Georgiades, Kyriakos; (2024) Resource-efficient quantum circuits in the context of near-term devices. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The one-way model in measurement-based quantum computing is equivalent to the circuit model and allows for depth reduction at the cost of adaptive measurements and ancilla overheads. The one-way model is also less compatible with devices of low qubit connectivity and has mainly been experimentally realised on photonics devices in the past. In this thesis, I introduce a tuneable hybrid model which allows for more precise control of the amount of depth reduction and width overheads achieved. This is done by splitting a circuit into multiple segments of equal depth and converting each segment into a separate measurement pattern. Finally, the patterns are linked in sequence. This approach is designed to make efficient use of the limited resources available in the NISQ era. I also introduce algorithms using graph theoretic techniques such as local complementation and pivoting to reduce the degree of graph states, for easier implementation on restricted architectures. Finally, I show the first experimental realization of the one-way model of a non-trivial quantum circuit on an ion trap device, also demonstrating the use of the hybrid model and local complementation algorithms in practice.

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