Variational algorithms for quantum dynamics with short depth quantum circuits

Quantum dynamics is the quintessential application of quantum computers. The naive approach to quantum dynamics requires quantum circuits of depth that scales linearly with the duration of time evolution. However, near-term quantum computers suffer from short coherence time and gate infidelities, which limit the depth of the circuits they can reliably run. Under the assumption of a fixed depth budget, it is interesting to ask what quantum algorithm is best suited to maximizing fidelity with the exactly evolved state. In this work we develop algorithmic approaches to this problem and explore the various trade-offs between the quantum resources involved. We further benchmark these approaches on various model systems.