Extracting Spectral Information from Noisy Quantum Data

量子计算描述了一种利用量子力学原理来解决科学和工程问题的创新计算方法。量子计算机的现有实现非常容易受到不想要的外部干扰，即所谓的“退相干”，这会导致量子信息的丢失。这种退相干对可以在量子计算机上有效模拟的问题的范围造成了很大的限制。在模拟物理上相关的和技术上有重要意义的量子力学系统的性质时，例如分子或固体，这种限制尤其严重。然而，关于这些系统的数学和物理性质存在着大量的知识。该项目旨在利用这一洞察力来提高量子计算机上量子力学模拟的准确性。它将通过设计精确而实用的方法来降低噪声和提高精度，从而促进科学的进步。到目前为止，所有建造的量子计算机都存在噪声和消相干问题。当量子计算机被用来模拟凝聚态和量子化学中的分子和固体的性质时，人们感兴趣的主要性质是编码在响应函数谱中的激发信息。这种光谱信息具有严格限制允许响应函数的数学特性，因此可以用作量子计算数据的“噪声过滤器”。这个项目将研究如何在实际算法中使用这些数学信息来降低量子数据的噪声。提出了使用合成数据和来自当今量子计算机的数据的实现和测试。此外，与密歇根大学自然历史博物馆的外展合作将向学校和图书馆的公众介绍包括量子相干在内的量子现象。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。

Quantum computing describes an innovative approach to computing that utilizes the principles of quantum mechanics to solve problems in science and engineering. Existing implementations of quantum computers are highly susceptible to unwanted external disturbances, known as “decoherence”, which result in the loss of quantum information. This decoherence poses a significant constraint on the range of problems that can be simulated effectively on quantum computers. The limitation is especially severe in the simulation of properties of physically relevant and technologically significant quantum mechanical systems, such as molecules or solids. However, substantial knowledge exists regarding the mathematical and physical properties of these systems. This project aims to leverage this insight to improve the accuracy of quantum mechanical simulations on quantum computers. It will do so by designing precise and practical methodologies for reducing noise and improving accuracy, thereby promoting the progress of science.All quantum computers built so far suffer from noise and decoherence issues. When quantum computers are used to simulate the properties of molecules and solids in condensed matter and quantum chemistry, the main property of interest is the excitation information encoded in the spectra of response functions. This spectral information has mathematical properties that severely constrain the allowed response functions, and that can therefore be employed as a ‘noise filter’ for quantum computing data. This project will investigate ways to employ this mathematical information in practical algorithms to reduce noise of quantum data. Implementations and tests with synthetic data and with data from present-day quantum computers are proposed. In addition, an outreach collaboration with the University of Michigan’s Museum of Natural History will introduce the public at schools and libraries to quantum phenomena including quantum coherence.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.