Single-shot quantum error correction with the three-dimensional subsystem toric code

• URL: http://arxiv.org/abs/2106.02621v1
• Date: Fri, 4 Jun 2021 17:35:00 GMT
• Title: Single-shot quantum error correction with the three-dimensional subsystem toric code
• Authors: Aleksander Kubica, Michael Vasmer
• Abstract summary: We introduce a new topological quantum code, the three-dimensional subsystem toric code (3D STC) The 3D STC can be realized by measuring geometrically-local parity checks of weight at most three on the cubic lattice with open boundary conditions.
• Score: 77.34726150561087
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce a new topological quantum code, the three-dimensional subsystem toric code (3D STC), which is a generalization of the stabilizer toric code. The 3D STC can be realized by measuring geometrically-local parity checks of weight at most three on the cubic lattice with open boundary conditions. We prove that single-shot quantum error correction (QEC) is possible with the 3D STC, i.e., one round of local parity-check measurements suffices to perform reliable QEC even in the presence of measurement errors. We also propose an efficient single-shot QEC strategy for the 3D STC and investigate its performance. In particular, we numerically estimate the resulting storage threshold against independent bit-flip, phase-flip and measurement errors to be $p_\text{STC} \approx 1.045\%$. Such a high threshold together with local parity-check measurements of small weight make the 3D STC particularly appealing for realizing fault-tolerant quantum computing.

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