Hypothesis elimination on a quantum computer
  Hypothesis elimination is a special case of Bayesian updating, where each piece of new data rules out a set of prior hypotheses. We describe how to use Grover's algorithm to perform hypothesis elimination for a class of probability distributions encoded on a register of qubits, and establish a lower bound on the required computational resources. 
Andrei N. Soklakov and Ruediger Schack (Royal Holloway, University of   London)