Quantum Computing for Discrete Optimization: A Highlight of Three
  Technologies
Quantum optimization has emerged as a promising frontier of quantum
computing, providing novel numerical approaches to mathematical optimization
problems. The main goal of this paper is to facilitate interdisciplinary
research between the Operations Research (OR) and Quantum Computing communities
by providing an OR scientist's perspective on selected quantum-powered methods
for discrete optimization. To this end, we consider three quantum-powered
optimization approaches that make use of different types of quantum hardware
available on the market. To illustrate these approaches, we solve three
classical optimization problems: the Traveling Salesperson Problem, Weighted
Maximum Cut, and Maximum Independent Set. With a general OR audience in mind,
we attempt to provide an intuition behind each approach along with key
references, describe the corresponding high-level workflow, and highlight
crucial practical considerations. In particular, we emphasize the importance of
problem formulations and device-specific configurations, and their impact on
the amount of resources required for computation (where we focus on the number
of qubits). These points are illustrated with a series of experiments on three
types of quantum computers: a neutral atom machine from QuEra, a quantum
annealer from D-Wave, and a gate-based device from IBM.
Alexey Bochkarev Raoul Heese Sven Jäger Philine Schiewe Anita Schöbel