@ARTICLE{Steane_quantumreed-muller, author = {A. M. Steane}, title = {Quantum Reed-Muller codes}, journal = {IEEE Trans. Inf. Theory}, year = {} }

Share

OpenURL

Abstract

A set of quantum error correcting codes based on classical Reed-Muller codes is described. The codes have parameters [[n,k,d]] = [[2 r, 2 r − C(r,t) − 2 ∑ t−1 i=0 C(r,i), 2t + 2 t−1]]. The study of quantum information is currently stimulating much interest. Most of the basic concepts of classical information theory have counterparts in quantum information theory, and among these is the idea of an error correcting code. An error correcting code is a means of storing information (whether quantum or classical) in a set of bits (ie either qubits or classical bits) in such a way that the information can be extracted even after a subset of the bits has changed in an unknown way. Such codes are a fundamental part of the study of classical information channels. The possibility of quantum error correction was only recently discovered [1, 2]. Importantly, it was shown that efficient quantum codes exist for arbitrarily large amounts of quantum information [3, 4]. The word ‘efficient ’ refers to the fact that the rate k/n of the