Toward fault-tolerant quantum computation without concatenation

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Abstract
It is known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own attractive features such as improved accuracy threshold, local operations, have also been studied. By iteratively distilling a certain two-qubit entangled state it is shown how to perform an encoded Toffoli gate, important for universal computation, on codes whose C-NOT operation is bitwise. For certain codes, over a very large range of block sizes, this technique requires at most one concatenation.

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