Single-shot error correction and universal fault-tolerant computation with the 3D subsystem toric code

Presenting Author: Aleksander Kubica, Amazon Web Services Center for Quantum Computing
Contributing Author(s): Michael Vasmer, Joseph Iverson

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 explain how to fault-tolerantly implement a universal gate set in the 3D STC without state distillation. Lastly, we 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 above 1%. 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.

Read this article online: https://arxiv.org/abs/2106.02621

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