{"id":{"repo_id":"lsu-thes","oai_identifier":"oai:repository.lsu.edu:gradschool_dissertations-1019"},"canonical_url":"https://search.dev.ndltd.org/etd/lsu-thes/oai:repository.lsu.edu:gradschool_dissertations-1019","repository":{"repo_id":"lsu-thes","name":"Lousiana State University","base_url":"https://repository.lsu.edu/do/oai/"},"display":{"title":"Extension of Shor's period-finding algorithm to infinite dimensional Hilbert spaces","abstract":"Over the last decade quantum computing has become a very popular field in various disciplines, such as physics, engineering, and mathematics. Most of the attraction stemmed from the famous Shor period--finding algorithm, which leads to an efficient algorithm for factoring positive integers. Many adaptations and generalizations of this algorithm have been developed through the years, some of which have not been ripened with full mathematical rigor. In this dissertation we use concepts from white noise analysis to rigorously develop a Shor algorithm adapted to find a hidden subspace of a function with domain a real Hilbert space. After reviewing the framework of quantum mechanics, we demonstrate how these principles can be used to develop algorithms which operate on a quantum computing device. We present a self-contained account of white noise analysis, including the main relevant results. Inspired by a generalized function in the algorithm, we develop a new distribution, the delta function for a subspace of an infinite dimensional Hilbert space. We then use this distribution to rigorously prove one of the main identities needed for the algorithm. Finally we provide a rigorous formulation of the hidden subspace algorithm in infinite dimensions.","abstract_html":"Over the last decade quantum computing has become a very popular field in various disciplines, such as physics, engineering, and mathematics. Most of the attraction stemmed from the famous Shor period--finding algorithm, which leads to an efficient algorithm for factoring positive integers. Many adaptations and generalizations of this algorithm have been developed through the years, some of which have not been ripened with full mathematical rigor. In this dissertation we use concepts from white noise analysis to rigorously develop a Shor algorithm adapted to find a hidden subspace of a function with domain a real Hilbert space. After reviewing the framework of quantum mechanics, we demonstrate how these principles can be used to develop algorithms which operate on a quantum computing device. We present a self-contained account of white noise analysis, including the main relevant results. Inspired by a generalized function in the algorithm, we develop a new distribution, the delta function for a subspace of an infinite dimensional Hilbert space. We then use this distribution to rigorously prove one of the main identities needed for the algorithm. Finally we provide a rigorous formulation of the hidden subspace algorithm in infinite dimensions.","abstract_has_math":false,"creators":["Becnel, Jeremy James"],"institution":"Mathematics","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Applied Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2006,"date_issued":"2006-01-01T08:00:00Z","date_published":"2006-01-01T08:00:00Z","updated_at":"2026-07-24T02:57:00Z","subjects":["white noise distribution theory"],"languages":[],"rights":["unrestricted","Release the entire work immediately for access worldwide."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-06222006-133421","https://repository.lsu.edu/gradschool_dissertations/20"],"render_values":[{"text":"etd-06222006-133421","href":null,"code":true},{"text":"https://repository.lsu.edu/gradschool_dissertations/20","href":"https://repository.lsu.edu/gradschool_dissertations/20","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.31390/gradschool_dissertations.20","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Becnel, Jeremy James"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2006-03-20"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-05-12T23:07:25Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Applied Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["white noise distribution theory"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["unrestricted","Release the entire work immediately for access worldwide."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-06222006-133421","10.31390/gradschool_dissertations.20","https://repository.lsu.edu/gradschool_dissertations/20"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Over the last decade quantum computing has become a very popular field in various disciplines, such as physics, engineering, and mathematics. Most of the attraction stemmed from the famous Shor period--finding algorithm, which leads to an efficient algorithm for factoring positive integers. Many adaptations and generalizations of this algorithm have been developed through the years, some of which have not been ripened with full mathematical rigor. In this dissertation we use concepts from white noise analysis to rigorously develop a Shor algorithm adapted to find a hidden subspace of a function with domain a real Hilbert space. After reviewing the framework of quantum mechanics, we demonstrate how these principles can be used to develop algorithms which operate on a quantum computing device. We present a self-contained account of white noise analysis, including the main relevant results. Inspired by a generalized function in the algorithm, we develop a new distribution, the delta function for a subspace of an infinite dimensional Hilbert space. We then use this distribution to rigorously prove one of the main identities needed for the algorithm. Finally we provide a rigorous formulation of the hidden subspace algorithm in infinite dimensions."]},{"key":"dc:title","label":"Title","values":["Extension of Shor's period-finding algorithm to infinite dimensional Hilbert spaces"]}]}],"canonical_facts":{"dc:creator":["Becnel, Jeremy James"],"dc:date":["2006-03-20"],"dc:date.available":["2022-05-12T23:07:25Z"],"dc:description.abstract":["Over the last decade quantum computing has become a very popular field in various disciplines, such as physics, engineering, and mathematics. Most of the attraction stemmed from the famous Shor period--finding algorithm, which leads to an efficient algorithm for factoring positive integers. Many adaptations and generalizations of this algorithm have been developed through the years, some of which have not been ripened with full mathematical rigor. In this dissertation we use concepts from white noise analysis to rigorously develop a Shor algorithm adapted to find a hidden subspace of a function with domain a real Hilbert space. After reviewing the framework of quantum mechanics, we demonstrate how these principles can be used to develop algorithms which operate on a quantum computing device. We present a self-contained account of white noise analysis, including the main relevant results. Inspired by a generalized function in the algorithm, we develop a new distribution, the delta function for a subspace of an infinite dimensional Hilbert space. We then use this distribution to rigorously prove one of the main identities needed for the algorithm. Finally we provide a rigorous formulation of the hidden subspace algorithm in infinite dimensions."],"dc:identifier":["etd-06222006-133421","10.31390/gradschool_dissertations.20","https://repository.lsu.edu/gradschool_dissertations/20"],"dc:rights":["unrestricted","Release the entire work immediately for access worldwide."],"dc:subject":["white noise distribution theory"],"dc:title":["Extension of Shor's period-finding algorithm to infinite dimensional Hilbert spaces"],"thesis:degree_discipline":["Applied Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"],"thesis:institution_name":["Mathematics"]},"updated_at":"2026-07-24T02:57:00Z"}