On Universal and FaultTolerant Quantum Computing
Abstract
A novel universal and faulttolerant 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 of two singlequbit gates (Hadamard and ${\sigma_z}^{1/4}$), and one doublequbit gate (ControlledNOT). Since the set consisting of ControlledNOT and Hadamard gates is not universal, the new basis achieves universality by including only one additional elementary (in the sense that it does not include angles that are irrational multiples of $\pi$) singlequbit gate, and hence, is potentially the simplest universal basis that one can construct. We also provide an alternative proof of universality for the only other known class of universal and faulttolerant basis proposed by Shor and by Kitaev.
 Publication:

arXiv eprints
 Pub Date:
 June 1999
 arXiv:
 arXiv:quantph/9906054
 Bibcode:
 1999quant.ph..6054B
 Keywords:

 Quantum Physics
 EPrint:
 10 pages, Latex. Emails addresses {boykin, talmo, pulver, vwani, vatan}@ee.ucla.edu