Handbook of theoretical computer science (vol. A)
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
Quantum computation and quantum information
Quantum computation and quantum information
Graph coloring with quantum heuristics
Eighteenth national conference on Artificial intelligence
Exponential algorithmic speedup by a quantum walk
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Guest Column: NP-complete problems and physical reality
ACM SIGACT News
Quantum Query Complexity of Some Graph Problems
SIAM Journal on Computing
Journal of the ACM (JACM)
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
OSC'10 Proceedings of the Third international conference on Optical supercomputing
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In this paper, we investigate quantum algorithms for graph colouring problems, in particular for 2- and 3-colouring of graphs. Our main goal is to establish a set of quantum representations and operations suitable for the problem at hand. We propose unitary- as well as measurement-based quantum computations, also taking inspiration from answer set programming, a form of declarative programming close to traditional logic programming. The approach used is one in which we first generate arbitrary solutions to the problem, then constraining these according to the problem's input. Though we do not achieve fundamental speed-ups, our algorithms show how quantum concepts can be used for programming and moreover exhibit structural differences. For example, we compute all possible colourings at the same time. We compare our algorithms with classical ones, highlighting how the same type of difficulties give rise to NP-complete behaviour, and propose possible improvements.