CAREER: Design and Analysis of Low-Overhead Fault-Tolerant Quantum Circuits

量子计算机有可能彻底改变计算的范式，因为与经典计算机相比，量子计算机在某些高影响力的计算任务中具有巨大的优势。释放量子计算机全部能力的主要障碍是它们对噪声和退相干的极端敏感性。尽管在过去的二十年中，容错协议的设计取得了重大进展，但量子设备上允许的噪声的基本限制以及纠正错误所需的开销尚未完全理解。该项目旨在开发数学框架来设计和分析低开销容错量子计算方案。此外，该项目还探索了可靠量子计算的最低要求。该研究的多学科性质为研究生和本科生提供了一个独特的教育环境，他们将在本项目期间接受培训和指导。本项目的目标是开发数学模型来描述量子电路中的错误传播，并使用它们来构建资源高效的计算子程序。该方法将使经典数据压缩和纠错码在设计低开销可靠量子计算机中的应用成为可能。开发的框架将用于了解可靠计算所需的最小资源，并通过直接结合量子处理器的硬件约束来发现资源高效的协议。系统的方法将提供一个机会，执行计算机辅助搜索，以找到优化的结构。将研究所开发的程序的应用程序，以保护关键的容错量子操作，如代码切换。这一努力的成功完成将在降低硬件要求方面取得进展，以构建能够进行精确大规模量子计算的可靠量子处理器。该项目由计算和通信基础部门的新兴技术核心研究计划基金会和刺激竞争力研究的既定计划（EPSCoR）共同资助该奖项反映了NSF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。

Quantum computers have the potential to revolutionize the paradigm of computing by offering a substantial advantage compared to classical computers for certain high-impact computational tasks. The main obstacle to unleashing the full power of quantum computers is their extreme susceptibility to noise and decoherence. Despite the significant progress in designing fault-tolerant protocols over the last two decades, the fundamental limits of the permissible noise on quantum devices and the required overhead to correct the errors are not fully understood. This project aims to develop mathematical frameworks to design and analyze low-overhead fault-tolerant quantum computing schemes. In addition, the project also explores the minimum requirements for reliable quantum computation. The multidisciplinary nature of the research provides a unique educational environment for both graduate and undergraduate students who will be trained and mentored during this project.The goal of this project is to develop mathematical models to describe error propagation in quantum circuits and use them to construct resource-efficient computing subroutines. The approach will enable the application of classical data compression and error correction codes in designing low-overhead reliable quantum computers. The developed framework will be used to understand the minimum resources required for reliable computation and to discover resource-efficient protocols by directly incorporating the hardware constraints of quantum processors. The systematic approach will provide an opportunity to perform computer-assisted search to find optimized constructions. The applications of the developed procedures to protect key fault-tolerant quantum operations such as code-switching will be investigated. The successful completion of this effort will make progress in lowering the hardware requirements to build reliable quantum processors capable of accurate large-scale quantum computation.This project is jointly funded by the Foundations of Emerging Technologies core research program in the Computing and Communication Foundations Division and the Established Program to Stimulate Competitive Research (EPSCoR).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.