01182nas a2200145 4500008004100000245011000041210006900151260001500220490000800235520071200243100001300955700001800968700001300986856003700999 2023 eng d00aLinear combination of Hamiltonian simulation for non-unitary dynamics with optimal state preparation cost0 aLinear combination of Hamiltonian simulation for nonunitary dyna c10/13/20230 v1313 a

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.

1 aAn, Dong1 aLiu, Jin-Peng1 aLin, Lin uhttps://arxiv.org/abs/2303.0102901051nas a2200133 4500008004100000245010100041210006900142260001400211520060600225100001300831700002300844700001300867856003700880 2023 eng d00aQuantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters0 aQuantum algorithm for linear nonunitary dynamics with nearoptima c12/6/20233 a

We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially enhance the accuracy of the recently introduced linear combination of Hamiltonian simulation (LCHS) method [An, Liu, and Lin, Physical Review Letters, 2023]. For the first time, this approach enables quantum algorithms to solve linear differential equations with both optimal state preparation cost and near-optimal scaling in matrix queries on all parameters.

1 aAn, Dong1 aChilds, Andrew, M.1 aLin, Lin uhttps://arxiv.org/abs/2312.0391601292nas a2200157 4500008004100000245012000041210006900161260000800230300000800238490000600246520080400252100001301056700001301069700001301082856003901095 2022 eng d00aTime-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schrödinger Equation0 aTimedependent Hamiltonian Simulation of Highly Oscillatory Dynam capr a6900 v63 a

We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm that is both insensitive to the rapid changes of the time-dependent Hamiltonian and exhibits commutator scaling. Our method can be used for efficient Hamiltonian simulation in the interaction picture. In particular, we demonstrate that for the simulation of the Schrödinger equation, our method exhibits superconvergence and achieves a surprising second order convergence rate, of which the proof rests on a careful application of pseudo-differential calculus. Numerical results verify the effectiveness and the superconvergence property of our method.

1 aAn, Dong1 aFang, Di1 aLin, Lin uhttps://arxiv.org/abs/2111.03103v2