Abstract

Quantum simulation, which is generically the task to employ quantum computers to simulate quantum physical models, has been one of the most significant motivations and applications of quantum computing. Quantum dynamics, unitary or nonunitary Markovian dynamics driven by local interactions, has been proved to be efficiently simulatable on quantum computers. Extending the underlying models in quantum computation and quantum simulation from unitary to general nonunitary evolution, and from continuous-time to discrete-time evo-lution is essential not only for quantum simulation of more general processes, e.g., dissipative processes with evident non-Markovian effects, but also for developing alternative quantum computing models and algorithms. In this thesis, we explore quantum simulation problems mainly from the following three themes. First, we extend quantum simulation framework of Hamiltonian-driven evolution to quan-tum simulation of quantum channels, combined with the scheme of algorithmic simulation that accepts a promised simulation accuracy, hence algorithmic quantum channel simulation. Our simulation scheme contains a classical preprocessing part, i.e. a classical algorithm for