Sanders, Barry Cyrilde Guise, HubertAmaro Alcala, David2024-10-242024-10-242024-10-21Amaro Alcala, D. (2024). Characterisation of universal qudit gates (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.https://hdl.handle.net/1880/120003To harness the potential of quantum computing, increasing the number of quantum units, a process known as scaling, is critical. Whereas qubits have traditionally been used as the units for quantum computing, the development of multi-level systems (qudits), which offer larger Hilbert spaces and advantages over qubits in cryptography and circuit complexity reduction, requires new methods to characterise the quality of quantum gates and ensure safe scaling. Randomised benchmarking offers a simple and inexpensive method for this characterisation. This thesis reports advances in the characterisation of universal single- and multi-qudit gates. I introduce the characterisation of universal qutrit gates through the definition of an optimal scheme that requires similar experimental resources as the standard method for non- universal gates. The feasibility of my qutrit scheme is tested numerically using parameters from experimental qutrit implementations. I then generalise my qutrit results and devise a general scheme for a qudit system with arbitrary d. Because using the same construction for qudits with d > 3 as in the qutrit case leads to more than two parameters, a different strategy was necessary. I note that my qudit characterisation obtains an estimate of the average error per gate; thus, this characterisation is collective. A more realistic characterisation requires estimating the average gate fidelity of a single non-Clifford gate. In the last part, I generalise my qudit method to individually, in contrast to the previous collective result, characterise non-Clifford gates. My schemes are relevant to at least two communities: experimental groups with a qudit platform, as my work effectively characterises a complete gate set, and randomised bench- marking theorists, who may be interested both in the gate set I introduce and in the schemes I developed.enUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.randomised benchmarkingquantum informationquantum gatesPhysicsPhysics--Theorydoctoral thesis