{"id":165719,"date":"2018-11-06T17:21:51","date_gmt":"2018-11-07T01:21:51","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/asymptotically-optimal-topological-quantum-compiling\/"},"modified":"2018-11-06T17:21:51","modified_gmt":"2018-11-07T01:21:51","slug":"asymptotically-optimal-topological-quantum-compiling","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/asymptotically-optimal-topological-quantum-compiling\/","title":{"rendered":"Asymptotically Optimal Topological Quantum Compiling"},"content":{"rendered":"
\n

We address the problem of compiling quantum operations into braid representations for non-Abelian quasiparticles described by the Fibonacci anyon model. We classify the single-qubit unitaries that can be represented exactly by Fibonacci anyon braids and use the classification to develop a probabilistically polynomial algorithm that approximates any given single-qubit unitary to a desired precision by an asymptotically depth-optimal braid pattern. We extend our algorithm in two directions: to produce braids that allow only single-strand movement, called weaves, and to produce depth-optimal approximations of two-qubit gates. Our compiled braid patterns have depths that are 20 to 1000 times shorter than those output by prior state-of-the-art methods, for precisions ranging between 1<\/span>0<\/span><\/span>\u2212<\/span>10<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> and 1<\/span>0<\/span>\u2212<\/span>30<\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/p>\n<\/div>\n

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

We address the problem of compiling quantum operations into braid representations for non-Abelian quasiparticles described by the Fibonacci anyon model. We classify the single-qubit unitaries that can be represented exactly by Fibonacci anyon braids and use the classification to develop a probabilistically polynomial algorithm that approximates any given single-qubit unitary to a desired precision by […]<\/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":[{"type":"user_nicename","value":"vadym","user_id":"34468"},{"type":"user_nicename","value":"alexeib","user_id":"30935"},{"type":"user_nicename","value":"ksvore","user_id":"32588"}],"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":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"112","msr_copyright":"","msr_conference_name":"","msr_doi":"10.1103\/PhysRevLett.112.140504","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Krysta M. 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