# Quantum Linear Algorithm for Edit Distance Using the Word QRAM Model

@inproceedings{Equi2021QuantumLA, title={Quantum Linear Algorithm for Edit Distance Using the Word QRAM Model}, author={Massimo Equi and Arianne Meijer-van de Griend and Veli Makinen}, year={2021} }

Many problems that can be solved in quadratic time have bit-parallel speed-ups with factor $w$, where $w$ is the computer word size. For example, edit distance of two strings of length $n$ can be solved in $O(n^2/w)$ time. In a reasonable classical model of computation, one can assume $w=\Theta(\log n)$. There are conditional lower bounds for such problems stating that speed-ups with factor $n^\epsilon$ for any $\epsilon>0$ would lead to breakthroughs in complexity theory. However, these…

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