Quantum walks, automata, and structured search
Sanjeev Naguleswaran, Ian Fuss, L.B. White · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2007
We explore the application of a quantum algorithm to optimisation problems over a structured space. For example, problems in automated planning can be represented as automata. These automata are shown to posses algebraic structure that can be exploited by a quantum period finding algorithm. The fact that the quantum walk also provides exponential speed-up over these same structures is of particular interest and results of our investigation will be presented.