A mathematical model of a quantum analog-computing device that would simulate the human decision-making process has been developed. Like the immune-inspired- computing model described in the preceding article, this model is intended to contribute to improvement in the autonomy of robots and spacecraft.

The device would include quantum recurrent networks that would represent motor dynamics, plus classical neural networks that would represent the evolution of probabilities of processes that, in turn, would represent mental dynamics. The decision-making process would be made autonomous by use of feedback from mental to motor dynamics. In the model, this feedback changes a stochastic matrix based upon distributions of the probabilities. The resulting coupled motor and mental dynamics are described by nonlinear Markov chains that can decrease entropy without recourse to an external source of information.

In terms of mental phenomena, the feedback would play the role of “common sense” in the form of invariants or patterns of behavior that can be abstracted from prior knowledge and experience and can be applied to whole classes of situations similar to those of immediate interest. Like “common sense,” this feedback would be used in the quantum decision maker to replace unavailable external information by information from an internal knowledge base. The human ability to do this is recognized and widely exploited in psychology and has been known, since the time of ancient philosophers, to follow from the fact that a human possesses a self-image and interacts with it.

In the model, a quantum recurrent network is regarded as a quantum system represented by an equation that describes the relationships among (1) the inputs to the network at time t, (2) the outputs of the network at a later time t + τ, (3) a set of unitary operators that are defined by the Hamiltonian operator of the quantum system and express the temporal evolution of the quantum system, and (4) a measurement operator that projects the evolved quantum state into one of the eigenvectors of the system. The effect of the measurement operator can be characterized as similar to that of a sigmoid function in a classical neural networks. Because of the stochastic nature of quantum measurements, the outputs at time t + τ are random; as such, these outputs form a Markovian stochastic process.

The internal knowledge base is stored in a mental submodel in the form of probability distributions. Formally, the knowledge base is represented by the synaptic weights of neural networks, and the knowledge is divided into two parts. The first part includes knowledge that pertains to personal experience, habits, and such inclinations as averseness or proneness to risk. The second part depends upon an objective formulated in terms of probability invariants. Dependence upon the objective can include learning modeled by real-time adjustment of synaptic weights, adapted from theory of neural networks. As soon as the synaptic weights are determined, the common-sense-simulator portion of the model follows an optimal strategy, regardless of unexpected changes in the external world.

This work was done by Michail Zak of Caltech for NASA’s Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at www.nasatech.com/tsp  under the Information Sciences category. NPO-21038