arXiv subjects
Publications and source records attributed to Tomer Shoham.
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.
We consider the problem of constructing differentially private nonparametric confidence intervals (CIs) for an arbitrary quantity using resampling. A growing body of work has adapted resampling ideas to the private setting, including private bootstrap methods \cite{brawner2018bootstrap, wang2025differentially,dette2025gaussian} and BLB-based subsample-and-aggregate approaches \cite{covington2025unbiased, chadha2024resampling}. However, existing methods typically rely on strong assumptions, such as asymptotic normality, or are tied to specific privacy mechanisms such as noise addition, and can be impractical in finite-sample regimes. We address these problems by introducing a simple, general framework that can convert any differentially private estimator satisfying mild conditions into a differentially private nonparametric CI for arbitrary target quantities. Our method repeatedly subsamples the data, applies the private estimator to each subset, and post-processes the resulting empirical CDF into a CI. The framework is black-box, and does not require a specific limiting distribution. We prove that the empirical CDF induced by our procedure converges to the sampling distribution of the private statistic, which implies that the resulting CI is asymptotically valid and tight, and provide heuristic guidance for choosing the hyperparameters. Empirically, our method outperforms competing general approaches, especially for non-smooth functionals and more challenging distributions.
Ratio statistics--such as relative risk and odds ratios--play a central role in hypothesis testing, model evaluation, and decision-making across many areas of machine learning, including causal inference and fairness analysis. However, despite privacy concerns surrounding many datasets and despite increasing adoption of differential privacy, differentially private ratio statistics have largely been neglected by the literature and have only recently received an initial treatment by Lin et al. [1]. This paper attempts to fill this lacuna, giving results that can guide practice in evaluating ratios when the results must be protected by differential privacy. In particular, we show that even a simple algorithm can provide excellent properties concerning privacy, sample accuracy, and bias, not just asymptotically but also at quite small sample sizes. Additionally, we analyze a differentially private estimator for relative risk, prove its consistency, and develop a method for constructing valid confidence intervals. Our approach bridges a gap in the differential privacy literature and provides a practical solution for ratio estimation in private machine learning pipelines.
Considerable effort in experimental quantum computing is devoted to noisy intermediate scale quantum computers (NISQ computers). Understanding the effect of noise is important for various aspects of this endeavor including notable claims for achieving quantum supremacy and attempts to demonstrate quantum error correcting codes. In this paper we use Fourier methods combined with statistical analysis to study the effect of noise. In particular, we use Fourier analysis to refine the linear cross-entropy fidelity estimator. We use both analytical methods and simulations to study the effect of readout and gate errors, and we use our analysis to study the samples of Google's 2019 quantum supremacy experiment.
In October 2019, Nature published a paper [6] describing an experimental work that was performed at Google. The paper claims to demonstrate quantum (computational) supremacy on a 53-qubit quantum computer. Since then we have been involved in a long-term project to study various statistical aspects of the Google experiment. In [30] we studied Google's statistical framework that we found to be very sound and offered some technical improvements. This document describes three main concerns (based on statistical analysis) about the Google 2019 experiment. The first concern is that the data do not agree with Google's noise model (or any other specific model). The second concern is that a crucial simple formula for a priori estimation of the fidelity seems to involve an unexpected independence assumption, and yet it gives very accurate predictions. The third concern is about statistical properties of the calibration process.
In October 2019, Nature published a paper describing an experiment that took place at Google. The paper claims to demonstrate quantum (computational) supremacy on a 53-qubit quantum computer. Since September 2019 we have been involved in a long-term project to study various statistical aspects of the Google experiment. We have been trying to gather the relevant data and information in order to reconstruct and verify those parts of the Google experiment that are based on classical computations (except when the required computation is too heavy), and to perform a statistical analysis on the data. This document describes the available data and information for the Google experiment, some main questions in the evaluation of the experiment, and some of our results and plans.
We consider a dataset $S$ held by an agency, and a vector query of interest, $f(S) \in \mathbb{R}^k$, to be posed by an analyst, which contains the information required for certain planned statistical inference. The agency releases the requested vector query with noise that guarantees a given level of Differential Privacy -- DP$(\varepsilon,δ)$ -- using the well-known Gaussian mechanism. The analyst can choose to pose the vector query $f(S)$ or to adjust it by a suitable transformation that can make the agency's response more informative. For any given level of privacy DP$(\varepsilon,δ)$ decided by the agency, we study natural situations where the analyst can achieve better statistical inference by adjusting the query with a suitable simple explicit transformation.
The notable claim of quantum supremacy presented by Google's team in 2019 consists of demonstrating the ability of a quantum circuit to generate, albeit with considerable noise, bitstrings from a distribution that is considered hard to simulate on classical computers. Verifying that the generated data is indeed from the claimed distribution and assessing the circuit's noise level and its fidelity is a purely statistical undertaking. The objective of this paper is to explain the relations between quantum computing and some of the statistical aspects involved in demonstrating quantum supremacy in terms that are accessible to statisticians, computer scientists, and mathematicians. Starting with the statistical analysis in Google's demonstration, which we explain, we study various estimators of the fidelity, and different approaches to testing the distributions generated by the quantum computer. We propose different noise models, and discuss their implications. A preliminary study of the Google data, focusing mostly on circuits of 12 and 14 qubits is discussed throughout the paper.