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Quantum Algorithms for Graph Connectivity and Formula Evaluation
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DOI：10.22331/q-2017-08-17-26.png)
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We give a new upper bound on the quantum query complexity of deciding st-connectivity on certain classes of planar graphs, and show the bound is sometimes , exponentially better than previous results. We then show Boolean formula evaluation reduces to deciding connectivity on just such a class of graphs. Applying the algorithm for st-connectivity to Boolean formula evaluation problems, we match the O(root N) bound on the quantum query complexity of evaluating formulas on N variables, give a quadratic speed-up over the classical query complexity of a certain class of promise Boolean formulas, and show this approach can yield superpolynomial quantum/classical separations. These results indicate that this st-connectivity-based approach may be the right way of looking at quantum algorithms for formula evaluation.
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IF:
5.4
论文数:
974
被引数:
1.0W
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