Benchmarking quantum simulators using quantum chaos

Benchmarking a quantum device is a central task in quantum science and technology, but remains experimentally challenging. In particular, existing methods either require prohibitively many experimental runs or are not suitable for analog quantum simulators with limited controllability. We propose a benchmarking protocol to estimate the fidelity between an experimentally prepared state and a target state, applicable to any analog quantum device. Our approach utilizes universal statistical fluctuations arising from quantum chaos (suitably defined in our context), which are generically present in many-body dynamics. Therefore, our protocol does not require fine-tuned dynamics, state preparation or measurements. It has a small sample complexity and improves in accuracy with increasing system size. The dominant cost is the computational cost of simulating the target state. We numerically demonstrate our protocol for a variety of quantum simulators such as itinerant particles on optical lattices, trapped ions, or neutral atoms, and discuss applications of our method for parameter estimation.