Abstract
Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node level from the root. We devise a quantum-mechanical algorithm that evolves a state, initially localized at the root, through the tree. We prove that if the classical strategy succeeds in reaching level in time polynomial in then so does the quantum algorithm. Moreover, we find examples of trees for which the classical algorithm requires time exponential in but for which the quantum algorithm succeeds in polynomial time. The examples we have so far, however, could also be solved in polynomial time by different classical algorithms.
- Received 11 July 1997
DOI:https://doi.org/10.1103/PhysRevA.58.915
©1998 American Physical Society