Quantum Error Correction Gottesman, Daniel
Errors are likely to be a serious problem for quantum computers, both because they are built of small components and because qubits are inherently more vulnerable to error than classical bits because of processes such as decoherence. Consequently, to build a large quantum computer, we will likely need quantum error-correcting codes, which split up quantum states among a number of qubits in such a way that it is possible to correct for small errors. I will give an overview of the theory of quantum error correction and a discussion of fault-tolerant quantum computation, which applies quantum error-correcting codes to allow more reliable quantum computations. I will cover Shor's 9-qubit code, stabilizer codes, CSS codes, and the threshold theorem, which says that arbitrarily long reliable quantum computations are possible, provided the error rate per gate or time step is below some constant threshold value.
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