A fault-tolerant one-way quantum computer - PiTP

Surface codesplaquettestabilizerOne qubit located on every edgesite stabilizerZ =ZZ ZZ ZXX XXZZZZZXXXXXXXZ XXZZsyndrome at endpointharmlesserrorequivalentharmfulerrors=X• Errors are represented by chains.• Homologically equivalent chains correspond to physicallyequivalent errors.• Harmfull errors stretch across the entire lattice (rare events).A. Kitaev,quant-ph/9707021 (1997).