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Actis: A Strictly Local Union–Find Decoder


Tim Chan1 and Simon C. Benjamin1,2

1Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
2Quantum Motion, 9 Sterling Way, London N7 9HJ, United Kingdom

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Fault-tolerant quantum computing requires classical hardware to perform the decoding necessary for error correction. The Union–Find decoder is one of the best candidates for this. It has remarkably organic characteristics, involving the growth and merger of data structures through nearest-neighbour steps; this naturally suggests the possibility of its realisation using a lattice of simple processors with nearest-neighbour links. In this way the computational load can be distributed with near-ideal parallelism. Here we show for the first time that this strict (rather than partial) locality is practical, with a worst-case runtime $mathcal O(d^3)$ and mean runtime subquadratic in the surface code distance $d$. A novel parity-calculation scheme is employed which can simplify previously proposed architectures, and our approach is optimised for circuit-level noise. We compare our local realisation with one augmented by long-range links; while the latter is of course faster, we note that local asynchronous logic could negate the difference.

Quantum computers have the potential to offer groundbreaking computational power, but only if protected from noise. This is done via error correction: a way to exchange many noisy qubits (units of computation) for fewer but more perfect qubits. The crucial subtask of monitoring measurements from the quantum processor to deduce when errors have occurred is called decoding. This must be performed extremely quickly in order to keep pace with the quantum machine. Here we modify an existing decoding algorithm to make it local i.e. runnable on a grid of identical processing cells, each communicating only with their nearest neighbours. Locality has various practical benefits in speed, layout and robustness. We test our local design and find that its runtime indeed behaves more favourably than the original algorithm; we then suggest the use of ‘asynchronous’ hardware to maximise our design’s absolute performance.

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Cited by

[1] Sam J. Griffiths and Dan E. Browne, “Union-find quantum decoding without union-find”, arXiv:2306.09767, (2023).

[2] Asmae Benhemou, Kaavya Sahay, Lingling Lao, and Benjamin J. Brown, “Minimising surface-code failures using a color-code decoder”, arXiv:2306.16476, (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2023-11-14 13:28:32). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2023-11-14 13:28:31: Could not fetch cited-by data for 10.22331/q-2023-11-14-1183 from Crossref. This is normal if the DOI was registered recently.


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