Linear Combination of Hamiltonian Simulation for Nonunitary Dynamics

ORAL · Invited

Abstract

We propose a simple method for simulating a general class of nonunitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem or on the spectral mapping theorem. The latter is the mathematical foundation of many quantum algorithms for solving a wide variety of tasks involving nonunitary processes, such as the quantum singular value transformation. The LCHS method can achieve optimal cost in terms of state preparation, and an improved LCHS method further achieves near-optimal dependence on all parameters in terms of matrix queries. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method.

* This work is supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator, the U.S. Department of Defense, the NSF QLCI program, and the Simons Quantum Postdoctoral Fellowship.

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Publication: 1. Dong An, Jin-Peng Liu, and Lin Lin. Linear Combination of Hamiltonian Simulation for Nonunitary Dynamics with Optimal State Preparation Cost. Phys. Rev. Lett. 131, 150603.
2. Dong An, Andrew M. Childs, and Lin Lin. Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters. In preparation.

Presenters

  • Dong An

    University of Maryland

Authors

  • Dong An

    University of Maryland

  • Andrew M Childs

    University of Maryland

  • Lin Lin

    University of California, Berkeley

  • Jin-Peng Liu

    Massachusetts Institute of Technology, University of Maryland