How to derive a quantum complexity lower bound

The modeling of computation using logic circuits occupies an important position in the fundamentals of complexity theory including quantum complexity theory. Consequently, research into methods for computing logic functions on quantum circuits as well as for minimizing and simplifying such circuits has become extremely important. In this paper we explicitly formulate the depth minimization problem for quantum logic circuits and show that this problem is closely related to a geometric approach to deriving a lower bound on the size of a quantum logic circuit. (C) 2007 Wiley Periodicals, Inc.