Creation of a persistent quantum bit using error correction

The construction of large, coherent quantum systems necessary for quantum computation remains an entreating but elusive goal, due to the ubiquitous nature of decoherence. Recent progress in quantum error correction schemes have given new hope to this field, but thus far, the codes presented in the literature assume a restricted number of errors and error free encoding, decoding, and measurement. We investigate a specific scenario without these assumptions; in particular, we evaluate a scheme to preserve a single quantum bit against phase damping using a three-qubit encoding based on Shor, and study the effect of decoherence not only during storage but also during processing. We derive an general upper limit on the allowable decoherence per time step. Physically, our results suggest the feasibility of engineering artificial metastable states through repeated error correction.