Certification of spin-based quantum simulators

Quantum simulators are engineered devices controllably designed to emulate complex and classically intractable quantum systems. A key challenge lies in certifying whether the simulator is truly mimicking the Hamiltonian of interest. However, neither classical simulations nor quantum tomography are practical to address this task because of their exponential scaling with system size. Therefore, developing novel certification techniques, suitable for large systems, is highly desirable. Here, in the context of fermionic spin-based simulators, we propose a global many-body spin to charge conversion scheme, which crucially does not require local addressability. A limited number of charge configuration measurements performed at different detuning potentials along a spin chain allow to discriminate the low-energy eigenstates of the simulator. This method, robust to charge decoherence, opens the way to certify large spin array simulators as the number of measurements is independent of system size and only scales linearly with the number of eigenstates to be certified.