Characterisation of universal qudit gates

Amaro Alcala, David

Characterisation of universal qudit gates

dc.contributor.advisor	Sanders, Barry Cyril
dc.contributor.advisor	de Guise, Hubert
dc.contributor.author	Amaro Alcala, David
dc.contributor.committeemember	Emerson, Joseph
dc.contributor.committeemember	Simon, Christoph
dc.contributor.committeemember	Scandolo, Carlo Maria
dc.contributor.committeemember	Feder, David
dc.date	2025-01
dc.date.accessioned	2024-10-24T18:16:07Z
dc.date.available	2024-10-24T18:16:07Z
dc.date.issued	2024-10-21
dc.description.abstract	To 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.
dc.identifier.citation	Amaro Alcala, D. (2024). Characterisation of universal qudit gates (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.
dc.identifier.uri	https://hdl.handle.net/1880/120003
dc.language.iso	en
dc.publisher.faculty	Graduate Studies
dc.publisher.institution	University of Calgary
dc.rights	University 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.
dc.subject	randomised benchmarking
dc.subject	quantum information
dc.subject	quantum gates
dc.subject.classification	Physics
dc.subject.classification	Physics--Theory
dc.title	Characterisation of universal qudit gates
dc.type	doctoral thesis
thesis.degree.discipline	Physics & Astronomy
thesis.degree.grantor	University of Calgary
thesis.degree.name	Doctor of Philosophy (PhD)
ucalgary.thesis.accesssetbystudent	I do not require a thesis withhold – my thesis will have open access and can be viewed and downloaded publicly as soon as possible.