Quantum algorithms for Hamiltonian simulation

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The Hamiltonian of a quantum system dictates its dynamics completely. The computation of these dynamics under a particular Hamiltonian is called the Hamiltonian simulation problem, and it allows prediction of the system behavior. Despite significant progress in Hamiltonian simulation on classical computers over the past century, the Hamiltonian simulation problem has remained an extremely challenging task over the past century due to the curse of dimensionality as the computation costs grow exponentially with system size. One of the motivations for Feynman's 1982 proposal for the design of quantum computers was in response to this problem. The aim of this PhD project is to develop quantum algorithms for Hamiltonian simulation. These include algorithms inspired by classical splitting methods, as well as variational quantum algorithms involving quantum circuit optimization.