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 by presenting a constructive algorithm, based on Cartan decomposition of the Lie algebra generated by the Hamiltonian, which 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 O(n2)-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.
Original language | English |
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Article number | 070501 |
Journal | Physical Review Letters |
Volume | 129 |
Issue number | 7 |
DOIs | |
State | Published - Aug 12 2022 |
Funding
The ideation, formal development, code development, and manuscript writing were supported by the Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award No. DE-SC0019469 (E. K., T. S., J. K. F., and A. F. K.). Final revision and editing was supported by the National Science Foundation under Grant No. PHY-1818914 (E. K. and A. F. K.). J. F. K. was also supported by the McDevitt bequest at Georgetown University. E. F. D. acknowledges DOE ASCR funding under the Quantum Computing Application Teams program, FWP No. ERKJ347. T. S. was supported in part by the U.S. Department of Energy, Office of Science, Office of Workforce Development for Teachers and Scientists (WDTS) under the Science Undergraduate Laboratory Internship program. Y. W. acknowledges DOE ASCR funding under the Quantum Application Teams program, FWP No. ERKJ335.