Quantum Annealing for Constrained Optimization

TL;DR

This paper introduces a novel encoding method for constrained optimization problems on quantum annealers that eliminates penalty terms, reducing resource requirements and simplifying implementation.

Contribution

The authors propose a new encoding technique that removes the need for penalty terms, decreasing the number of physical qubits and couplers needed for quantum annealing.

Findings

The method effectively encodes constraints without penalty terms.

It reduces the physical qubit count and complexity of embedding.

The approach enhances the practicality of quantum annealers for constrained problems.

Abstract

Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealers that promise to solve certain combinatorial optimization problems of practical relevance faster than their classical analogues. The applicability of such devices for many theoretical and real-world optimization problems, which are often constrained, is severely limited by the sparse, rigid layout of the devices' quantum bits. Traditionally, constraints are addressed by the addition of penalty terms to the Hamiltonian of the problem, which in turn requires prohibitively increasing physical resources while also restricting the dynamical range of the interactions. Here, we propose a method for encoding constrained optimization problems on quantum annealers that eliminates the need for penalty terms and thereby reduces the number of required couplers and removes the need for minor embedding, greatly reducing the number of required physical qubits. We argue the advantages of the proposed technique and illustrate its effectiveness. We conclude by discussing the experimental feasibility of the suggested method as well as its potential to appreciably reduce the resource requirements for implementing optimization problems on quantum annealers, and its significance in the field of quantum computing.