Locality and Digital Quantum Simulation of Power-Law Interactions

The propagation of information in non-relativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We show that Lieb-Robinson bounds provide tighter estimates for the gate count in quantum algorithms for simulating power-law interacting Hamiltonians. In addition, we prove new Lieb-Robinson bounds using techniques from quantum simulation algorithms. This brings the analysis full circle, revealing a deep connection between Lieb-Robinson bounds and digital quantum simulation.