decomposition; Evolutionary algorithms; Gate counting; Gates (circuits); Lie groups; Physics - Quantum Physics; Physics - Strongly Correlated Electrons; Quantum computers; Quantum computing; Qubits (quantum computing); Simulation
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2104.00728

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.