On The Power of Exact Quantum Polynomial Time
  We investigate the power of quantum computers when they are required to return an answer that is guaranteed correct after a time that is upper-bounded by a polynomial in the worst case. In an oracle setting, it is shown that such machines can solve problems that would take exponential time on any classical bounded-error probabilistic computer. 
Gilles Brassard (Universite de Montreal) and Peter Hoyer (Odense   University)