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实现的解决方案成为可能，并应用于多体量子物理学，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。为了能够扩展到一个成熟的量子计算机，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，这导致迫切需要高效且噪声鲁棒的表征和验证协议来测试当前的量子设备。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直接应用于这个问题。该项目将研究并提出新颖，高效和强大的方法来表征，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。这项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。该项目的主要成果是建立学术界与产业界的合作（在此过程中有两名学生担任导师），并在莱斯大学引入量子计算课程。该项目的重点是通过高效、抗噪声和可证明的量子态层析成像以及新颖的量子计算验证和认证工具，对量子态和过程进行基准测试和测试。 本研究提出通过以下三条途径研究新的理论和实践方法：i）通过使用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状态断层扫描的设置，其中只有少数测量-与完整的断层扫描相比-可从低秩（高纯）量子状态获得，并将用于超出最先进方法范围的设置。ii）通过使用噪声鲁棒优化和技术来增强最先进的验证方法。所提出的研究涉及新的，定制的非凸算法的情况下，测量被污染的非均匀噪声。iii）通过设计有效和抗噪声的方案来验证和证明实验相关的量子操作。这个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个组成部分公开提供，以提高现有量子信息处理器的可重复性。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

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.