How "Quantum" is your Quantum Computer? Macrorealism-based Benchmarking via Mid-Circuit Parity Measurements

Abstract: To perform meaningful computations, Quantum Computers (QCs) must scale to macroscopic levels - i.e., to a large number of qubits - an objective pursued by most quantum companies. How to efficiently test their quantumness at these scales? We show that the violation of Macrorealism (MR), being the fact that classical systems possess definite properties that can be measured without disturbances, provide a fruitful avenue to this aim. The No Disturbance Condition (NDC) - the equality used here to test MR - can be violated by two consecutive parity measurements on $N$ qubits and found to be independent of $N$ under ideal conditions. However, realistic noisy QCs show a quantum-to-classical transition as $N$ increases, giving a foundationally-motivated scalable benchmarking metric. Two methods are formulated to implement this metric: one that involves a mid-circuit measurement, probing the irreversible collapse of the wavefunction, in contrast to the reversible entanglement generated in the other. Both methods are designed to be clumsiness-loophole free: the unwanted classical disturbances are negligible within statistical error. Violation of MR is detected on a IBM QC up to $N = 38$ qubits, increasing $N$ by one order of magnitude over best known results of MR. Two QCs are benchmarked using the proposed NDC metric, showing a three-fold improvement in their quantumness from one generation to the next.