ABSTRACT
In Fig. 2b of this Review, two of the gates were inadvertently swapped. At the top right, 'Xa+c' should have been 'Zb', and at the bottom right 'Zb' should have been 'Xa+c'. Fig. 2b has been corrected online. The Supplementary Information of this Author Correction contains the original, incorrect Fig. 2b, for transparency.
ABSTRACT
A practical quantum computer must not merely store information, but also process it. To prevent errors introduced by noise from multiplying and spreading, a fault-tolerant computational architecture is required. Current experiments are taking the first steps toward noise-resilient logical qubits. But to convert these quantum devices from memories to processors, it is necessary to specify how a universal set of gates is performed on them. The leading proposals for doing so, such as magic-state distillation and colour-code techniques, have high resource demands. Alternative schemes, such as those that use high-dimensional quantum codes in a modular architecture, have potential benefits, but need to be explored further.
