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

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 exponential ones 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 as 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.

A review on quantum computing and deep learning algorithms and their applications

“…On the other hand, a classical simulation of the Quantum Approximate Optimization Algorithm was presented, in this work Medvidović and Carleo ( 2021 ), was developed A neural-network of the many qubit wave function, focusing on states relevant for the Quantum Approximate Optimization Algorithm. A practical application can be seen in Dalyac et al ( 2021 ) where CA was used for hard industrial optimization problems. The case study in the field of smart-charging of electric vehicles.…”

Quantum approximate optimization algorithm for qudit systems with long-range interactions

“…A simple variant of the EV charging problem without constraints and preemptive charging was discussed in Ref. [55] using the QAOA for qubits.…”

Quantifying the Impact of Precision Errors on Quantum Approximate Optimization Algorithms

“…We expect this scenario to be fairly generic for QAOA circuits. While short finite-depth QAOA circuits are currently being investigated for NISQ applications in optimization, it is expected that for computationally hard optimization problems it is not unreasonable to expect the number of layer to increase at least super-polynomially with problem size [55].…”