Driver Hamiltonians for constrained optimization in quantum annealing

TL;DR

This paper introduces a general method for constructing driver Hamiltonians that encode problem constraints directly, improving the efficiency of quantum annealing for complex optimization problems.

Contribution

It provides guidelines for designing driver Hamiltonians that commute with constraints, reducing the need for penalty terms in quantum annealing.

Findings

Applicable to diverse problems like graph isomorphism and 3SAT

Reduces reliance on penalty terms for constraints

Enhances scalability for quantum annealers

Abstract

One of the current major challenges surrounding the use of quantum annealers for solving practical optimization problems is their inability to encode even moderately sized problems---the main reason for this being the rigid layout of their quantum bits as well as their sparse connectivity. In particular, the implementation of constraints has become a major bottleneck in the embedding of practical problems, because the latter is typically achieved by adding harmful penalty terms to the problem Hamiltonian --- a technique that often requires an `all-to-all' connectivity between the qubits. Recently, a novel technique designed to obviate the need for penalty terms was suggested; it is based on the construction of driver Hamiltonians that commute with the constraints of the problem, rendering the latter constants of motion. In this work we propose general guidelines for the construction of such driver Hamiltonians given an arbitrary set of constraints. We illustrate the broad applicability of our method by analyzing several diverse examples, namely, graph isomorphism, not-all-equal 3SAT, and the so-called Lechner, Hauke and Zoller constraints. We also discuss the significance of our approach in the context of current and future experimental quantum annealers.