Abstract

Recent advances in adiabatic quantum computing and quantum annealers has centered around using more advance and novel Hamiltonians to solve optimization problems. One of these advances has centered around the development of driver Hamiltonians that commute with the constraints of an optimization problem. This approach has been shown to be able to use sparser connectivity to embed several practical problems on quantum devices in comparison to other methods. Designing the driver Hamiltonians that successfully commute with several constraints has largely been based on strong intuition for specific problems and with no general algorithm for arbitrary constraints. In this work, we develop an algebraic framework for reasoning about the commutation of Hamiltonians with linear constraints-one that allows us to classify the complexity of finding a driver Hamiltonian for a set of constraints as NP-Hard …

Date

2020

Authors

Hannes Leipold, Federico Spedalieri

Journal

Bulletin of the American Physical Society

Volume

65

Publisher

American Physical Society