A nearly optimal discrete query quantum algorithm for evaluating NAND formulas
Andris Ambainis
TL;DR
This paper introduces nearly optimal discrete query quantum algorithms for evaluating balanced and arbitrary binary NAND formulas, significantly improving efficiency over classical methods.
Contribution
It provides the first nearly optimal discrete query quantum algorithms for general binary NAND formula evaluation, extending previous continuous-time approaches.
Findings
O(√N) query complexity for balanced formulas
O(N^{1/2 + O(1/√log N)}) complexity for arbitrary formulas
Advances quantum query algorithms for NAND formula evaluation
Abstract
We present an O(\sqrt{N}) discrete query quantum algorithm for evaluating balanced binary NAND formulas and an O(N^{{1/2}+O(\frac{1}{\sqrt{\log N}})}) discrete query quantum algorithm for evaluating arbitrary binary NAND formulas.
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Advanced Data Storage Technologies · Coding theory and cryptography