Markov processes in quantum information science

This proposal suggests the investigation and application of Markov processes in quantum information science. The project is to be carried out at the Massachusetts Institute of Technology during a period of two years and at the University of Vienna during the return phase of one year. The theory of quantum mechanics has not only emerged as the basis of our understanding of matter on a small scale, but has also changed the way we think about the processing of information in physical systems. During the recent years a large amount of the research has been focused on the investigation and experimental control of quantum mechanical systems with ever increasing degrees of freedom. These systems hold the promise of becoming the physical architecture to implement quantum information processing protocols, which exceed the power of current classical protocols. The strongest adversary to this endeavor is the phenomenon of decoherence, which arises due to the system`s interaction with the environment. The result of this interaction is the dissipation and loss of quantum information in the system. In recent approaches to quantum information processing novel proposals have been put forward makeing ample use of quantum Markov processes. These processes can be understood as the formal framework of open system evolution. In these approaches, the goal is to actively engineer a specific type of dissipation, rather than avoiding it completely, to achieve the quantum information processing task. Recently, it has been shown that the dissipation in a specially engineered open system can actually serve as a resource for quantum computation and state preparation, which is as universal as unitary quantum information processing itself. In this proposal we want to further develop the theoretical basis for the applications of quantum Markov processes to quantum information processing. The central goals of this proposal can be cast into three objectives: 1. The development of a mathematical theory to give explicit bounds on the convergence rate of quantum Markov processes to its steady state and the construction of perturbation bounds for the steady state subspace. 2. The engineering of dissipative quantum memory and the investigation of its stability to noise. 3. The development of Markov chain based quantum algorithms for the simulation of quantum physics, in particular, the construction of quantum algorithms for physically restricted forms of quantum computing. These architectures have the prospect of becoming experimentally available in the foreseeable future.