Qualifying quantum approaches for hard industrial optimization problems. A case study in the field of smart-charging of electric vehicles

TL;DR

This paper evaluates quantum algorithms for industrial NP-hard problems in smart-charging of electric vehicles, comparing their performance to classical approximation algorithms on specific instances, showing promising results.

Contribution

It develops and tests tailored QAOA implementations for electric vehicle charging problems, demonstrating quantum algorithms can match or outperform classical approximations on certain instances.

Findings

Quantum algorithms match classical approximation ratios

Quantum algorithms outperform classical methods on some instances

Results are promising but limited to small problem sizes

Abstract

In order to qualify quantum algorithms for industrial NP-Hard problems, comparing them to available polynomial approximate classical algorithms and not only to exact ones -- exponential by nature -- , is necessary. This is a great challenge as, in many cases, bounds on the reachable approximation ratios exist according to some highly-trusted conjectures of Complexity Theory. An interesting setup for such qualification is thus to focus on particular instances of these problems known to be "less difficult" than the worst-case ones and for which the above bounds can be outperformed: quantum algorithms should perform at least as well as the conventional approximate ones on these instances, up to very large sizes. We present a case study of such a protocol for two industrial problems drawn from the strongly developing field of smart-charging of electric vehicles. Tailored implementations of the Quantum Approximate Optimization Algorithm (QAOA) have been developed for both problems, and tested numerically with classical resources either by emulation of Pasqal's Rydberg atom based quantum device or using Atos Quantum Learning Machine. In both cases, quantum algorithms exhibit the same approximation ratios than conventional approximation algorithms, or improve them. These are very encouraging results, although still for instances of limited size as allowed by studies on classical computing resources. The next step will be to confirm them on larger instances, on actual devices, and for more complex versions of the problems addressed.