Abstract
In this chapter, we explain how to perform topological fault-tolerant quantum computation on the surface code. All operations employed are nearest-neighbor (at most) two-qubit gates and single-qubit measurements on a 2D array of qubits. This property is quite favorable for the fabrication of qubits and their control lines on a chip. Fault-tolerance ensures that no local noise during any sort of operations ever spoil the quantum computation, if the noise strength is smaller than a certain threshold value, as seen below.
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