{"id":238340,"date":"2018-11-06T17:12:26","date_gmt":"2018-11-07T01:12:26","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/improved-quantum-ternary-arithmetics-2\/"},"modified":"2018-11-06T17:12:26","modified_gmt":"2018-11-07T01:12:26","slug":"improved-quantum-ternary-arithmetics-2","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/improved-quantum-ternary-arithmetics-2\/","title":{"rendered":"Improved Quantum Ternary Arithmetic"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Qutrit (or ternary) structures arise naturally in many quantum systems, particularly in certain non-abelian anyon systems. We present efficient circuits for ternary reversible and quantum arithmetics. Our main result is the derivation of circuits for two families of ternary quantum adders, namely ripple carry adders and carry look-ahead adders. The main difference to the binary case is the more complicated form of the ternary carry, which leads to higher resource counts for implementations over a universal ternary gate set. Our ternary ripple adder circuit has a circuit depth of O(n) and uses only 1 ancilla, making it more efficient in both, circuit depth and width than previous constructions. Our ternary carry lookahead circuit has a circuit depth of only O(log(n)) , while using with O(n) ancillas. Our approach works on two levels of abstraction: at the first level, descriptions of arithmetic circuits are given in terms of gates sequences that use various types of non-Clifford reflections. Two choices of elementary gate sets correspond to two possible mappings onto two different prospective quantum computing architectures which we call the metaplectic and the supermetaplectic basis, respectively. Finally, we develop a method to factor diagonal unitaries using multi-variate polynomial over the ternary finite field which allows to characterize classes of gates that can be implemented exactly over the supermetaplectic basis.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Qutrit (or ternary) structures arise naturally in many quantum systems, particularly in certain non-abelian anyon systems. We present efficient circuits for ternary reversible and quantum arithmetics. Our main result is the derivation of circuits for two families of ternary quantum adders, namely ripple carry adders and carry look-ahead adders. The main difference to the binary [&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":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[243138],"msr-publication-type":[193715],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-238340","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-quantum","msr-locale-en_us"],"msr_publishername":"Rinton Press","msr_edition":"Quantum Information and Computation","msr_affiliation":"","msr_published_date":"2016-07-01","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"0862-0884","msr_chapter":"","msr_isbn":"","msr_journal":"Quantum Information and Computation","msr_volume":"16","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"9-10","msr_organization":"","msr_how_published":"","msr_notes":"See also arXiv preprint arXiv:1512.03824","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":"426753","msr_publicationurl":"http:\/\/www.rintonpress.com\/journals\/qiconline.html#v16n910","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"1512.03824","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/07\/1512.03824.pdf","id":426753,"label_id":0},{"type":"url","title":"http:\/\/www.rintonpress.com\/journals\/qiconline.html#v16n910","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_attachments":[{"id":0,"url":"http:\/\/www.rintonpress.com\/journals\/qiconline.html#v16n910"}],"msr-author-ordering":[{"type":"text","value":"A. Bocharov","user_id":0,"rest_url":false},{"type":"text","value":"S. X. Cui","user_id":0,"rest_url":false},{"type":"text","value":"M. Roetteler","user_id":0,"rest_url":false},{"type":"text","value":"K. M. Svore","user_id":0,"rest_url":false},{"type":"user_nicename","value":"alexeib","user_id":30935,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=alexeib"},{"type":"user_nicename","value":"ksvore","user_id":32588,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=ksvore"},{"type":"user_nicename","value":"martinro","user_id":32823,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=martinro"}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[170888],"publication":[],"video":[],"download":[],"msr_publication_type":"article","related_content":{"projects":[{"ID":170888,"post_title":"Language-Integrated Quantum Operations: LIQUi|&gt;","post_name":"language-integrated-quantum-operations-liqui","post_type":"msr-project","post_date":"2011-12-19 10:19:35","post_modified":"2018-11-02 11:06:22","post_status":"publish","permalink":"https:\/\/www.microsoft.com\/en-us\/research\/project\/language-integrated-quantum-operations-liqui\/","post_excerpt":"LIQUi|&gt; is a software architecture and toolsuite for quantum computing. It includes a programming language, optimization and scheduling algorithms, and quantum simulators. LIQUi|&gt; can be used to translate a quantum algorithm written in the form of a high-level program into the low-level machine instructions for a quantum device. LIQUi|&gt; is being developed by the Quantum Architectures and Computation Group (QuArC)\u00a0at Microsoft Research. About LIQUi|&gt; To aid in the development and understanding of quantum protocols, quantum&hellip;","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-project\/170888"}]}}]},"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/238340"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-research-item"}],"version-history":[{"count":2,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/238340\/revisions"}],"predecessor-version":[{"id":426756,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/238340\/revisions\/426756"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=238340"}],"wp:term":[{"taxonomy":"msr-content-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-content-type?post=238340"},{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=238340"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=238340"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=238340"},{"taxonomy":"msr-product-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-product-type?post=238340"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=238340"},{"taxonomy":"msr-platform","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-platform?post=238340"},{"taxonomy":"msr-download-source","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-download-source?post=238340"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=238340"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=238340"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=238340"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=238340"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=238340"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=238340"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=238340"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}