Diagrammatic Quantum Computation

Existing quantum computers are on the verge of solving practical problems that are intractable for classical computers.

The obstacles that are holding current generation quantum computers back are their limited number of qubits and the presence of noise, both of which prohibit lengthy computations.

Tools that decrease the size of a given computation can hence greatly increase the scope of problems current quantum computers can solve. This project will build such tools.Firstly, we develop new methods and software for optimising quantum circuits. Secondly, we build powerful verification methods that ensure correctness of our optimisations.

Thirdly, we develop classical simulators of quantum circuits to allow the testing of quantum computations.While these might seem like disparate problems, in our approach they become aspects of a single problem which is solved by employing powerful graph-theoretic simplification methods that combine techniques from measurement-based quantum computation, tensor networks and the ZX-calculus.

This allows us to develop simplifications that would be hard to find with previous methods.

In summary, this project unifies the problems of optimisation, verification and simulation of quantum circuits while improving upon the state-of-the-art.