Quantum computing by simulations is based upon similarity between mathematical formalism of quantum mechanics and phenomena to be computed. It exploits a dynamical convergence of several competing phenomena to an attractor which can represent an extrenum of a function, an image, a solution to a system of ODE, or a stochastic process. In this chapter, a quantum version of recurrent nets (QRN) as an analog computing device is discussed. This concept is introduced by incorporating classical feedback loops into conventional quantum networks. It is shown that the dynamical evolution of such networks, which interleave quantum evolution with measurement and reset operations, exhibit novel dynamical properties.

Moreover, decoherence in quantum recurrent networks is less problematic than in conventional quantum network architectures due to the modest phase coherence times needed for network operation. It is proven that a hypothetical quantum computer can implement an exponentially larger number of the degrees of freedom within the same size.