Quantum simulation of open quantum systems.
Over the last two decades the field of quantum simulations has experienced incredible growth, which, coupled with progress in the development of controllable quantum platforms, has recently begun to allow for the realisation of quantum simulations of a plethora of quantum phenomena in a variety of controllable quantum platforms. Within the context of these developments, we investigate within this thesis methods for the quantum simulation of open quantum systems. More specically, in the first part of the thesis we consider the simulation of Markovian open quantum systems, and begin by leveraging previously constructed universal sets of single-qubit Markovian processes, as well as techniques from Hamiltonian simulation, for the construction of an efficient algorithm for the digital quantum simulation of arbitrary single-qubit Markovian open quantum systems. The algorithm we provide, which requires only a single ancillary qubit, scales slightly superlinearly with respect to time, which given a recently proven no fast-forwarding theorem for Markovian dynamics, is therefore close to optimal. Building on these results, we then proceed to explicitly construct a universal set of Markovian processes for quantum systems of any dimension. Specifically, we prove that any Markovian open quantum system, described by a one-parameter semigroup of quantum channels, can be simulated through coherent operations and sequential simulations of processes from the universal set. Under the assumption that these universal Markovian processes can be efficiently implemented, this allows us to propose an efficient algorithm for a wide class of Markovian open quantum systems, while simultaneously providing a tool for combining and exploiting existing simulation methods. In the second part of this thesis we then consider the simulation of many-body non- Markovian open quantum systems. In particular, we develop an algorithmic procedure for the quantum simulation of system propagators which are not completely positive maps, which allows us to provide an explicit algorithm for the digital quantum simulation of many-body locally-indivisible non-Markovian open quantum systems described by time-dependent master equations. Finally we construct generalised Suzuki-Lie-Trotter theorems which allow us to analyse the efficiency of our method, which is expected to be experimentally achievable for a variety of interesting cases.