{"id":152645,"date":"2018-11-06T17:24:14","date_gmt":"2018-11-07T01:24:14","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/the-tunnelling-salesman-truncated-variational-approximations-for-quantum-mechanical-global-optimization\/"},"modified":"2018-11-06T17:24:14","modified_gmt":"2018-11-07T01:24:14","slug":"the-tunnelling-salesman-truncated-variational-approximations-for-quantum-mechanical-global-optimization","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/the-tunnelling-salesman-truncated-variational-approximations-for-quantum-mechanical-global-optimization\/","title":{"rendered":"The Tunnelling Salesman: Truncated Variational Approximations for Quantum Mechanical Global Optimization"},"content":{"rendered":"<div class=\"asset-content\">\n<p>In this work we present a novel method for global optimization, exploiting the mathematics of quantum mechanics, and in particular the tunnelling phenomenon. We consider a quantum mechanical system with a single particle in a potential specified by the cost function of our optimization problem. We assume the groundstate of the system is localised to the global minimum of the potential function, a condition which can be assured by choosing the particle mass sufficiently large. We then approximate this groundstate using a variational approach to optimise an expansion in terms of a truncated basis set of harmonic oscillator wave functions. We show how to encode integer factoring and travelling salesman problems in terms of finding the global minimum of a quartic polynomial cost function. We demonstrate our quantum algorithm on one- and two-dimensional toy problems, and apply it to factoring biprimes with 10 bits.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this work we present a novel method for global optimization, exploiting the mathematics of quantum mechanics, and in particular the tunnelling phenomenon. We consider a quantum mechanical system with a single particle in a potential specified by the cost function of our optimization problem. We assume the groundstate of the system is localised to [&hellip;]<\/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":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"MSR-TR-2002-100","msr_organization":"","msr_pages_string":"9","msr_page_range_start":"9","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Oliver B. Downs, Hagai Attias, Christopher J.C. 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