A QUBO Formulation of Minimum Multicut Problem Instances in Trees for D-Wave Quantum Annealers

William Cruz-Santos,Marco Lanzagorta,Salvador E Venegas-Andraca

doi:10.1038/s41598-019-53585-5

William Cruz-Santos, Marco Lanzagorta + Show 1 more

Open Access

https://doi.org/10.1038/s41598-019-53585-5

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Abstract

Quantum annealing algorithms were introduced to solve combinatorial optimization problems by taking advantage of quantum fluctuations to escape local minima in complex energy landscapes typical of NP − hard problems. In this work, we propose using quantum annealing for the theory of cuts, a field of paramount importance in theoretical computer science. We have proposed a method to formulate the Minimum Multicut Problem into the QUBO representation, and the technical difficulties faced when embedding and submitting a problem to the quantum annealer processor. We show two constructions of the quadratic unconstrained binary optimization functions for the Minimum Multicut Problem and we review several tradeoffs between the two mappings and provide numerical scaling analysis results from several classical approaches. Furthermore, we discuss some of the expected challenges and tradeoffs in the implementation of our mapping in the current generation of D-Wave machines.

Highlights

Quantum Annealing algorithms (QA) constitute a paradigm of quantum computation focused on solving combinatorial optimization problems[1,2,3,4,5,6,7,8,9]
Let us review the road map for solving an optimization problem using a quantum annealing approach: (i) Select an optimization combinatorial problem. (ii) Construct a pseudo-Boolean function on binary variables for the selected optimization problem, so that those assignments that minimize the expression correspond to solutions of the given problem
It is not always possible to directly obtain a quadratic unconstrained Boolean optimization problem (QUBO) expression for a given optimization problem, so in practice we have a high degree pseudo-Boolean function which is to be transformed into a QUBO expression at a later stage. (iii) Once we have computed a QUBO expression for the selected problem, the step is to embed the logical problem into the fixed architecture of the quantum processor

Summary

Introduction

Quantum Annealing algorithms (QA) constitute a paradigm of quantum computation focused on solving combinatorial optimization problems[1,2,3,4,5,6,7,8,9]. To solve a problem using the D-Wave architecture, we must express it as a quadratic unconstrained Boolean optimization problem (QUBO) or an equivalent Ising function defined on logical variables.

Results

Conclusion