Quantum Reed-Solomon Codes
Markus Grassl, Willi Geiselmann, Thomas Beth, Universität Karlsruhe · 1999
. We introduce a new class of quantum error--correcting codes derived from (classical) Reed--Solomon codes over finite fields of characteristic two. Quantum circuits for encoding and decoding based on the discrete cyclic Fourier transform over finite fields are presented. 1 Introduction During the last years it has been shown that computers taking advantage of quantum mechanical phenomena outperform currently used computers. The striking examples are integer factoring in polynomial time (see [18]) and finding pre--images of an n--ary Boolean function ("searching") in time O( p 2 n ) (see [12]). Quantum computers are not only of theoretical nature---there are several suggestions how to physically realize them (see, e. g., [6, 7]). On the way towards building a quantum computer, one very important problem is to stabilize quantum mechanical systems since they are very vulnerable. A theory of quantum error--correcting codes has already been established (see [15]). Nevertheless, the pr...