{"id":{"repo_id":"creighton","oai_identifier":"oai:cdr.creighton.edu:10504/130475"},"canonical_url":"https://search.dev.ndltd.org/etd/creighton/oai:cdr.creighton.edu:10504/130475","repository":{"repo_id":"creighton","name":"Creighton University","base_url":"https://cdr.creighton.edu/server/oai/request"},"display":{"title":"Implementing Quantum Gates With Length-3 Dynamic Graphs","abstract":"The continuous-time quantum walk is a quantum version of a random walk that evolves by Schrodinger's equation. With the Hamiltonian equal to the adjacency matrix of a sequence of graphs, called a dynamic graph, continuous-time quantum walks have been shown to implement quantum gates, including the T gate, Hadamard gate, and the Controlled{NOT gate. Since these gates make up a universal set of quantum gates, they can implement any other arbitrary quantum gate up to an arbitrary approximation. This process, however, can be tedious and ine cient. To alleviate this, we have developed a parameterized dynamic graph on which a continuous-time quantum walk can implement any arbitrary single-qubit quantum gate, and we have also extended this result to implement any two-qubit controlled-unitary quantum gate. These dynamic graphs have at most length three. Using these, we implemented Draper's quantum addition circuit, which is based on the quantum Fourier transform, using a continuous-time quantum walk on a dynamic graph.","abstract_html":"The continuous-time quantum walk is a quantum version of a random walk that evolves by Schrodinger's equation. With the Hamiltonian equal to the adjacency matrix of a sequence of graphs, called a dynamic graph, continuous-time quantum walks have been shown to implement quantum gates, including the T gate, Hadamard gate, and the Controlled{NOT gate. Since these gates make up a universal set of quantum gates, they can implement any other arbitrary quantum gate up to an arbitrary approximation. This process, however, can be tedious and ine cient. To alleviate this, we have developed a parameterized dynamic graph on which a continuous-time quantum walk can implement any arbitrary single-qubit quantum gate, and we have also extended this result to implement any two-qubit controlled-unitary quantum gate. These dynamic graphs have at most length three. Using these, we implemented Draper's quantum addition circuit, which is based on the quantum Fourier transform, using a continuous-time quantum walk on a dynamic graph.","abstract_has_math":false,"creators":["Adisa, Ibukunoluwa Adebimpe"],"institution":"Creighton University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Wong, Thomas"],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-05-04","date_published":"2021-05-04","updated_at":"2026-07-24T01:52:24Z","subjects":[],"languages":["en_US"],"rights":["Copyright is retained by the Author. A non-exclusive distribution right is granted to Creighton University and to ProQuest following the publishing model selected above."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10504/130475","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Wong, Thomas"]},{"key":"dc:creator","label":"Author","values":["Adisa, Ibukunoluwa Adebimpe"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2021-05-17T17:08:54Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2021-05-17T17:08:54Z"]},{"key":"dc:date.issued","label":"Date","values":["2021-05-04"]},{"key":"dc:publisher","label":"Institution","values":["Creighton University"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright is retained by the Author. A non-exclusive distribution right is granted to Creighton University and to ProQuest following the publishing model selected above."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10504/130475"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The continuous-time quantum walk is a quantum version of a random walk that evolves by Schrodinger's equation. With the Hamiltonian equal to the adjacency matrix of a sequence of graphs, called a dynamic graph, continuous-time quantum walks have been shown to implement quantum gates, including the T gate, Hadamard gate, and the Controlled{NOT gate. Since these gates make up a universal set of quantum gates, they can implement any other arbitrary quantum gate up to an arbitrary approximation. This process, however, can be tedious and ine cient. To alleviate this, we have developed a parameterized dynamic graph on which a continuous-time quantum walk can implement any arbitrary single-qubit quantum gate, and we have also extended this result to implement any two-qubit controlled-unitary quantum gate. These dynamic graphs have at most length three. Using these, we implemented Draper's quantum addition circuit, which is based on the quantum Fourier transform, using a continuous-time quantum walk on a dynamic graph."]},{"key":"dc:title","label":"Title","values":["Implementing Quantum Gates With Length-3 Dynamic Graphs"]}]}],"canonical_facts":{"dc:contributor.advisor":["Wong, Thomas"],"dc:creator":["Adisa, Ibukunoluwa Adebimpe"],"dc:date.accessioned":["2021-05-17T17:08:54Z"],"dc:date.available":["2021-05-17T17:08:54Z"],"dc:date.issued":["2021-05-04"],"dc:description.abstract":["The continuous-time quantum walk is a quantum version of a random walk that evolves by Schrodinger's equation. With the Hamiltonian equal to the adjacency matrix of a sequence of graphs, called a dynamic graph, continuous-time quantum walks have been shown to implement quantum gates, including the T gate, Hadamard gate, and the Controlled{NOT gate. Since these gates make up a universal set of quantum gates, they can implement any other arbitrary quantum gate up to an arbitrary approximation. This process, however, can be tedious and ine cient. To alleviate this, we have developed a parameterized dynamic graph on which a continuous-time quantum walk can implement any arbitrary single-qubit quantum gate, and we have also extended this result to implement any two-qubit controlled-unitary quantum gate. These dynamic graphs have at most length three. Using these, we implemented Draper's quantum addition circuit, which is based on the quantum Fourier transform, using a continuous-time quantum walk on a dynamic graph."],"dc:identifier.uri":["http://hdl.handle.net/10504/130475"],"dc:language.iso":["en_US"],"dc:publisher":["Creighton University"],"dc:rights":["Copyright is retained by the Author. A non-exclusive distribution right is granted to Creighton University and to ProQuest following the publishing model selected above."],"dc:title":["Implementing Quantum Gates With Length-3 Dynamic Graphs"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T01:52:24Z"}