Quantum Computing is Scalable on a Planar Array of Qubits with Fabrication Defects

To successfully execute large-scale algorithms, a quantum computer will need to perform its elementary operations near perfectly. This is fundamental challenge since all physical qubits suffer considerable level of noise. Moreover, real systems are likely have finite yield, i.e., some nonzero proportion the components in complex device may be irredeemably broken at fabrication stage. We present threshold theorem showing that an arbitrarily large computation can completed with vanishing probability failure using two-dimensional array noisy density defects. complete our proof we introduce robust protocol measure high-weight stabilizers compensate for regions inactive qubits. obtain result surface-code architecture. Our approach therefore readily compatible ongoing experimental efforts build computer.