We describe a protocol for cross-platform verification of quantum simulators and quantum computers. We show how to measure directly the overlap Tr[rho(1) rho(2)] and the purities Tr[rho(2)(1)(,2)], and thus a fidelity of two, possibly mixed, quantum states rho(1) and rho(2) prepared in separate experimental platforms. We require only local measurements in randomized product bases, which are communicated classically. As a proof of principle, we present the measurement of experiment-theory fidelities for entangled 10-qubit quantum states in a trapped ion quantum simulator.
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