Direct Estimates and Confidence Intervals for Fidelity of Quantum States

量子态保真度的直接估计和置信区间

• 批准号: 2112901
• 负责人: Stephen Becker
• 金额: $ 24.9万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2112901&HistoricalAwards=false
• 关键词: Direct; Estimates; Confidence; Intervals; Fidelity

Quantum mechanics is science's most detailed theory of the physical world, and fully exploiting quantum mechanics is enabling new technologies such as quantum computers. A fundamental requirement when building quantum systems is to verify that the experimentalist has actually built what they intended to build. For this reason, experimentalists test quantum systems by taking (inherently probabilistic) measurements. The aim of this project is to process these measurements in a new way in order to give a more accurate and reliable estimate of how much the actual quantum state differs from the intended quantum state. This more reliable verification procedure is an important step in constructing fault-tolerant quantum computers, and as such, this project contributes toward creating useful quantum computers. Thus the broader impact of the project includes the potential impacts of quantum computing, as well as generally contributing to the progress of science.The technical goal of the project is to estimate the fidelity between two quantum states with high certainty; in particular, the proposed method produces a rigorous confidence interval within which the fidelity lies (within a desired probability of failure). The approach is novel in the field, as it uses a computationally constructed statistic, and is applied directly to the raw data without requiring data-averaging or full tomography. The method has advantages over existing direct methods as well as over maximum likelihood tomography methods. The intellectual contributions of the proposed work will be showing that the certification problem fits inside a very specific existing statistical framework, deriving the estimators and solving related optimization problems, and extending both the theory and applications, e.g., to quantum channels and entanglement witnesses.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.

量子力学是科学上对物理世界最详细的理论，充分利用量子力学正在使量子计算机等新技术成为可能。在构建量子系统时，一个基本要求是验证实验者是否真的建造了他们想要建造的东西。出于这个原因，实验者通过测量(本质上是概率的)测量来测试量子系统。这个项目的目的是以一种新的方式处理这些测量，以便更准确和可靠地估计实际量子态与预期量子态的差异有多大。这一更可靠的验证过程是构建容错量子计算机的重要一步，因此，该项目有助于创造有用的量子计算机。因此，该项目的更广泛的影响包括量子计算的潜在影响，以及总体上对科学进步的贡献。该项目的技术目标是以高确定性估计两个量子态之间的保真度；特别是，所提出的方法产生一个严格的置信度区间，保真度位于该区间内(在期望的失败概率内)。这种方法在该领域是新颖的，因为它使用了计算构造的统计量，并且直接应用于原始数据，而不需要数据平均或全面层析。该方法不仅优于现有的直接方法，也优于最大似然层析成像方法。拟议工作的智力贡献将表明，认证问题符合非常具体的现有统计框架，推导估计器并解决相关的优化问题，并将理论和应用扩展到量子通道和纠缠目击者。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。