{"id":166319,"date":"2018-11-06T17:22:56","date_gmt":"2018-11-07T01:22:56","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/leveraging-automorphisms-of-quantum-codes-for-fault-tolerant-quantum-computation\/"},"modified":"2018-11-06T17:22:56","modified_gmt":"2018-11-07T01:22:56","slug":"leveraging-automorphisms-of-quantum-codes-for-fault-tolerant-quantum-computation","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/leveraging-automorphisms-of-quantum-codes-for-fault-tolerant-quantum-computation\/","title":{"rendered":"Leveraging automorphisms of quantum codes for fault-tolerant quantum computation"},"content":{"rendered":"<div class=\"asset-content\">\n<p>Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant computations is the ability to perform a universal set of quantum gates that act on the code space of an underlying quantum code. To implement such a universal gate set fault-tolerantly is an expensive task in terms of physical operations, and any possible shortcut to save operations is potentially beneficial and might lead to a reduction in overhead for fault-tolerant computations. We show how the automorphism group of a quantum code can be used to implement some operators on the encoded quantum states in a fault-tolerant way by merely permuting the physical qubits. We derive conditions that a code has to satisfy in order to have a large group of operations that can be implemented transversally when combining transversal CNOT with automorphisms. We give several examples for quantum codes with large groups, including codes with parameters [[8,3,3]], [[15,7,3]], [[22,8,4]], and [[31,11,5]].<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant computations is the ability to perform a universal set of quantum gates that act on the code space of an underlying quantum code. To implement such a universal gate [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[243138],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-166319","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-quantum","msr-locale-en_us"],"msr_publishername":"","msr_edition":"Proceedings of the 2013 IEEE International Symposium on Information Theory (ISIT'13), Istanbul, Turkey","msr_affiliation":"","msr_published_date":"2013-01-01","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"534\u2013538","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"See also arXiv preprint 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