AppQSim: Application-oriented benchmarks for Hamiltonian simulation on a quantum computer

We introduce AppQSim, a benchmarking suite for quantum computers focused on applications of Hamiltonian simulation. We consider five different settings for which we define a precise task and score: condensed matter and material simulation (dynamic and static properties), nuclear magnetic resonance simulation, chemistry ground-state preparation, and classical optimization. These five different benchmark tasks display different resource requirements and scalability properties. We introduce a metric to evaluate the quality of the output of a tested quantum hardware, called distinguishability cost, defined as the minimal number of gates that a perfect quantum computer would have to run to certify that the output of the benchmarked hardware is incorrect.