Experimental violations of Leggett-Garg's inequalities on a quantum
  computer
Leggett-Garg's inequalities predict sharp bounds for some classical
correlation functions that address the quantum or classical nature of real-time
evolutions. We experimentally observe the violations of these bounds on single-
and multi-qubit systems, in different settings, exploiting the IBM Quantum
platform. In the multi-qubit case we introduce the Leggett-Garg-Bell's
inequalities as an alternative to the previous ones. Measuring these
correlation functions, we find quantum error mitigation to be essential to spot
inequalities violations. Accessing only two qubit readouts, we assess
Leggett-Garg-Bell's inequalities to emerge as the most efficient quantum
coherence witnesses to be used for investigating quantum hardware, as the
complexity of their calculation does not scale with the number of constituents
of the system. Our analysis highlights the limits of nowadays quantum
platforms, showing that the above-mentioned correlation functions deviate from
theoretical prediction as the number of qubits and the depth of the circuit
grow.
Alessandro Santini Vittorio Vitale