Vasmer, Michael and Kubica, Aleksander (2022) Morphing Quantum Codes. PRX Quantum, 3 (3). Art. No. 030319. ISSN 2691-3399. doi:10.1103/prxquantum.3.030319. https://resolver.caltech.edu/CaltechAUTHORS:20220808-967210000
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Abstract
We introduce a morphing procedure that can be used to generate new quantum codes from existing quantum codes. In particular, we morph the 15-qubit Reed-Muller code to obtain a [[10,1,2]] code that is the smallest-known stabilizer code with a fault-tolerant logical T gate. In addition, we construct a family of hybrid color-toric codes by morphing the color code. Our code family inherits the fault-tolerant gates of the original color code, implemented via constant-depth local unitaries. As a special case of this construction, we obtain toric codes with fault-tolerant multiqubit control-Z gates. We also provide an efficient decoding algorithm for hybrid color-toric codes in two dimensions and numerically benchmark its performance for phase-flip noise. We expect that morphing may also be a useful technique for modifying other code families such as triorthogonal codes.
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| Additional Information: | Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. (Received 29 December 2021; accepted 13 July 2022; published 8 August 2022) M.V. thanks Dan Browne, Simon Burton, and Chris Chubb for insightful discussions and Raymond Laflamme for valuable comments on an earlier draft of this paper. A.K. acknowledges funding provided by the Simons Foundation through the “It from Qubit” Collaboration. This work was completed prior to A.K. joining the AWS Center for Quantum Computing. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities. | |||||||||
| Group: | AWS Center for Quantum Computing | |||||||||
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| Issue or Number: | 3 | |||||||||
| DOI: | 10.1103/prxquantum.3.030319 | |||||||||
| Record Number: | CaltechAUTHORS:20220808-967210000 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20220808-967210000 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 116168 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | George Porter | |||||||||
| Deposited On: | 09 Aug 2022 20:12 | |||||||||
| Last Modified: | 09 Aug 2022 20:12 |
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