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- W4290804501 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.12 MoreReceived 29 December 2021Accepted 13 July 2022DOI:https://doi.org/10.1103/PRXQuantum.3.030319Published 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.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum error correctionQuantum gatesQuantum memoriesSurface code quantum computingTopological quantum computingQuantum Information" @default.
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- W4290804501 date "2022-08-08" @default.
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- W4290804501 title "Morphing Quantum Codes" @default.
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- W4290804501 doi "https://doi.org/10.1103/prxquantum.3.030319" @default.
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