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arXiv · 2104.00728

Fixed Depth Hamiltonian Simulation via Cartan Decomposition

Efekan Kökcü·Thomas Steckmann·Yan Wang·J. K. Freericks·Eugene F. Dumitrescu·Alexander F. Kemper
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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.

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Efekan Kökcü, Thomas Steckmann, Yan Wang, J. K. Freericks, Eugene F. Dumitrescu, Alexander F. Kemper. 2021-04-01. Fixed Depth Hamiltonian Simulation via Cartan Decomposition. https://doi.org/10.1103/physrevlett.129.070501

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