Quantum Computer as an Inference Engine

We propose a new family of quantum computing algorithms which generalize the Deutsch-Jozsa, Simon and Shor ones. The goal of our algorithms is to estimate conditional probability distributions. Such estimates are useful in applications of Decision Theory and Artificial Intelligence, where inferences are made based on uncertain knowledge. The family of algorithms that we propose is based on a construction method that generalizes a Fredkin-Toffoli (FT) construction method used in the field of classical reversible computing. FT showed how, given any binary deterministic circuit, one can construct another binary deterministic circuit which does the same calculations in a reversible manner. We show how, given any classical stochastic network (classical Bayesian net), one can construct a quantum network (quantum Bayesian net) which can perform the same calculations as the classical one, but in a (piecewise) reversible manner. Thus, we extend the FT construction method so that it can be applied to any stochastic circuit, not just binary deterministic ones.