We propose a simple method for simulating a general class of non-unitary 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 non-unitary processes, such as the quantum singular value transformation (QSVT). 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.
Ref: [1] Dong An, Jin-Peng Liu, Lin Lin. Physical Review Letters, 131(15):150603, 2023.

My name is Jin-Peng Liu (刘锦鹏). I am a Tenure Track Assistant Professor at YMSC, Tsinghua University.
 I was a Postdoctoral Associate at Center for Theoretical Physics, MIT, hosted by Aram Harrow in 2023-2024. I was a Simons Quantum Postdoctoral Fellow at Simons Institute, UC Berkeley, hosted by Umesh Vazirani and Lin Lin in 2022-2023.
 I received my Ph.D. in AMSC at University of Maryland in 2022, advised by Andrew Childs. I received my B.S. in Hua Loo Keng Class at Beihang and Chinese Academy of Sciences in 2017, supervised by Ya-xiang Yuan.
 My research focuses on Quantum for Science and AI+QS. I attempt to develop, analyze, and optimize provably efficient quantum algorithms for science and AI problems, including topics: (i) robust quantum simulations; (ii) efficient quantum scientific computation; (iii) scalable quantum machine learning, toward end-to-end applications in areas such as quantum chemistry, biology and epidemiology, fluid dynamics, finance, machine learning, and artificial general intelligence.