FET: Small: Decoding Quantum Error-Correcting Codes for Quantum Computing and Communication

量子计算机有望解决许多使普通（经典）计算机能力紧张的困难计算任务，特别是在模拟量子力学系统和寻找各种数学问题的最佳解决方案方面。然而，建造大规模量子计算机需要克服退相干或量子噪声的挑战。这个问题的一般答案是已知的：量子纠错，实现量子计算的容错。目前这一代嘈杂的中尺度量子（NISQ）处理器太小，噪音太大，无法真正利用量子纠错（QEC），但随着它们尺寸的增长和质量的提高，这将很快成为可能。完全容错量子计算（FTQC）的要求非常高；但在未来几年内，某些容错元素应该是可能实现的。该项目旨在开发在近期机器中实用的容错量子计算方法。该方法使用量子隐形传态来处理存储在有效量子代码中的量子比特（量子位），以保护它们免受退相干的影响。他的奖项将支持攻读博士学位的学生，并将丰富南加州大学广泛的教育工作。这些努力现在不仅包括教师、博士后和博士生，还包括量子信息科学硕士项目的硕士生，以及越来越多的本科生。该项目将建立在一种基于高速率多量子位块码编码逻辑量子位的方法之上。在不久的将来，将有可能使用量子错误检测代码，用n个物理量子比特编码n - 2个逻辑量子比特，并使用一组通用的编码门。这种方案不能完全容错，但它可以是弱容错，能够通过最终（或中间）测量检测任何单个故障，并在没有检测到错误的情况下进行后选择。对于小型计算，这将比未编码的量子电路有改进。随着量子比特数的增加和噪声率的降低，可以添加更多的FTQC元素，直到实现完全容错。该项目还将解决准备辅助状态的问题，辅助状态是基于远程传输的FTQC的构建模块，通过使用基于标志的方法和错误检测的组合，将状态准备和验证结合到一个过程中。研究人员还将为QEC代码寻求快速准确的解码算法，以便在量子计算过程中实时使用。该项目将通过机器学习方法开发解码算法。此外，该项目还将探索QEC代码在量子信息科学中其他问题的应用。该奖项反映了美国国家科学基金会的法定使命，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 promise to solve many difficult computational tasks that strain the abilities of ordinary (classical) computers, especially in simulating quantum-mechanical systems and finding optimal solutions to a variety of mathematical problems. However, building large-scale quantum computers requires overcoming the challenge of decoherence, or quantum noise. The general answer to this is known: quantum error correction, to achieve fault-tolerant quantum computation. The current generation of noisy, intermediate scale quantum (NISQ) processors are too small and noisy to take real advantage of quantum error correction (QEC), but as they grow in size and improve in quality, this will soon become possible. Fully fault-tolerant quantum computing (FTQC) is very demanding; but some elements of fault-tolerance should be possible in the next few years. This project aims to develop methods of fault-tolerant quantum computation that will be practical in near-term machines. The approach uses quantum teleportation to process quantum bits (qubits) stored in efficient quantum codes that protect them against decoherence. his award will support Ph.D. students working towards their degrees, and will enrich the broad educational efforts at the University of Southern California. These efforts now include not only faculty, postdocs and Ph.D. students, but master's students in the MS program in Quantum Information Science, and a growing number of undergraduate students.This project will build upon an approach based on encoding logical qubits in multi-qubit block codes with high rates. In the very near term it will be possible to use quantum error-detecting codes that encode n–2 logical qubits in n physical qubits, with a universal set of encoded gates. Such a scheme cannot be fully fault-tolerant, but it can be weakly fault-tolerant, able to detect any single fault by a final (or intermediate) measurement and post-select on no error being detected. For small computations this will give an improvement over an unencoded quantum circuit. As qubit counts increase and noise rates diminish, more elements of FTQC can be added until full fault-tolerance is achieved. This project will also tackle the problem of preparing ancilla states, which are the building blocks of teleportation-based FTQC by combining state preparation and verification into a single process, using a combination of flag-based methods and error detection. The investigators will also pursue fast and accurate decoding algorithms for QEC codes that could be used in real time during a quantum computation. This project will develop decoding algorithms via machine learning methods. In addition, the project will explore applications of QEC codes to other problems in quantum information science. TThis 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.