EFFECTS OF NOISE ON QUANTUM ERROR-CORRECTION ALGORITHMS

It has recently been shown that there are efficient algorithms for qua ntum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation, however, are limited by decoherence, in whi ch the effect of an external environment causes random errors in the q uantum calculation. To combat this problem, quantum error correction s chemes have been proposed, in which a single quantum bit (qubit) is '' encoded'' as a state of some larger number of qubits, chosen to resist particular types of errors. Most such schemes are vulnerable, however , to errors in the encoding and decoding itself. We examine two such s chemes, in which a single qubit is encoded in a state of n qubits whil e subject to dephasing or to arbitrary isotropic noise. Using both ana lytical and numerical calculations, we argue that error correction rem ains beneficial in the presence of weak noise, and that there is an op timal time between error correction steps, determined by the strength of the interaction with the environment and the parameters set by the encoding.