  The advent of near-term digital quantum computers could offer us an exciting
opportunity to investigate quantum many-body phenomena beyond that of classical
computing. To make the best use of the hardware available, it is paramount that
we have methods that accurately simulate Hamiltonian dynamics for limited
circuit depths. In this paper, we propose a method to classically optimise
unitary brickwall circuits to approximate quantum time evolution operators. Our
method is scalable in system size through the use of tensor networks. We
demonstrate that, for various three-body Hamiltonians, our approach produces
quantum circuits that can outperform Trotterization in both their accuracy and
the quantum circuit depth needed to implement the dynamics, with the exact
details being dependent on the Hamiltonian. We also explain how to choose an
optimal time step that minimises the combined errors of the quantum device and
the brickwall circuit approximation.
