Further Statistical Study of NISQ Experiments

TL;DR

The paper interrogates Google's Formula (77) for predicting quantum-circuit fidelity in the 2019 quantum-supremacy claim, using newly retrieved per-gate fidelities and patch-circuit data to test the claimed accuracy. It finds substantial discrepancies between the published predictions and the data, and shows that readout and gate-error data alone do not explain the observed XEB fidelities, especially for patch circuits. Extending the analysis to other NISQ experiments (Quantinuum RG circuits, Harvard/QuEra neutral atoms, USTC 83-qubit sampling) reveals similar data-access and modelling challenges, with mixed success for refined error models. The work argues for greater data transparency and larger, well-documented samples to reliably assess quantum-supremacy claims and to enable independent verification.

Abstract

We revisit and extend some topics that we studied in our previous works (Rinott, Kalai and Shoham 2022; Kalai, Rinott and Shoham, 2023,2024) regarding the Google 2019 "quantum supremacy" experiment. We extend our analysis of the prediction based on Google's digital error model (Formula (77)), based on more detailed data provided by Google. We also provide some preliminary analysis for a few other NISQ experiments.

Figures (9)

• Figure 1: RGB values and gate error rates for some exemplary Sycamore-53 qubits and gates retrieved from Figure 2b in Aru+19.
• Figure 2: This figure shows the XEB values for the ten full circuits (blue dots) with 26 qubits and the ten 26-qubit patches for the ten patch circuits with 53 qubits and depth 14 (orange dots). The values of the ten orange circuits are consistently higher than those of the ten blue circuits. What could be the physical or engineering reason that the 26-qubit patches exhibit systematically higher XEB values?
• Figure 3: Proportion of measured 1's as a function of circuit depth for Quantinuum's H2 trapped-ion quantum processor DHL+25. Each data point corresponds to one of the 1000 "XEB” circuits.
• Figure 4: XEB and MLE fidelity estimates as a function of circuit size (i.e., the number of qubits, $n$) for Quantinuum's H2 trapped-ion quantum processor DHL+25. The maximum likelihood fidelity estimate (MLE) is calculated by Eq. (4.14) in RSK22 and is restricted to the interval $[0,1]$. For some of the circuits, no MLE solution in [0, 1] exists; these MLE data points are not shown. The different XEB mean values are calculated by using: (1) all values (both within and outside the interval [0,1]), (2) winsorized (values greater than 1 are regarded as 1, negative values are regarded as 0), (3) only the values within the interval [0,1].
• Figure 5: XEB and MLE fidelity estimates as a function of circuit depth for Quantinuum's H2 trapped-ion quantum processor DHL+25. As in Figure \ref{['fig_Quantinuum_XEB_MLE_d12']}, the MLE data points without an MLE solution in [0, 1] are not shown.