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Topological stabilizer codes with different spatial dimensions have complementary properties.Here I show that the spatial dimension can be switched using gauge fixing.Combining 2D and 3D gauge color codes in a 3D qubit lattice, fault-tolerant quantum computation can be achieved with constant time overhead on the number of logical gates, up to efficient global classical computation, using only local quantum operations.Single-shot error correction plays a crucial role.
Héctor Bombín (Wed,) studied this question.