Bounds on Trotter Depth for Quantum Simulation of Some Important Condensed Matter Models

Trotterization of quantum algorithms is typically regarded as a difficult problem in the context of quantum computing because the Trotterized algorithmic complexity is estimated to scale prohibitively with the number of particles in the system. Typical complexity estimates are given in several orders of magnitude even for a relatively small number of particles. Nevertheless, information can still be obtained regarding the difficulty by comparing the relative scaling of the Trotter depth. In this way, we can determine which models will be of greater or lesser utility as quantum technology advances and the algorithms themselves become tractable. We consider some representative models and algorithms and compare their relative complexity. We also present novel methods for calculating the Trotter error based on their physical considerations. We draw conclusions regarding which models are more or less tractable for near-term quantum devices.