• DOI:10.1186/s41313-022-00043-x
• Corpus ID: 232222677

Constant-depth circuits for dynamic simulations of materials on quantum computers

@article{Bassman2022ConstantdepthCF,
  title={Constant-depth circuits for dynamic simulations of materials on quantum computers},
  author={Lindsay Bassman and Roel Van Beeumen and Ed Younis and Ethan Smith and Costin Iancu and Wibe A. de Jong},
  journal={Materials Theory},
  year={2022},
  volume={6},
  pages={1-18}
}

• Lindsay Bassman, R. Van Beeumen, +3 authors W. D. de Jong
• Published 12 March 2021
• Computer Science
• Materials Theory

Dynamic simulation of materials is a promising application for near-term quantum computers. Current algorithms for Hamiltonian simulation, however, produce circuits that grow in depth with increasing simulation time, limiting feasible simulations to short-time dynamics. Here, we present a method for generating circuits that are constant in depth with increasing simulation time for a specific subset of one-dimensional (1D) materials Hamiltonians, thereby enabling simulations out to arbitrarily long times. Furthermore, by removing the effective limit on the number of feasibly simulatable time-steps, the constant-depth circuits enable Trotter error to be made negligibly small by allowing simulations to be broken into arbitrarily many time-steps. For an N -spin system, the constant-depth circuit contains only O ( N 2 ) $\mathcal {O}(N^{2})$ CNOT gates. Such compact circuits enable us to successfully execute long-time dynamic simulation of ubiquitous models, such as the transverse field Ising and XY models, on current quantum hardware for systems of up to 5 qubits without the need for complex error mitigation techniques. Aside from enabling long-time dynamic simulations with minimal Trotter error for a specific subset of 1D Hamiltonians, our constant-depth circuits can advance materials simulations on quantum computers more broadly in a number of indirect ways.