Constantin Dalyac | LIP6 - Équipe QI

Quantum many-body dynamics for combinatorial optimisation and machine learning

Fri, 20 Oct 2023 00:00:00 +0000

The goal of this thesis is to explore and qualify the use of N-body quantum dynamics to Tsolve hard industrial problems and machine learning tasks. As a collaboration between industrial and academic partners, this thesis explores the capabilities of a neutral atom device in tackling real-world problems. First, we look at combinatorial optimisation problems and showcase how neutral atoms can naturally encode a famous combinatorial optimisation problem called the Maximum Independent Set on Unit-Disk graphs. These problems appear in industrial challenges such as Smart-Charging of electric vehicles. The goal is to understand why and how we can expect a quantum approach to solve this problem more efficiently than classical method and our proposed algorithms are tested on real hardware using a dataset from EDF, the French Electrical company. We furthermore explore the use of 3D neutral atoms to tackle problems that are out of reach of classical approximation methods. Finally, we try to improve our intuition on the types of instances for which a quantum approach can(not) yield better results than classical methods. In the second part of this thesis, we explore the use of quantum dynamics in the field of machine learning. In addition of being a great chain of buzzwords, Quantum Machine Learning (QML) has been increasingly investigated in the past years. In this part, we propose and implement a quantum protocol for machine learning on datasets of graphs, and show promising results regarding the complexity of the associated feature space. Finally, we explore the expressivity of quantum machine learning models and showcase examples where classical methods can efficiently approximate quantum machine learning models.

Classically Approximating Variational Quantum Machine Learning with Random Fourier Features

Sun, 27 Nov 2022 00:00:00 +0000

Many applications of quantum computing in the near term rely on variational quantum circuits (VQCs). They have been showcased as a promising model for reaching a quantum advantage in machine learning with current noisy intermediate scale quantum computers (NISQ). It is often believed that the power of VQCs relies on their exponentially large feature space, and extensive works have explored the expressiveness and trainability of VQCs in that regard. In our work, we propose a classical sampling method that may closely approximate a VQC with Hamiltonian encoding, given only the description of its architecture. It uses the seminal proposal of Random Fourier Features (RFF) and the fact that VQCs can be seen as large Fourier series. We provide general theoretical bounds for classically approximating models built from exponentially large quantum feature space by sampling a few frequencies to build an equivalent low dimensional kernel, and we show experimentally that this approximation is efficient for several encoding strategies. Precisely, we show that the number of required samples grows favorably with the size of the quantum spectrum. This tool therefore questions the hope for quantum advantage from VQCs in many cases, but conversely helps to narrow the conditions for their potential success. We expect VQCs with various and complex encoding Hamiltonians, or with large input dimension, to become more robust to classical approximations.

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

Wed, 23 Feb 2022 00:00:00 +0000

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

Tue, 05 Jan 2021 00:00:00 +0000

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.