Lower Bounds on Quantum Query Complexity
  Shor's and Grover's famous quantum algorithms for factoring and searching show that quantum computers can solve certain computational problems significantly faster than any classical computer. We discuss here what quantum computers_cannot_ do, and specifically how to prove limits on their computational power. We cover the main known techniques for proving lower bounds, and exemplify and compare the methods. 
Peter Hoyer (U Calgary), Robert Spalek (CWI)