Linear Combination of Hamiltonian Simulation for Nonunitary Dynamics*

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.