{"id":164459,"date":"2018-11-06T17:22:28","date_gmt":"2018-11-07T01:22:28","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/efficient-decomposition-of-single-qubit-gates-into-v-basis-circuits\/"},"modified":"2018-11-06T17:22:28","modified_gmt":"2018-11-07T01:22:28","slug":"217-efficient-decomposition-of-single-qubit-gates-into-v-basis-circuits","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/217-efficient-decomposition-of-single-qubit-gates-into-v-basis-circuits\/","title":{"rendered":"Efficient Decomposition of Single-Qubit Gates into V Basis Circuits"},"content":{"rendered":"
\n

We develop efficient algorithms for compiling single-qubit unitary gates into circuits over the universal V<\/span><\/span><\/span><\/span><\/span> basis<\/i>. The V<\/span><\/span><\/span><\/span><\/span> basis<\/i> is an alternative universal basis to the more commonly studied basis consisting of Hadamard and \u03c0<\/span>\/<\/span>8<\/span><\/span><\/span><\/span><\/span><\/span> gates. We propose two classical algorithms for quantum circuit compilation: the first algorithm has expected polynomial time [in precision log<\/span>(<\/span>1<\/span>\/<\/span>\u03b5<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span>] and produces an \u03b5<\/span><\/span><\/span><\/span><\/span> approximation to a single-qubit unitary with a circuit depth \u2264<\/span>12<\/span><\/span>log<\/span>5<\/span><\/span>(<\/span>2<\/span>\/<\/span>\u03b5<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span><\/span>. The second algorithm performs optimized direct search and yields circuits a factor of 3 to 4 times shorter than our first algorithm, but requires time exponential in log<\/span>(<\/span>1<\/span>\/<\/span>\u03b5<\/span>)<\/span><\/span><\/span><\/span><\/span><\/span>; however, we show that in practice the runtime is reasonable for an important range of target precisions. Decomposing into the V<\/span><\/span><\/span><\/span><\/span> basis may offer advantages when considering the fault-tolerant implementation of quantum circuits.<\/p>\n<\/div>\n

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

We develop efficient algorithms for compiling single-qubit unitary gates into circuits over the universal V basis. The V basis is an alternative universal basis to the more commonly studied basis consisting of Hadamard and \u03c0\/8 gates. We propose two classical algorithms for quantum circuit compilation: the first algorithm has expected polynomial time [in precision log(1\/\u03b5)] […]<\/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":"alexeib","user_id":"30935"},{"type":"user_nicename","value":"gurevich","user_id":"31929"},{"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":"1","msr_journal":"Physical Review A","msr_number":"","msr_organization":"","msr_pages_string":"13","msr_page_range_start":"13","msr_page_range_end":"","msr_series":"","msr_volume":"88","msr_copyright":"","msr_conference_name":"","msr_doi":"10.1103\/PhysRevA.88.012313","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Krysta M. 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