  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.
