QUBOs for Sorting Lists and Building Trees

TL;DR

This paper demonstrates how sorting lists and constructing trees can be formulated as QUBO problems, enabling solutions via neurocomputing and quantum computing methods, thus bridging data structures with advanced optimization techniques.

Contribution

It introduces a novel approach to model fundamental data structure tasks as QUBOs, facilitating their solution with neurocomputing and quantum algorithms.

Findings

QUBO formulations for sorting and trees

Solutions via Hopfield nets and quantum computing

Potential for neurocomputing in data structure problems

Abstract

We show that the fundamental tasks of sorting lists and building search trees or heaps can be modeled as quadratic unconstrained binary optimization problems (QUBOs). The idea is to understand these tasks as permutation problems and to devise QUBOs whose solutions represent appropriate permutation matrices. We discuss how to construct such QUBOs and how to solve them using Hopfield nets or adiabatic) quantum computing. In short, we show that neurocomputing methods or quantum computers can solve problems usually associated with abstract data structures.