https://doi.org/10.1140/epjqt/s40507-025-00457-9
Research
Testing time order and Leggett-Garg inequalities with noninvasive measurements on public quantum computers
1
Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland
2
Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, ul. Bartycka 18, 00-716, Warsaw, Poland
3
Center of Excellence in Artificial Intelligence, AGH University, al. Mickiewicza 30, 30-059, Cracow, Poland
4
Faculty of Physics, University of Warsaw, ul. Pasteura 5, PL02-093, Warsaw, Poland
5
Faculty of Physics and Applied Informatics, University of Lodz, ul. Pomorska 149/153, PL90-236, Lodz, Poland
6
Departament de Física, Institut d’Aplicacions Computacionals de Codi Comunitari (IAC3), Campus UIB, E-07122, Palma de Mallorca, Balearic Islands, Spain
7
CRISP – Centre de Recerca Independent de sa Pobla, Balearic Islands, 07420, sa Pobla, Spain
8
Fachbereich Physik, Universität Konstanz, D-78457, Konstanz, Germany
a
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Received:
8
November
2025
Accepted:
15
December
2025
Published online:
5
January
2026
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.
Key words: Leggett-Garg inequalities / Weak measurements / Quantum computers / Temporal order / Macrorealism
© The Author(s) 2026
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