11 - Can quantum systems learn? Quantum updating

Summary

Learning is a criticai aspect of any intelligent cognitive system. How can this be done within a QIP approach? This is a relatively new field, but some progress has already been achieved (Ivancevic & Ivancevic, 2010). There are at least three ways to accomplish learning using quantum principles. One way is to update the agent's belief state based on experience (Schack et al., 2001), as done in Bayesian learning models (Griffiths et al., 2008). A second way is to update the weights in a unitary matrix using gradient descent of an error function (Zak & Williams, 1998), as done in connectionist learning models (Rumelhart & McClelland, 1986). A third way is to update the amplitudes assigned to control U gate actions based on rewards and punishments (Dong et al., 2010), as done with reinforcement learning algorithms (Sutton & Barto, 1998). This chapter reviews all three approaches.

Quantum state updating based on experience

For the first type of quantum learning model, consider how to update an agent's belief state based on experience. In Chapter 4 we presented a quantum model for probability judgments, and in that chapter the initial belief state denoted |ψ⟩ was given or assumed to be already known in advance – when new facts were presented, inferences were made from the known state |ψ⟩ using Luder's rule. However, where does this initial state |ψ⟩ come from? Now we examine how this initial state |ψ⟩ can be learned or estimated from experience. Principles borrowed from quantum state tomography can be used to model the estimation of a quantum state (Schack et al., 2001).