FET: Small: Collaborative Research: Efficient and Robust Characterization of Quantum Systems

量子信息和算法的进步使传统技术无法企及的解决方案得以实现，应用于多体量子物理、化学、密码学、通信和机器学习。虽然量子计算机的原型正在建造中，但它们仍然容易出错：将噪声降低到可容忍和可控的水平面临着技术障碍。为了能够扩展到成熟的量子计算机，必须对当前和不久的将来原型的行为进行表征、验证和严格认证。后一项任务在数据采集、处理和存储方面带来了沉重的负担，因此迫切需要高效、抗噪声的表征和验证协议来测试当前的量子器件。该研究小组成员在新的优化理论和算法、压缩感知和验证技术方面所做的工作对这一问题有直接的应用。该项目将研究并提出新颖、高效、稳健的方法来表征、验证和认证量子系统实现的行为，以更好地获取和处理量子信息。该研究将对如何在现代数据科学应用中使用非凸算法产生积极影响。这项提案的关键成果将是建立一个学术-行业合作（在这个过程中有两名学生的指导），并在莱斯大学引入量子计算课程。该项目专注于对量子态和过程进行基准测试和测试，通过高效、抗噪声和可证明的量子态断层扫描，以及用于量子计算的新型验证和认证工具。本研究提出探索新的理论和实践方法，通过以下三个途径：i)通过可证明的方法来分布非凸计算和优化大规模量子态层析成像任务。所提出的方法补充了压缩感知量子态层析成像的设置，其中只有少数测量-与完整层析成像相比-可以从低秩（高纯）量子态中获得，并将用于最先进方法无法达到的设置中。ii)通过使用抗噪声优化和技术对最先进的验证方法进行鲁棒化。提出的研究涉及新的，定制的非凸算法的情况下，测量被非均匀噪声污染。iii)通过设计有效和抗噪声的方案来验证和证明与实验相关的量子操作。该项目将研究验证门和错误模型行为的方案，这反过来将有助于证明基本物理操作的质量。该提案的结果将作为开源软件框架的一部分公开提供，以提高可用量子信息处理器的可重复性。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Advances in quantum information and algorithms enable solutions that are beyond the reach of conventional technologies, with applications in many-body quantum physics, chemistry, cryptography, communication, and machine learning. While prototypes for quantum computers are being built, these are still prone to errors: reducing the noise to a tolerable and controllable level faces technical hurdles. To be able to scale-up to a full-fledged quantum computer, it is imperative to characterize, verify, and rigorously certify the behavior of current and near-future prototypes. The latter task incurs a heavy burden in data acquisition, processing and storage that leads to a pressing need for efficient and noise-robust characterization and verification protocols to test current quantum devices. The work done by members of this research team on novel optimization theory and algorithms, compressed sensing, and verification techniques have direct applications to this problem. The project will investigate and propose novel, highly-efficient, and robust methodologies to characterize, verify, and certify the behavior of quantum systems implementations, for better acquisition and processing of quantum information. The research will affect positively on how non-convex algorithms could be used in modern data science applications. Key broader outcomes of this proposal will be the establishment of an academic-industry collaboration (with the mentorship of two students in the process), and the introduction of quantum computing courses to Rice University.This project focuses on benchmarking and testing quantum states and processes, through efficient, noise-robust and provable quantum state tomography, as well as novel validation and certification tools for quantum computing. This research proposes to investigate new theoretical and practical approaches, via the following three paths: i) By using provable methods for distributing non-convex computations and optimization for the task of large-scale quantum state tomography. The proposed method complements the setting of compressed sensing quantum state tomography, where only a few measurements --compared to full tomography-- are available from a low-rank (highly-pure) quantum state and will be used in settings that are beyond the reach of state-of-the-art approaches. ii) By robustifying state-of-the-art validation methods using noise-robust optimization and techniques. The proposed research involves new, customized non-convex algorithms for the case where measurements are contaminated with non-homogeneous noise. iii) By designing efficient and noise-robust schemes for validating and certifying experimentally-relevant quantum operations. This project will study schemes to validate gates and error models behavior, which in turn will help certify the quality of the basic physical operations. The results of this proposal will be publicly available as an integrated part of an open-source software framework, in order to enhance reproducibility on available quantum information processors.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.