Fault-tolerant computation without concatenation
Eric Dennis · arXiv (Cornell University) · 1999
It has been known that 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 (probably ∼ 10 −3 –10 −6). Other, un-concatenated codes with their own attractive features—e.g., an accuracy threshold ∼ 10 −2 —have also been studied. A method to obtain universal computation is presented here which does not rely on any concatenated structure within the code itself, but instead emulates this structure with logical qubits in order to construct an encoded Toffoli gate. This realizes ∼ 10 −2 as a threshold for fault-tolerant quantum computation. 1 QEC codes and universal computation In the “space ” of all possible quantum error-correcting codes, much recent work has focused on a relatively small class, namely concatenated codes [1]–[7]. The basic idea behind these is to improve the results of a given few-qubit code by