Fault-tolerant quantum computation with constant error

In the past year many developments have taken place in the area of quantum error corrections. Recently Shor showed how to perform fault tolerant quantum computation when, , the probability for a fault in one time step per qubit or per gate, is polylogarithmically small. This paper closes the gap and shows how to perform fault tolerant quantum computation when the error probability, , is smaller than some constant threshold, 0 . The cost is polylogarithmic in time and space, and no measurements are used during the quantum computation. The same result is shown also for quantum circuits which operate on nearest neighbors only.