An interpretation of Union-Find Decoder on Weighted Graphs

Paths, trees, and flowers

Edmonds, J · 1965

Earlier work this paper cites.

An o (v— v— c— e—) algoithm for finding maximum matching in general graphs

Micali, S. & Vazirani, V. V · 1980

Earlier work this paper cites.

Faster scaling algorithms for general graph matching problems

Gabow, H. N. & Tarjan, R. E · 1991

Earlier work this paper cites.

Quantum codes on a lattice with boundary

Bravyi, S. B. & Kitaev, A. Y · 1998

Earlier work this paper cites.

Maximum skew-symmetric flows and matchings

Goldberg, A. V. & Karzanov, A. V · 2004

Earlier work this paper cites.

Understanding and using linear programming (Springer Science & Business Media, 2006)

Matousek, J. & Gärtner, B · 2006

Earlier work this paper cites.

Blossom V: a new implementation of a minimum cost perfect matching algorithm

Kolmogorov, V · 2009

Earlier work this paper cites.

Fault-tolerant quantum computing with color codes

Original

Landahl, A. J., Anderson, J. T. & Rice, P. R · 2011

Earlier work this paper cites.

How to write a 21st century proof

Original

Lamport, L · 2012

Cited alongside, same era.

An introduction to topological quantum codes

Original

Bombín, H · 2013

Cited alongside, same era.

Low-distance surface codes under realistic quantum noise

Tomita, Y. & Svore, K. M · 2014

Cited alongside, same era.

Minimum weight perfect matching of fault-tolerant topological quantum error correction in average o ⁡ ( 1 ) o(1) parallel time (2014)

Fowler, A. G · 2014

Cited alongside, same era.

The surface code with a twist

Yoder, T. J. & Kim, I. H · 2017

Cited alongside, same era.

Linear-time maximum likelihood decoding of surface codes over the quantum erasure channel

The xzzx surface code

Bonilla Ataides, J. P., Tuckett, D. K., Bartlett, S. D., Flammia, S. T. & Brown, B. J · 2021

Later among the works it cites.

Almost-linear time decoding algorithm for topological codes

Delfosse, N. & Nickerson, N. H · 2021

Later among the works it cites.

Practical quantum error correction with the xzzx code and kerr-cat qubits

Darmawan, A. S., Brown, B. J., Grimsmo, A. L., Tuckett, D. K. & Puri, S · 2021

Later among the works it cites.

Interpretation of union find decoder on weighted graphs and application to xzzx surface code (2022)

Wu, Y., Liyanage, N., Puri, S. & Zhong, L · 2022

Closest in time.

Personal communication

Oscar, H. & Gidney, C · 2022

Closest in time.

Decoder for the triangular color code by matching on a möbius strip

Sahay, K. & Brown, B. J · 2022

Closest in time.