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

TL;DR

The paper addresses fundamental questions about realism and temporal order in quantum mechanics by testing Leggett-Garg inequalities (LGIs) and time-order noninvariance using genuinely noninvasive weak measurements on public quantum computers. It develops a POVM-based weak-measurement framework with tunable strength $\lambda$ and implements two protocols on IBM and IonQ hardware, including fractional gates on IBM Heron, to realize noninvasive detectors. The experiments show LG violations and time-order differences across multiple 3-qubit groups, with violations exceeding classical bounds by large margins and strong concordance with the weak-measurement model, while also revealing device-specific calibration effects. The work demonstrates that public quantum devices can serve as practical, reproducible testbeds for foundational questions and provides a sensitive hardware benchmark for weak measurements and temporal-order tests in near-term quantum systems.

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.

Figures (27)

• Figure 1: The scheme of weak measurement. The system $S$ interacts with the ancillary detector $D$ which gains information from the weakly-measured system scaled by the measurement strength $\lambda$, while causing disturbance to the system of the order $\lambda^2$.
• Figure 2: The detection scheme to test LG inequalities and weak order of measurements. Two weak detectors of $A$ and $B$ measure the state $\rho$ before the final measurement $C$. The time order of the measurement is from the left to the right: $A\to B\to C$ in the upper and $B\to A\to C$ in the lower case.
• Figure 3: The notation of the $ECR$ gate in the convention $ECR_\downarrow|ab\rangle$.
• Figure 4: Protocol (I) with a single $CX$ gate. Weak measurement of $Z$ on the upper qubit, by the lower (meter) qubit with the strength of the measurement defined by $\sin\theta$. The control and target qubit are depicted by $\bullet$ and $\oplus$ respectively.
• Figure 5: Protocol (I) with a single $CZ$ gate and a fractional $RX$, represented by $X_\theta$. Weak measurement of $Z$ on the upper qubit, by the lower (meter) qubit with the strength of the measurement defined by $\sin\theta$. The $CZ$ gate is depicted as linked $\bullet$ (the gate is symmetric).

Theorems & Definitions (1)

• Theorem 1