FET: Small: Foundations of Quantum State Learning and Testing

FET：小型：量子态学习和测试的基础

• 批准号: 1909310
• 负责人: Ryan O'Donnell
• 金额: $ 47万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-10-01 至 2022-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1909310&HistoricalAwards=false
• 关键词: FET; Small; Foundations; Quantum; State

The goal of this project is to advance our scientific understanding of how to most efficiently learn or test the state of a quantum particle system. Whenever researchers/engineers build a quantum device -- say, for a quantum teleportation experiment, or as a component of a quantum computer -- they need to check whether it works as intended. That is, they need to be able to determine the quantum state of the particles it produces. Given enough samples from the device, it is possible to determine the quantum state to any desired accuracy. But due to the expensive nature of quantum experiments, it is important to seek highly efficient strategies for estimating the unknown state, ones that use as few samples as possible. The overarching goal of the project is to try to mathematically determine the optimal samples vs. accuracy tradeoff for problems such as: a) learning an unknown quantum state; b) testing whether an unknown state is equal to a desired target state, etc. Success in the project will tell us the efficiency benchmark against which all practical state-learning methodologies can be judged. Additionally, the project contains a significant educational component involving undergraduate and graduate students in the research effort, and the insights gained will also filter into a free online quantum computing course curriculum.At a more technical level, the project seeks to understand the optimal sample complexity of many basic problems in quantum state tomography and estimation. Proposed problems include: a) estimating a d-dimensional state's eigenvalues using o(d^2) samples; b) quantum tomography and state certification with respect to more stringent measures of accuracy, such as chi-squared divergence; c) testing whether a d x d quantum state is separable (unentangled) or far from separable using o(d^4) samples; d) performing 'm-measurement shadow tomography' with a number of samples linear in log(m) and polylogarithmic in the dimension; and e) improving the computational efficiency of known sample-optimal algorithms. For many of these problems, the investigator plans to use and extend the representation theory-based quantum learning framework developed recently with other researchers.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.

该项目的目标是推进我们对如何最有效地学习或测试量子粒子系统状态的科学理解。 每当研究人员/工程师建造一个量子设备时，比如说，为了量子隐形传态实验，或者作为量子计算机的一个组件，他们需要检查它是否按预期工作。 也就是说，他们需要能够确定它产生的粒子的量子态。 如果从设备中获得足够的样本，就有可能以任何期望的精度确定量子态。 但由于量子实验的昂贵性，重要的是寻求高效的策略来估计未知状态，即使用尽可能少的样本。 该项目的首要目标是尝试在数学上确定最佳样本与准确性权衡的问题，如：a）学习未知的量子状态; B）测试未知状态是否等于所需的目标状态等。 此外，该项目还包含一个重要的教育部分，涉及本科生和研究生的研究工作，所获得的见解也将过滤到一个免费的在线量子计算课程。在更技术的层面上，该项目旨在了解量子态层析成像和估计中许多基本问题的最佳样本复杂性。 提出的问题包括：a）使用o（d^2）个样本估计d维状态的本征值; B）量子层析成像和关于更严格的准确性测量（例如卡方发散）的状态认证; c）测试d × d量子状态是否是可分离的（未纠缠的）或远离可分离的使用o（d^4）样本; d）利用对数（m）线性和维度上的多对数的多个样本执行“m测量阴影断层摄影”;以及e）提高已知样本最佳算法的计算效率。对于其中的许多问题，研究人员计划使用和扩展最近与其他研究人员一起开发的基于表示论的量子学习框架。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。

项目成果

Optimizing strongly interacting fermionic Hamiltonians

• DOI: 10.1145/3519935.3519960
• 发表时间: 2021-10
• 期刊: Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing
• 作者: M. Hastings;R. O'Donnell

Mean estimation when you have the source code; or, quantum Monte Carlo methods

• DOI: 10.48550/arxiv.2208.07544
• 发表时间: 2022-08
• 作者: Robin Kothari;R. O'Donnell

The Quantum Union Bound made easy

• DOI: 10.1137/1.9781611977066.25
• 发表时间: 2021-03
• 作者: R. O'Donnell;R. Venkateswaran

Lower Bounds for Testing Complete Positivity and Quantum Separability

测试完全正性和量子可分离性的下限

• DOI: 10.1007/978-3-030-61792-9_30
• 发表时间: 2020
• 期刊: LATIN 2020: Theoretical Informatics
• 作者: Bădescu, Costin;O'Donnell, Ryan
• 通讯作者: O'Donnell, Ryan

Quantum Approximate Counting with Nonadaptive Grover Iterations

具有非自适应 Grover 迭代的量子近似计数

• DOI: 10.4230/lipics.stacs.2021.59
• 发表时间: 2021
• 期刊: 38th International Symposium on Theoretical Aspects of Computer Science
• 作者: Venkateswaran, Ramgopal;O'Donnell, Ryan
• 通讯作者: O'Donnell, Ryan