{"id":313262,"date":"2018-11-06T17:11:07","date_gmt":"2018-11-07T01:11:07","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=313262"},"modified":"2018-11-06T17:11:07","modified_gmt":"2018-11-07T01:11:07","slug":"quadratic-form-expansions-unitaries","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/quadratic-form-expansions-unitaries\/","title":{"rendered":"Quadratic Form Expansions for Unitaries"},"content":{"rendered":"

We introduce techniques to analyze unitary operations in terms of quadratic form expansions, a form similar to a sum over paths in the computational basis where the phase contributed by each path is described by a quadratic form over R.We show how to relate such a form to an entangled resource akin to that of the one-way measurement model of quantum computing. Using this, we describe various conditions under which it is possible to efficiently implement a unitary operation U, either when provided a quadratic form expansion for U as input, or by finding a quadratic form expansion for U from other input data. <\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

We introduce techniques to analyze unitary operations in terms of quadratic form expansions, a form similar to a sum over paths in the computational basis where the phase contributed by each path is described by a quadratic form over R.We show how to relate such a form to an entangled resource akin to that of 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(TQC'08)","msr_affiliation":"","msr_published_date":"2008-01-01","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"29-46","msr_chapter":"","msr_isbn":"","msr_journal":"Springer Lecture Notes in Computer Science","msr_volume":"5106","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":"459192","msr_publicationurl":"https:\/\/arxiv.org\/abs\/0801.2461","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"Quadratic Form Expansions for 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