Majorana-XYZ subsystem code

Tobias Busse; Lauri Toikka

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arXiv · 2603.26311

Majorana-XYZ subsystem code

Tobias Busse·Lauri Toikka

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Abstract

Building fault-tolerant quantum computers is a current priority for the quantum computing industry and academic counterparts. We present a quantum error correction code encoding a single logical qubit into $n=L^2$ physical qubits with distance $d = L$ as a subsystem code, and $n-O(\sqrt{n})$ logical qubits with distance $d=3$ as a standard stabiliser code. The logical single-qubit gates in the subsystem code are transversal. Under independent $X,Z$ noise we find a threshold of $1.4\% \pm 0.1\%$ for odd distance and $1.8\% \pm 0.2\%$ for even distance for the subsystem variant. The code detects every 1- and 2-qubit error, and additionally every error of weight 3 and higher (constrained by the distance) that is not a product of the 3-qubit check operations. These operations act on the gauge qubits leaving the subsystem code space invariant. The code can be implemented by qubits in a triangular configuration with the plaquettes as 3-qubit check operations.

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BibTeX RIS

Tobias Busse, Lauri Toikka. 2026-03-27. Majorana-XYZ subsystem code. https://arxiv.org/abs/2603.26311

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