Testing time order and Leggett-Garg inequalities with noninvasive measurements on public quantum computers

TL;DR

This paper demonstrates the first violation of Leggett-Garg inequalities and time-order noninvariance on public quantum computers, using noninvasive measurements and weak disturbance protocols to probe foundational quantum principles.

Contribution

It introduces a novel experimental approach on accessible quantum hardware to test fundamental quantum inequalities and temporal order, utilizing fractional gates and weak measurements.

Findings

Violations of Leggett-Garg inequality beyond 5 standard deviations.

Successful implementation of noninvasive weak measurements on public quantum devices.

Quantum hardware deviations from theoretical predictions exceed device error rates.

Abstract

We demonstrate the first violation of the Leggett-Garg inequality and time-order noninvariance on public quantum computers using genuine noninvasive measurements. By gathering sufficiently large statistics, we have been able to violate Leggett-Garg inequality and time-order invariance. The detailed analysis of the data on 10 qubit sets from 5 devices available on IBM Quantum and one on IonQ reveals violations beyond 5 standard deviations in almost all cases. We implemented our protocols using fractional gates, newly available on the IBM Heron devices, allowing us to benchmark them in application to weak measurements. The noninvasiveness is supported by a qualitative and quantitative agreement with the model of weak disturbance. Moreover, our data expose statistically significant deviations from theoretical predictions that exceed declared device error rates, establishing weak measurement protocols as a sensitive benchmark for quantum hardware. These advances transform public quantum computers into practical testbeds for probing foundational questions of realism and temporal order with unprecedented accessibility and precision.