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

TL;DR

It is shown that the violation of Macrorealism (MR) provides a fruitful avenue to this aim, and two QCs are benchmarked using the proposed NDC metric, showing a three-fold improvement in their quantumness from one generation to the next.

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.

Figures (4)

• Figure 1: Diagram of the circuit implementing the parity NDC protocol on $N$-qubits via (i) an initial rotation, (ii) a parity measurement classically-controlled by bit $c_p$, (iii) a second rotation, and (iv) a final parity measurement.
• Figure 2: Circuits implementing (a) the H-method and (b) the M-method of the parity NDC protocol on an ensemble of $N$ qubits ($q_{1},...,q_N$) with two ancilla qubits ($a_{1}$, $a_2$) for implementing $N$-qubits parity measurements with outcomes stored in $2$ classical bits ($c_{1}$ and $c_{2}$), and a classical bit ($c_p$), which controls the intermediate measurement via: (a) classically controlling a Hadamard gate applied on the ancilla $a_1$ (the gate is implemented when $c_p=0$), or (b) classically controlling a mid-circuit $Z$-measurement on the ancilla $a_1$ (the measurement is implemented when $c_p=1$). The legend is given in (c).
• Figure 3: Violation of MR via the parity NDC protocol as a function of the rotation angle $\theta$ for the (a) H-Method and (b) M-Method, in the ideal case (green line), and the one detected in ibm_brisbane (red line) and ibm_marrakesh (blue line) QCs.
• Figure 4: Violation of MR detected on IBM QCs via the parity NDC protocol as a function of the number of qubits $N$ (with $\theta=\pi/4$) implementing (a) the H-method and (b) the M-method, both used to benchmark ibm_brisbane and ibm_marrakesh QCs; The methods are clumsy-loophole free on both QCs as shown in (c), with $\theta=\pi$, as the detected unmitigated CDs (orange line) was reduced to zero within statistical error (purple line).