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For quantum error-correcting codes to be realizable, it is important that the qubits subject to the code constraints exhibit some form of limited connectivity.
A separator theorem for planar graphs
R. J. Lipton and R. E. Tarjan · 1979
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A separator theorem for graphs of bounded genus
J. R. Gilbert, J. P. Hutchinson, and R. E. Tarjan · 1984
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A separator theorem for nonplanar graphs
N. Alon, P. Seymour, and R. Thomas · 1990
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A unified geometric approach to graph separators
S. Teng, G. Miller, and S. Vavasis · 1991
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Faster shortest-path algorithms for planar graphs
M. R. Henzinger, P. Klein, S. Rao, and S. Subramanian · 1997
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Quantum computations: algorithms and error correction
A. Y. Kitaev · 1997
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A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
S. Bravyi and B. Terhal · 2009
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Tradeoffs for reliable quantum information storage in 2D systems
S. Bravyi, D. Poulin, and B. Terhal · 2010
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Tradeoffs for reliable quantum information storage in surface codes and color codes
N. Delfosse · 2013
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Fault tolerance of quantum low-density parity check codes with sublinear distance scaling
A. A. Kovalev and L. P. Pryadko · 2013
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Fault-tolerant quantum computation with constant overhead
D. Gottesman · 2014
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Limits on the storage of quantum information in a volume of space
S. T. Flammia, J. Haah, M. J. Kastoryano, and I. H. Kim · 2017
N. Delfosse, M. E. Beverland, and M. A. Tremblay · 2021
Later among the works it cites.
Connectivity constrains quantum codes
N. Baspin and A. Krishna · 2022
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Quantifying nonlocality: How outperforming local quantum codes is expensive
N. Baspin and A. Krishna · 2022
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A linear-algebraic and lattice-theoretical look at the cleaning lemma of quantum coding theory
G. Kalachev and S. Sadov · 2022
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A lower bound on the overhead of quantum error correction in low dimensions
N. Baspin, O. Fawzi, and A. Shayeghi · 2023
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Cited alongside, same era.