Linear Combination of Hamiltonian Simulation for Nonunitary Dynamics with Optimal State Preparation Cost

Dong An; Jin-Peng Liu; Lin Lin

doi:10.1103/PhysRevLett.131.150603

Linear Combination of Hamiltonian Simulation for Nonunitary Dynamics with Optimal State Preparation Cost

Phys Rev Lett. 2023 Oct 13;131(15):150603. doi: 10.1103/PhysRevLett.131.150603.

Authors

Dong An¹, Jin-Peng Liu^{2

3

4}, Lin Lin^{2

5

6}

Affiliations

¹ Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA.
² Department of Mathematics, University of California, Berkeley, California 94720, USA.
³ Simons Institute for the Theory of Computing, University of California, Berkeley, California 94720, USA.
⁴ Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
⁵ Lawrence Berkeley National Laboratory, Applied Mathematics and Computational Research Division, Berkeley, California 94720, USA.
⁶ Challenge Institute for Quantum Computation, University of California, Berkeley, California 94720, USA.

PMID: 37897749
DOI: 10.1103/PhysRevLett.131.150603

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. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method with near-optimal dependence on all parameters.