{"id":165839,"date":"2014-11-01T00:00:00","date_gmt":"2014-11-01T00:00:00","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/msr-research-item\/repeat-until-success-non-deterministic-decomposition-of-single-qubit-unitaries\/"},"modified":"2018-10-16T20:16:20","modified_gmt":"2018-10-17T03:16:20","slug":"repeat-until-success-non-deterministic-decomposition-of-single-qubit-unitaries","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/repeat-until-success-non-deterministic-decomposition-of-single-qubit-unitaries\/","title":{"rendered":"Repeat-Until-Success: Non-deterministic decomposition of single-qubit unitaries"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We present a non-deterministic circuit decomposition technique for approximating an arbitrary single-qubit unitary to within distance epsilon that requires significantly fewer non-Clifford gates than deterministic decomposition techniques. We develop &#8220;Repeat-Until-Success&#8221; (RUS) circuits and characterize unitaries that can be exactly represented as an RUS circuit. Our RUS circuits operate by conditioning on a given measurement outcome and using only a small number of non-Clifford gates and ancilla qubits. We construct an algorithm based on RUS circuits that approximates an arbitrary single-qubit Z-axis rotation to within distance epsilon, where the number of T gates scales as 1.3 log(1\/epsilon) &#8211; 2.79, an improvement of roughly three-fold over state-of-the-art techniques. We then extend our algorithm and show that a scaling of 2.4 log(1\/epsilon) &#8211; 3.3 can be achieved for arbitrary unitaries and a small range of epsilon, which is roughly twice as good as optimal deterministic decomposition methods.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We present a non-deterministic circuit decomposition technique for approximating an arbitrary single-qubit unitary to within distance epsilon that requires significantly fewer non-Clifford gates than deterministic decomposition techniques. We develop &#8220;Repeat-Until-Success&#8221; (RUS) circuits and characterize unitaries that can be exactly represented as an RUS circuit. Our RUS circuits operate by conditioning on a given measurement outcome [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"Rinton Press","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"Quantum Information and Computation","msr_number":"","msr_organization":"","msr_pages_string":"1277-1301","msr_page_range_start":"1277","msr_page_range_end":"1301","msr_series":"","msr_volume":"14","msr_copyright":"","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Adam Paetznick, Krysta M. Svore","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"","msr_host":"","msr_version":"","msr_duration":"","msr_original_fields_of_study":"","msr_release_tracker_id":"","msr_s2_match_type":"","msr_citation_count_updated":"","msr_published_date":"2014-11-05","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_s2_pdf_url":"","msr_year":2014,"msr_citation_count":0,"msr_influential_citations":0,"msr_reference_count":0,"msr_s2_match_confidence":0,"msr_microsoftintellectualproperty":true,"msr_s2_open_access":false,"msr_s2_author_ids":[],"msr_pub_ids":[],"msr_hide_image_in_river":0,"footnotes":""},"msr-research-highlight":[],"research-area":[13552],"msr-publication-type":[193715],"msr-publisher":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-165839","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-hardware-devices","msr-locale-en_us"],"msr_publishername":"Rinton Press","msr_edition":"","msr_affiliation":"","msr_published_date":"2014-11-05","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"1277-1301","msr_chapter":"","msr_isbn":"","msr_journal":"Quantum Information and Computation","msr_volume":"14","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"204587","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"repeat.pdf","viewUrl":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2016\/02\/repeat.pdf","id":204587,"label_id":0}],"msr_related_uploader":"","msr_citation_count":0,"msr_citation_count_updated":"","msr_s2_paper_id":"","msr_influential_citations":0,"msr_reference_count":0,"msr_arxiv_id":"","msr_s2_author_ids":[],"msr_s2_open_access":false,"msr_s2_pdf_url":null,"msr_attachments":[{"id":204587,"url":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-content\/uploads\/2016\/02\/repeat.pdf"}],"msr-author-ordering":[{"type":"text","value":"Adam Paetznick","user_id":0,"rest_url":false},{"type":"user_nicename","value":"ksvore","user_id":32588,"rest_url":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=ksvore"}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[],"publication":[],"video":[],"msr-tool":[],"msr_publication_type":"article","related_content":[],"_links":{"self":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/165839","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item"}],"about":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-research-item"}],"version-history":[{"count":1,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/165839\/revisions"}],"predecessor-version":[{"id":525547,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/165839\/revisions\/525547"}],"wp:attachment":[{"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/media?parent=165839"}],"wp:term":[{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=165839"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=165839"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=165839"},{"taxonomy":"msr-publisher","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-publisher?post=165839"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=165839"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=165839"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=165839"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=165839"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=165839"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=165839"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=165839"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=165839"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}