A high threshold code for modular hardware with asymmetric noise

Abstract

We consider an approach to fault tolerant quantum computing based on a simple error detecting code operating as the substrate for a conventional surface code. We develop a customised decoder to process the information about the likely location of errors, obtained from the error detect stage, with an advanced variant of the minimum weight perfect matching algorithm. A threshold gate-level error rate of 1.42% is found for the concatenated code given highly asymmetric noise. This is superior to the standard surface code and remains so as we introduce a significant component of depolarising noise; specifically, until the latter is 70% the strength of the former. Moreover, given the asymmetric noise case, the threshold rises to 6.24% if we additionally assume that local operations have 20 times higher fidelity than long range gates. Thus for systems that are both modular and prone to asymmetric noise our code structure can be very advantageous.

arXiv comment11 pages, 6 figures

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Cited by in corpus (10)

• The XZZX Surface Code
• Fault-tolerant thresholds for the surface code in excess of 5% under biased noise
• Lindblad Tomography of a Superconducting Quantum Processor
• Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead
• Looped Pipelines Enabling Effective 3D Qubit Lattices in a Strictly 2D Device
• Generating Fault-Tolerant Cluster States from Crystal Structures
• Tailored cluster states with high threshold under biased noise
• A cellular automaton decoder for a noise-bias tailored color code
• Surface Code Design for Asymmetric Error Channels
• Practical quantum error correction with the XZZX code and Kerr-cat qubits