Dynamical Aspects of Information Storage in Quantum-Mechanical Systems

TL;DR

This paper investigates how information is stored and maintained in noisy quantum systems using statistical dynamics, introducing strictly contractive quantum channels to model realistic quantum operations and analyze thermodynamics and error thresholds.

Contribution

It introduces the concept of strictly contractive quantum channels to model nonideal quantum systems and explores their implications for thermodynamics and error correction in quantum information storage.

Findings

Strictly contractive channels model realistic quantum noise.

Thermodynamic analysis estimates resources for reliable quantum computation.

Bounds on maximum tolerable error rates are derived.

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.