Nondeterministic testing of Sequential Quantum Logic propositions on a   quantum computer
  In the past few years it has been shown that universal quantum computation can be obtained by projective measurements alone, with no need for unitary gates. This suggests that the underlying logic of quantum computing may be an algebra of sequences of quantum measurements rather than an algebra of products of unitary operators. Such a Sequential Quantum Logic (SQL) was developed in the late 70's and has more recently been applied to the consistent histories framework of quantum mechanics as a possible route to the theory of quantum gravity. In this letter, I give a method for deciding the truth of a proposition in SQL with nonzero probability of success on a quantum computer. 
M. S. Leifer