A new universal and fault-tolerant quantum basis

A novel universal and fault-tolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists only of two single-qubit gates (Hadamard and sigma(z)(1/4)), and one two-qubit gate (Controlled-NOT), Moreover, a new general method for fault-tolerant implementation of quantum gates like Toffoli is introduced. This method is a generalization of the methods suggested by Shor (Proc, FOCS'96, 1996, p. 56) and later by Knill et al. (Proc. Roy. Sec. London Ser. A 454 (1998) 365). (C) 2000 Elsevier Science B.V. All rights reserved.