Quantum optimization of complex systems with a quantum annealer

We perform an in-depth comparison of quantum annealing with several classical optimization techniques, namely, thermal annealing, Nelder-Mead, and gradient descent. The focus of our study is large quasicontinuous potentials that must be encoded using a domain wall encoding. To do this, it is important to first understand the properties of a system that is discretely encoded onto an annealer, in terms of its quantum phases, and the importance of thermal versus quantum effects. We therefore begin with a direct study of the 2D Ising model on a quantum annealer, and compare its properties directly with those of the thermal 2D Ising model. These properties include an Ising-like phase transition that can be induced by either a change in quantumness of the theory (by way of the transverse field component on the annealer), or by scaling the Ising couplings up or down. This behavior is in accord with what is expected from the physical understanding of the quantum system. We then go on to demonstrate the efficacy of the quantum annealer at minimizing several increasingly hard two-dimensional potentials. For all potentials, we find the general behavior that Nelder-Mead and gradient descent methods are very susceptible to becoming trapped in false minima, while the thermal anneal method is somewhat better at discovering the true minimum. However, and despite current limitations on its size, the quantum annealer performs a minimization very markedly better than any of these classical techniques. A quantum anneal can be designed so the system almost never gets trapped in a false minimum, and rapidly and successfully minimizes the potentials.

Automated summary

This study provides an in-depth comparison between quantum annealing and classical optimization techniques. The results show that, despite its size limitations, the quantum annealer significantly outperforms classical techniques in minimizing potentials. The study also reveals that Nelder-Mead and gradient descent methods are prone to being trapped in false minima, while the thermal anneal method performs slightly better.