Experimental violations of Leggett-Garg's inequalities on a quantum computer

TL;DR

This paper experimentally demonstrates violations of Leggett-Garg inequalities on IBM Quantum hardware, introduces Leggett-Garg-Bell's inequalities for multi-qubit systems, and assesses their effectiveness as quantum coherence witnesses.

Contribution

The study introduces Leggett-Garg-Bell's inequalities for multi-qubit systems and evaluates their practicality as coherence witnesses on current quantum hardware.

Findings

Violations of Leggett-Garg inequalities observed on quantum hardware.

Leggett-Garg-Bell's inequalities are efficient for coherence detection.

Quantum errors affect the measurement of correlation functions.

Abstract

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.