Quantum Algorithms for the Minimum Steiner Tree problem with application to Binary Near-Perfect Phylogenies

Abstract

We present a quantum algorithm in bioinformatics for solving the Binary Near-Perfect Phylogeny Problem (BNPP) with a complexity bound of $O(8.926^q + 8^q nm2)$, where n is the number of input taxa and m is the sequence length for each taxon with each character in the sequence being a binary bit using the QRAM model. We give another polynomial space exact algorithm for the Minimum Steiner Tree (MST) problem with complexity $O^*(e^{(1+g(k,l))k})$ in the circuit model.