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Automating quantum circuit transformations for optimisation and fault-tolerance

1st September 2019 to 1st July 2023
Quantum computers have the ability to reshape the modern world, offering huge computational speed-ups in solving a wide variety of hard problems in mathematics, physics, chemistry, and computer science. However, emerging quantum computational hardware faces stringent limitations in memory, computational power, and tolerance to noise, making it crucial to design software that squeezes as much benefit from this hardware as possible. A typical form taken by quantum software at a low level is that of a quantum circuit, which describes a sequence of basic operations the hardware should perform on a fixed piece of (quantum) memory.

This project, funded by the Airforce Office of Scientific Research (AFOSR), aims to develop new techniques for automatically transforming quantum circuits into improved versions of themselves that consume fewer resources and are more robust to noise. It builds on the theoretical basis of the ZX-calculus, a mathematical theory which exposes the underlying algebraic relationships between certain kinds of quantum mechanical processes. This algebraic structure gives a novel way to represent and transform quantum circuits, which will be exploited to develop new circuit optimisation techniques and combine these with new and existing techniques in quantum error correction and fault-tolerant quantum computation. We will provide tools that perform these circuit transformations automatically, which will not only produce the transformed circuits, but also independently-verifiable proofs that this transformation has been done correctly, without introducing bugs in the process.

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