发表机构
University of Colorado, Boulder（科罗拉多大学博尔德分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对量子保真度估计缺乏严格不确定性量化的问题，本文提出贝叶斯启发的共形预测框架，结合经典与神经网络点估计器，在多类实验挑战下验证其鲁棒性，为量子系统验证提供可靠方法。
AI 中文摘要
量子保真度估计是量子信息与计算领域的一项基础任务，用于在含噪声量子硬件上对量子态及量子过程的质量进行基准测试。现有方法得到的保真度点估计通常缺乏可靠执行和验证这些任务所需的严格不确定性量化。尽管贝叶斯框架和自助法被广泛用于不确定性量化，但它们对模型误设较为敏感，或在非渐近 regime 中缺乏形式化的覆盖保证。本文提出一种混合的“贝叶斯启发”共形预测框架，用于为量子态保真度估计提供无分布的严格预测区间，该框架经谨慎使用可近似与玻恩定则的量子随机性相关的置信区间。该框架需要一个点估计器，我们同时考虑经典点估计器和数据驱动的神经网络估计器。我们在多种不同的实验挑战下评估该方法的鲁棒性，包括有限样本噪声、层析不完备性、物理模型误差和分布外数据。结果表明，共形化估计器在传统方法失效的情况下仍能保持统计有效性，为现代量子系统的验证提供了一种可扩展且可靠的方法。我们的方法中表现最佳的变体基于类条件共形预测，因为它最接近真实置信区间所需的条件覆盖。
英文摘要
Quantum fidelity estimation is a fundamental task in quantum information and computing to benchmark the quality of quantum states, and hence of quantum processes, on noisy quantum hardware. Point estimates of fidelity by existing methods generally lack the rigorous uncertainty quantification required for reliable preparation and verification of these tasks. While Bayesian and bootstrap frameworks are widely used for uncertainty quantification, they are sensitive to model misspecification or lack formal coverage guarantees in non-asymptotic regimes. This paper introduces a hybrid "Bayesian-informed" conformal prediction-based framework to provide distribution-free, rigorous prediction intervals for quantum state fidelity estimation which can be used, with care, to approximate confidence intervals with respect to the quantum randomness of Born's rule. The framework requires a point estimator, and we consider both classical point estimators as well as data-driven neural net estimators. We evaluate the robustness of the methodology across a diverse range of experimental challenges, including finite-sample noise, tomographic incompleteness, physical model error, and out-of-distribution data. Our results demonstrate that conformalized estimators maintain statistical validity where traditional methods fail, offering a scalable and reliable approach for the verification of modern quantum systems. The best performing variant of our methodology is based on a class-conditional conformal prediction, as this most closely approximates the conditional coverage desired for a true confidence interval.
Comments18 pages, 9 figures
