A QUBO formulation for the Tree Containment problem

TL;DR

This paper introduces a novel QUBO formulation for the NP-complete Tree Containment problem in phylogenetics, enabling quantum computing approaches to analyze evolutionary relationships efficiently.

Contribution

It presents the first QUBO model for Tree Containment, bridging quantum computing and phylogenetics, with a formulation requiring O(n_N n_T) logical qubits.

Findings

QUBO formulation for Tree Containment problem

Requires O(n_N n_T) logical qubits

Connects quantum computing with phylogenetics

Abstract

Phylogenetic (evolutionary) trees and networks are leaf-labeled graphs that are widely used to represent the evolutionary relationships between entities such as species, languages, cancer cells, and viruses. To reconstruct and analyze phylogenetic networks, the problem of deciding whether or not a given rooted phylogenetic network embeds a given rooted phylogenetic tree is of recurring interest. This problem, formally know as Tree Containment, is NP-complete in general and polynomial-time solvable for certain classes of phylogenetic networks. In this paper, we connect ideas from quantum computing and phylogenetics to present an efficient Quadratic Unconstrained Binary Optimization formulation for Tree Containment in the general setting. For an instance (N,T) of Tree Containment, where N is a phylogenetic network with n_N vertices and T is a phylogenetic tree with n_T vertices, the number of logical qubits that are required for our formulation is O(n_N n_T).