Good Quantum Error-Correcting Codes Exist
Quantum Physics
2009-10-28 v2
Abstract
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting n qubits can be used to faithfully reconstruct the original quantum state of the k encoded qubits. Quantum error-correcting codes are shown to exist with asymptotic rate k/n = 1 - 2H(2t/n) where H(p) is the binary entropy function -p log p - (1-p) log (1-p). Upper bounds on this asymptotic rate are given.
Cite
@article{arxiv.quant-ph/9512032,
title = {Good Quantum Error-Correcting Codes Exist},
author = {A. R. Calderbank and Peter W. Shor},
journal= {arXiv preprint arXiv:quant-ph/9512032},
year = {2009}
}
Comments
Latex, 23 pages, 1 figure. Revised April 1996 to give more intuition and an example. Submitted to Phys. Rev. A