Fixed Depth Hamiltonian Simulation via Cartan Decomposition

• URL: http://arxiv.org/abs/2104.00728v4
• Date: Wed, 29 Jun 2022 19:20:03 GMT
• Title: Fixed Depth Hamiltonian Simulation via Cartan Decomposition
• Authors: Efekan K\"okc\"u, Thomas Steckmann, Yan Wang, J. K. Freericks, Eugene F. Dumitrescu, Alexander F. Kemper
• Abstract summary: We present a constructive algorithm for generating 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. 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.
• Score: 59.20417091220753
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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