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

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.