Tailored cluster states with high threshold under biased noise

Abstract

Fault-tolerant cluster states form the basis for scalable measurement-based quantum computation. Recently, new stabilizer codes for scalable circuit-based quantum computation have been introduced that have very high thresholds under biased noise where the qubit predominantly suffers from one type of error, e.g. dephasing. However, extending these advances in stabilizer codes to generate high-threshold cluster states for biased noise has been a challenge, as the standard method for foliating stabilizer codes to generate fault-tolerant cluster states does not preserve the noise bias. In this work, we overcome this barrier by introducing a generalization of the cluster state that allows us to foliate stabilizer codes in a bias-preserving way. As an example of our approach, we construct a foliated version of the XZZX code which we call the XZZX cluster state. We demonstrate that under a circuit-level noise model, our XZZX cluster state has a threshold more than double the usual cluster state when dephasing errors are more likely than errors which cause bit flips by a factor of $O(100)$ or more.

Main text: 12 pages, 7 figures. Supplement: 5 pages, 5, figures

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• High threshold codes for neutral atom qubits with biased erasure errors
• High-threshold quantum computing by fusing one-dimensional cluster states
• Robust teleportation of a surface code and cascade of topological quantum phase transitions
• Tailoring fusion-based error correction for high thresholds to biased fusion failures
• Encoded-Fusion-Based Quantum Computation for High Thresholds with Linear Optics
• Leveraging Qubit Loss Detection in Fault Tolerant Quantum Algorithms
• Time-bin entanglement in the deterministic generation of linear photonic cluster states
• Tailoring Dynamical Codes for Biased Noise: The X${}^3$Z${}^3$ Floquet Code
• Preservation of entanglement in local noisy channels
• Simulated-annealing decoder for the XZZX code with greedy-matching initialization