{"id":314021,"date":"2018-11-06T17:09:16","date_gmt":"2018-11-07T01:09:16","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=314021"},"modified":"2018-11-06T17:09:16","modified_gmt":"2018-11-07T01:09:16","slug":"efficient-quantum-circuits-non-qubit-quantum-error-correcting-codes","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/efficient-quantum-circuits-non-qubit-quantum-error-correcting-codes\/","title":{"rendered":"Efficient Quantum Circuits for Non-Qubit Quantum Error-Correcting Codes"},"content":{"rendered":"<p><span style=\"font-family: Palatino Linotype;\">We present two methods for the construction of quantum circuits for quantum error-correcting codes (QECC). The underlying quantum systems are tensor products of subsystems (qudits) of equal dimension which is a prime power. For a QECC encoding k qudits into n qudits, the resulting quantum circuit has O(n(n-k)) gates. The running time of the classical algorithm to compute the quantum circuit is O(n(n-k)^2).<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We present two methods for the construction of quantum circuits for quantum error-correcting codes (QECC). The underlying quantum systems are tensor products of subsystems (qudits) of equal dimension which is a prime power. For a QECC encoding k qudits into n qudits, the resulting quantum circuit has O(n(n-k)) gates. The running time of the classical [&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":[193715],"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-314021","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-quantum","msr-locale-en_us"],"msr_publishername":"","msr_edition":"International Journal of Foundations of Computer Science 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