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Dynamic simulation of materials is a promising application for near-termquantum computers. Current algorithms for Hamiltonian simulation, however,produce circuits that grow in depth with increasing simulation time, limitingfeasible simulations to short-time dynamics. Here, we present a method forgenerating circuits that are constant in depth with increasing simulation timefor a subset of one-dimensional materials Hamiltonians, thereby enablingsimulations out to arbitrarily long times. Furthermore, by removing theeffective limit on the number of feasibly simulatable time-steps, theconstant-depth circuits enable Trotter error to be made negligibly small byallowing simulations to be broken into arbitrarily many time-steps. Composed oftwo-qubit matchgates on nearest-neighbor qubits, these constant-depth circuitsare constructed based on a set of multi-matchgate identity relationships. Foran $N$-spin system, the constant-depth circuit contains only $\mathcal{O}(N^2)$CNOT gates. When compared to standard Hamiltonian simulation algorithms, ourmethod generates circuits with order-of-magnitude fewer gates, which allows usto successfully simulate the long-time dynamics of systems with up to 5 spinson available quantum hardware. This paves the way for simulations of long-timedynamics for scientifically and technologically relevant quantum materials,enabling the observation of interesting and important atomic-level physics.

Constant-Depth Circuits for Dynamic Simulations of Materials on Quantum Computers