{"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":"","msr-author-ordering":null,"msr_publishername":"APS","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"Physical Review Letters","msr_number":"","msr_organization":"","msr_pages_string":"080502","msr_page_range_start":"80502","msr_page_range_end":"","msr_series":"","msr_volume":"114","msr_copyright":"","msr_conference_name":"","msr_doi":"10.1103\/PhysRevLett.114.080502","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Krysta M. 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