Detector Readout of Analog Quantum Simulators

An important step in quantum simulation is to measure the many-body correlations of the simulated model. For a practical quantum simulator composed of a finite number of qubits and cavities, in contrast to many-body systems in the thermodynamic limit, a measurement device can generate strong backaction on the simulator, which could prevent the accurate readout of the correlation functions. Here we calculate the readout of a detector coupled to analog quantum simulators. We show that reliable characterization of the many-body correlations of the simulators can be achieved when the coupling operators obey the Wick’s theorem. Our results are illustrated with two examples: a simulator for an harmonic oscillator and a simulator for the free electron gas. We also present a method, which under certain constraints, allows for the reconstruction of the ideal correlators from the measurements on a perturbed quantum simulator.