Property Testing for Quantum Engineering

理论博士项目将开发算法来回答这样一个问题：“给定一个工程化的量子系统，它是否具备执行容错量子计算(FTQC)所需的特性？或者它远远不具备这些特性？”将使用理论计算机科学的方法。这个项目将重点放在最小化这些算法的空间和时间复杂性上。这个项目将开发超快的性能测试算法来回答这个问题。因此，它将通过避免目前昂贵得令人望而却步的、耗时的、本身容易出错的测试方案来消除FTQC发展的严重瓶颈，即测量和处理指数级的许多数字来做出决定。这应该会加速FTQC的发展，并促进更广泛的量子工程和技术的更大进步。该项目的另一个目标是推进华威在量子认证方面的最新成果。量子认证是一种实用和可扩展的方法，用于确定任意大小的噪声量子计算机输出的正确性，它是计算机本身效用的最终仲裁者。与FTQC一样，量子认证依赖于对量子计算机中噪声性质的数学假设，必须在现实世界的系统中进行验证。物理学和理论计算机科学之间的密切互动将使学生在物理、计算机科学和量子技术市场的未来处于独特的有利地位。

The theoretical PhD project will develop algorithms that answer the question: "Given an engineered quantum system, does it have the properties necessary to perform fault-tolerant quantum computation (FTQC)? Or is it far from having those properties?" Methods of theoretical computer science will be used. Emphasis will be placed on minimising the space and time complexity of these algorithms.This project will develop ultra-fast property testing algorithms to answer this question. It will thus remove a severe bottleneck in the development of FTQC by avoiding the present prohibitively expensive, time-consuming, and itself error prone testing regimen of measuring and processing exponentially many numbers to make a decision. This should accelerate the development of FTQCs and facilitate greater advances in quantum engineering and technologies more generally. Another aim of this project is to advance recent results from Warwick on quantum accreditation. Quantum accreditation is a practical and scalable method of ascertaining the correctness of the outputs of arbitrary-sized noisy quantum computers the ultimate arbiter of the utility of the computer itself. Like FTQC, quantum accreditation relies on mathematical assumptions on the nature of the noise in the quantum computer and must be validated in real-world systems. A close interaction between physics and theoretical computer science will place the student in a uniquely beneficial position for a future in physics, computer science, and the quantum technologies market.