Dynamical Aspects of Information Storage in Quantum-Mechanical Systems

Abstract

We study information storage in noisy quantum registers and computers using the methods of statistical dynamics. We develop the concept of a strictly contractive quantum channel in order to construct mathematical models of physically realizable, i.e., nonideal, quantum registers and computers. Strictly contractive channels are simple enough, yet exhibit very interesting features, which are meaningful from the physical point of view. In particular, they allow us to incorporate the crucial assumption of finite precision of all experimentally realizable operations. Strict contractivity also helps us gain insight into the thermodynamics of noisy quantum evolutions (approach to equilibrium). Our investigation into thermodynamics focuses on the entropy-energy balance in quantum registers and computers under the influence of strictly contractive noise. Using entropy-energy methods, we are able to appraise the thermodynamical resources needed to maintain reliable operation of the computer. We also obtain estimates of the largest tolerable error rate. Finally, we explore the possibility of going beyond the standard circuit model of error correction, namely constructing quantum memory devices on the basis of interacting particle systems at low temperatures.