Related papers: Morphing quantum codes

Morphing quantum codes

URL: http://arxiv.org/abs/2112.01446v2
Date: Tue, 16 Aug 2022 22:17:12 GMT
Title: Morphing quantum codes
Authors: Michael Vasmer and Aleksander Kubica
Abstract summary: We morph the 15-qubit Reed-Muller code to obtain the smallest known stabilizer code with a fault-tolerant logical $T$ gate. We construct a family of hybrid color-toric codes by morphing the color code.
Score: 77.34726150561087
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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 multi-qubit 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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