基于生成程序的公式求值量子算法
Span-program-based quantum algorithm for evaluating formulas
摘要：
我们给出了一个量子算法，用于在扩展的门集合上评估公式，包括所有的两位和三位二进制门（例如，NAND，3-多数）。该算法是最佳的只读一次公式，每个门的输入在一定意义上平衡。主要的新工具是一个经典的线性代数计算模型之间的对应关系，“跨度程序”，和加权二分图。跨度程序的评估对应于相关联的图的特征值为零的特征向量。因此，量子计算机可以通过将谱估计应用于图来评估跨度程序。例如，评估平衡三元多数公式的经典复杂性是未知的，并且随机化α-β修剪的自然推广已知是次优的。相比之下，我们的算法推广了最佳量子AND-OR公式评估算法，是最佳的平衡三进制多数公式的评估。
英文摘要：
We give a quantum algorithm for evaluating formulas over an extended gate set, including all two- and three-bit binary gates (e.g., NAND, 3-majority). The algorithm is optimal on read-once formulas for which each gate's inputs are balanced in a certain sense. The main new tool is a correspondence between a classical linear-algebraic model of computation, "span programs," and weighted bipartite graphs. A span program's evaluation corresponds to an eigenvalue-zero eigenvector of the associated graph. A quantum computer can therefore evaluate the span program by applying spectral estimation to the graph. For example, the classical complexity of evaluating the balanced ternary majority formula is unknown, and the natural generalization of randomized alpha-beta pruning is known to be suboptimal. In contrast, our algorithm generalizes the optimal quantum AND-OR formula evaluation algorithm and is optimal for evaluating the balanced ternary majority formula.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
