Mathematica: a system for doing mathematics by computer (2nd ed.)
Mathematica: a system for doing mathematics by computer (2nd ed.)
Nanosystems: molecular machinery, manufacturing, and computation
Nanosystems: molecular machinery, manufacturing, and computation
Partial constraint satisfaction
Artificial Intelligence - Special volume on constraint-based reasoning
Minimizing conflicts: a heuristic repair method for constraint satisfaction and scheduling problems
Artificial Intelligence - Special volume on constraint-based reasoning
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
The hardest constraint problems: a double phase transition
Artificial Intelligence
Exploiting the deep structure of constraint problems
Artificial Intelligence
Randomized algorithms
Phase transitions and the search problem
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
An introduction to quantum computing for non-physicists
ACM Computing Surveys (CSUR)
Solving highly constrained search problems with quantum computers
Journal of Artificial Intelligence Research
Exploiting the deep structure of constraint satisfaction problems with quantum computers
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Property analysis of symmetric travelling salesman problem instances acquired through evolution
EvoCOP'05 Proceedings of the 5th European conference on Evolutionary Computation in Combinatorial Optimization
Quantum search in structured database
ICNC'05 Proceedings of the First international conference on Advances in Natural Computation - Volume Part III
Self-control of the time complexity of a constraint satisfaction problem solver program
Journal of Systems and Software
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We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem structure as used by classical backtrack methods to avoid unproductive search choices. This quantum algorithm is much more likely to find solutions than the simple direct use of quantum parallelism. Furthermore, empirical evaluation on small problems shows this quantum algorithm displays the same phase transition behavior, and at the same location, as seen in many previously studied classical search methods. Specifically, difficult problem instances are concentrated near the abrupt change from underconstrained to overconstrained problems.