Implementation for Solving Random Satisfiability Problems through CNOT-based circuits in a NMR Quantum Processor

Details Implementation for Solving Random Satisfiability Problems through CNOT-based circuits in a NMR Quantum Processor Implementation for Solving Random Satisfiability Problems through CNOT-based circuits in a NMR Quantum Processor

2003-08-25

arxiv.org/abs/quant-ph/0308130v1

Physics

Quantum Physics

17 pages, 7 figures

Scientific paper

We give a general method of construting quantum circuit for random \QTR{it}{satisfiability} (SAT) problems with the basic logic gates such as multi-qubit controlled-NOT and NOT gates. The sizes of these circuits are almost the same as the sizes of the SAT formulas. Further, a parallelization scheme is described to solve random SAT problems efficiently through these quantum circuits in \QTR{it}{nuclear magnetic resonance} (NMR) ensemble quantum computing. This scheme exploits truly mixed states as input states rather than pseudo-pure states, and combines with the topological nanture of the NMR spectrum to identify the solutions to SAT problems in a parallel way. Several typical SAT problems have been experimentally demonstrated by this scheme with good performances.

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