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Spanprogrambased quantum algorithm for evaluating formulas
, 2008
"... We give a quantum algorithm for evaluating formulas over an extended gate set, including all two and threebit binary gates (e.g., NAND, 3majority). The algorithm is optimal on readonce formulas for which each gate’s inputs are balanced in a certain sense. The main new tool is a correspondence be ..."
Abstract

Cited by 34 (6 self)
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We give a quantum algorithm for evaluating formulas over an extended gate set, including all two and threebit binary gates (e.g., NAND, 3majority). The algorithm is optimal on readonce formulas for which each gate’s inputs are balanced in a certain sense. The main new tool is a correspondence between a classical linearalgebraic model of computation, “span programs,” and weighted bipartite graphs. A span program’s evaluation corresponds to an eigenvaluezero 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 alphabeta pruning is known to be suboptimal. In contrast, our algorithm generalizes the optimal quantum ANDOR formula evaluation algorithm and is optimal for evaluating the balanced ternary majority formula.