量子计算与决策树
Quantum Computation and Decision Trees
摘要：
许多有趣的计算问题可以用决策树来重新表述。一个自然的经典算法是在树上运行一个随机游走，从根开始，看看树是否包含从根开始的n层节点。我们设计了一种量子力学算法，它通过树来演化一种状态，最初定位在根处。我们证明，如果经典策略成功地在n中的时间多项式中达到n级，那么量子算法也是如此。此外，我们发现树的例子，经典算法需要在n的时间指数，但量子算法成功的多项式时间。然而，到目前为止，我们的例子也可以通过不同的经典算法在多项式时间内求解。
英文摘要：
Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if the tree contains a node n levels from the root. We devise a quantum mechanical algorithm that evolves a state, initially localized at the root, through the tree. We prove that if the classical strategy succeeds in reaching level n in time polynomial in n, then so does the quantum algorithm. Moreover, we find examples of trees for which the classical algorithm requires time exponential in n, but for which the quantum algorithm succeeds in polynomial time. The examples we have so far, however, could also be solved in polynomial time by different classical algorithms.
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