Property Testing for Quantum Engineering

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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.