  In the paper we develop a method for constructing quantum algorithms for
computing Boolean functions by quantum ordered read-once branching programs
(quantum OBDDs). Our method is based on fingerprinting technique and
representation of Boolean functions by their characteristic polynomials. We use
circuit notation for branching programs for desired algorithms presentation.
For several known functions our approach provides optimal QOBDDs. Namely we
consider such functions as Equality, Palindrome, and Permutation Matrix Test.
We also propose a generalization of our method and apply it to the Boolean
variant of the Hidden Subgroup Problem.
