Hamiltonian simulation using quantum singular value transformation: complexity analysis and application to the linearized Vlasov-Poisson equation

Quantum computing can be used to speed up the simulation time (more precisely, the number of queries of the algorithm) for physical systems; one such promising approach is the Hamiltonian simulation (HS) algorithm. Recently, it was proven that the quantum singular value transformation (QSVT) achieves the minimum simulation time for HS. An important subroutine of the QSVT-based HS algorithm is the amplitude amplification operation, which can be realized via the oblivious amplitude amplification or the fixed-point amplitude amplification in the QSVT framework. In this work, we execute a detailed analysis of the error and number of queries of the QSVT-based HS and show that the oblivious method is better than the fixed-point one in the sense of simulation time. Based on this finding, we apply the QSVT-based HS to the one-dimensional linearized Vlasov-Poisson equation and demonstrate that the linear Landau damping can be successfully simulated.