{"id":167930,"date":"2014-12-01T00:00:00","date_gmt":"2014-12-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/efficient-approximation-of-diagonal-unitaries-over-the-cliffordt-basis\/"},"modified":"2018-10-16T20:08:13","modified_gmt":"2018-10-17T03:08:13","slug":"efficient-approximation-of-diagonal-unitaries-over-the-cliffordt-basis","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/efficient-approximation-of-diagonal-unitaries-over-the-cliffordt-basis\/","title":{"rendered":"Efficient Approximation of Diagonal Unitaries over the Clifford+T Basis"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We present an algorithm for the approximate decomposition of diagonal operators, focusing specifically on decompositions over the Clifford+T basis, that minimize the number of phase-rotation gates in the synthesized approximation circuit. The equivalent T-count of the synthesized circuit is bounded by k C0 log2(1=&#8221;)+E(n; k), where k is the number of distinct phases in the diagonal n-qubit unitary, &#8221; is the desired precision, C0 is a quality factor of the implementation method (1 < C0 < 4), and E(n; k) is the total entanglement cost (in T gates). We determine an optimal decision boundary in (k; n; &#8220;)-space where our decomposition algorithm achieves lower entanglement cost than previous state-of-the-art techniques. Our method outperforms state-of-the-art techniques for a practical range of &#8221; values and diagonal operators and can reduce the number of T gates exponentially in n when k << 2n.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We present an algorithm for the approximate decomposition of diagonal operators, focusing specifically on decompositions over the Clifford+T basis, that minimize the number of phase-rotation gates in the synthesized approximation circuit. The equivalent T-count of the synthesized circuit is bounded by k C0 log2(1=&#8221;)+E(n; k), where k is the number of distinct phases in the [&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":[13552],"msr-publication-type":[193726],"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-167930","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-hardware-devices","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2014-12-17","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"","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":"","msr_publicationurl":"https:\/\/arxiv.org\/abs\/1412.5608","msr_doi":"","msr_publication_uploader":[{"type":"url","title":"https:\/\/arxiv.org\/abs\/1412.5608","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_attachments":[{"id":0,"url":"https:\/\/arxiv.org\/abs\/1412.5608"}],"msr-author-ordering":[{"type":"text","value":"Jonathan 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