Quantum walks, automata, and structured search

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.

[1]  Langford B. White,et al.  Automated Planning Using Quantum Computation , 2006, ICAPS.

[2]  I. Fuss,et al.  Momentum Dynamics of One Dimensional Quantum Walks , 2006, quant-ph/0604197.

[3]  Sarah L. Hickmott,et al.  Reduced MDP Representation of a Logistical Planning Problem Using Petri-Nets , 2005, Australian Conference on Artificial Intelligence.

[4]  Langford B. White,et al.  Quantum search in stochastic planning , 2005, SPIE International Symposium on Fluctuations and Noise.

[5]  Viv Kendon,et al.  Quantum walks on general graphs , 2003, quant-ph/0306140.

[6]  John Watrous,et al.  Continuous-Time Quantum Walks on the Symmetric Group , 2003, RANDOM-APPROX.

[7]  Andrew M. Childs,et al.  An Example of the Difference Between Quantum and Classical Random Walks , 2001, Quantum Inf. Process..

[8]  Andris Ambainis,et al.  Quantum walks on graphs , 2000, STOC '01.

[9]  L. White,et al.  An analysis of quantum walks , 2007 .

[10]  Stefan Edelkamp.  Automated Planning: Theory and Practice , 2007, Künstliche Intell..