{"id":166509,"date":"2018-11-06T17:21:01","date_gmt":"2018-11-07T01:21:01","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/efficient-synthesis-of-universal-repeat-until-success-circuits\/"},"modified":"2018-11-06T17:21:01","modified_gmt":"2018-11-07T01:21:01","slug":"efficient-synthesis-of-universal-repeat-until-success-circuits","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/efficient-synthesis-of-universal-repeat-until-success-circuits\/","title":{"rendered":"Efficient Synthesis of Universal Repeat-Until-Success Quantum Circuits"},"content":{"rendered":"
\n

Recently it was shown that the resources required to implement unitary operations on a quantum computer can be reduced by using probabilistic quantum circuits called repeat-until-success (RUS) circuits. However, the previously best-known algorithm to synthesize a RUS circuit for a given target unitary requires exponential classical runtime. We present a probabilistically polynomial-time algorithm to synthesize a RUS circuit to approximate any given single-qubit unitary to precision \u03f5<\/span><\/span><\/span><\/span><\/span> over the Clifford<\/span>+<\/span>T<\/span><\/span><\/span><\/span><\/span><\/span> basis. Surprisingly, the T<\/span><\/span><\/span><\/span><\/span> count of the synthesized RUS circuit surpasses the theoretical lower bound of 3<\/span>\u2009<\/span>log<\/span><\/span>2<\/span><\/span><\/span>(<\/span>1<\/span>\/<\/span>\u03f5<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span> that holds for purely unitary single-qubit circuit decomposition. By taking advantage of measurement and an ancilla qubit, RUS circuits achieve an expected T<\/span><\/span><\/span><\/span><\/span> count of 1.15<\/span>\u2009<\/span>log<\/span><\/span>2<\/span><\/span><\/span>(<\/span>1<\/span>\/<\/span>\u03f5<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span> for single-qubit z<\/span><\/span><\/span><\/span><\/span> rotations. Our method leverages the fact that the set of unitaries implementable by RUS protocols has a higher density in the space of all unitaries compared to the density of purely unitary implementations.<\/p>\n<\/div>\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Recently it was shown that the resources required to implement unitary operations on a quantum computer can be reduced by using probabilistic quantum circuits called repeat-until-success (RUS) circuits. However, the previously best-known algorithm to synthesize a RUS circuit for a given target unitary requires exponential classical runtime. We present a probabilistically polynomial-time algorithm to synthesize […]<\/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":[13561,243138],"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-166509","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-research-area-quantum","msr-locale-en_us"],"msr_publishername":"APS","msr_edition":"","msr_affiliation":"","msr_published_date":"2015-02-27","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"080502","msr_chapter":"","msr_isbn":"","msr_journal":"Physical Review Letters","msr_volume":"114","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":"426849","msr_publicationurl":"http:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.114.080502","msr_doi":"10.1103\/PhysRevLett.114.080502","msr_publication_uploader":[{"type":"file","title":"1404.5320","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2015\/02\/1404.5320.pdf","id":426849,"label_id":0},{"type":"url","title":"http:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.114.080502","viewUrl":false,"id":false,"label_id":0},{"type":"doi","title":"10.1103\/PhysRevLett.114.080502","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_attachments":[{"id":0,"url":"http:\/\/journals.aps.org\/prl\/abstract\/10.1103\/PhysRevLett.114.080502"}],"msr-author-ordering":[{"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":"martinro","user_id":32823,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=martinro"},{"type":"text","value":"Krysta M. 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