Metaplectic quantum basis is a universal multi-qutrit quantum basis, formed by the ternary Clifford group and the axial reflection gate R<\/i>=|0\u27e9\u27e80|+|1\u27e9\u27e81|\u2212|2\u27e9\u27e82| . It is arguably, a ternary basis with the simplest geometry. Recently Cui, Kliuchnikov, Wang and the Author have proposed a compilation algorithm to approximate any two-level Householder reflection to precision \u03b5<\/i>\u00a0 by a metaplectic circuit of R<\/i>\u00a0 -count at most C<\/i>log\u00a03\u00a0(1\/\u03b5<\/i>)+O<\/i>(loglog1\/\u03b5<\/i>)\u00a0 with C<\/i>=8\u00a0. A new result in this note takes the constant down to C<\/i>=5\u00a0 for non-exceptional target reflections under a certain credible number-theoretical conjecture. The new method increases the chances of obtaining a truly optimal circuit but may not guarantee the true optimality. Efficient approximations of an important ternary quantum gate proposed by Howard, Campbell and others is also discussed. Apart from this, the note is mostly didactical: we demonstrate how to leverage Lenstra’s integer geometry algorithm from 1983 for circuit synthesis.<\/p>\n","protected":false},"excerpt":{"rendered":"
Metaplectic quantum basis is a universal multi-qutrit quantum basis, formed by the ternary Clifford group and the axial reflection gate R=|0\u27e9\u27e80|+|1\u27e9\u27e81|\u2212|2\u27e9\u27e82| . It is arguably, a ternary basis with the simplest geometry. Recently Cui, Kliuchnikov, Wang and the Author have proposed a compilation algorithm to approximate any two-level Householder reflection to precision \u03b5\u00a0 by a […]<\/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-240050","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-quantum","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2018-01-02","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"Quantum Information and Computation","msr_volume":"18","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":"482220","msr_publicationurl":"http:\/\/arxiv.org\/abs\/1606.02315","msr_doi":"","msr_publication_uploader":[{"type":"file","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/uploads\/prod\/2016\/06\/1606.02315.pdf","id":"482220","title":"1606.02315","label_id":"243132","label":0},{"type":"url","viewUrl":"false","id":"false","title":"http:\/\/arxiv.org\/abs\/1606.02315","label_id":"243109","label":0}],"msr_related_uploader":"","msr_attachments":[{"id":0,"url":"http:\/\/arxiv.org\/abs\/1606.02315"}],"msr-author-ordering":[{"type":"user_nicename","value":"Alex Bocharov","user_id":30935,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Alex Bocharov"}],"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|>","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|> is a software architecture and toolsuite for quantum computing. It includes a programming language, optimization and scheduling algorithms, and quantum simulators. LIQUi|> 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|> is being developed by the Quantum Architectures and Computation Group (QuArC)\u00a0at Microsoft Research. 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