Slimane Thabet | LIP6 - Équipe QI

Quantum machine learning on near term hardware with unstructured and graph structured data

Mon, 12 May 2025 00:00:00 +0000

Machine learning enabled the resolution of many real world problems that other traditional computational method struggled to solve, or could solve in more expensive ways. Quantum computing is a paradigm of computation using the quantum states of matter that enables a large computational speed up on some problems. The recent progress in the development of quantum hardware encouraged the research of concrete applications of quantum computers. It then became natural to look for ways in which quantum computers can be applied for machine learning. This thesis is a contribution towards this goal. The first part aims at understanding the general capabilities of variational quantum circuits (VQC) for machine learning tasks given vector data inputs, and have a clearer idea on the necessary conditions in order to expect a quantum advantage. VQCs are a family of quantum algorithms where one finds gates parameters that minimizes a cost function, in the same way as neural networks. They are effectively linear models in a high dimensional feature space. I show that although VQCs are costly to evaluate, one can sometimes construct cheap classical approximators called classical surrogate using the technique of random features regression. If this approximation is possible, the quantum advantage is limited. I also highlight the fact that learning a classical model on the same feature map will lead to a solution called the Minimum Norm Least Square (MNLS) estimator, but the training dynamics of the quantum circuits will not necessarily lead to the same solution. This separation is the source of quantum advantage, I show that it is sufficient that the weight vector of quantum models has a large norm, and I give concrete examples. The second part explores the use of quantum computers to perform machine learning tasks on graph structured data. Machine learning on graph data encompasses many real world applications, and algorithms for vector data cannot be directly applied. I aimed in this part to develop quantum algorithms adapted to the graph structure of the data. The main idea is to encode the graph into a Hamiltonian that has the same topology. One then prepares a quantum state by evolving this Hamiltonian, and the measurements are incorporated in a classical machine learning algorithm. This approach is especially suited to neutral atoms quantum computers. With such platforms, one can indeed easily create a quantum system with the desired connectivity, and the geometry can be changed at each run. I developed a large family of algorithms, inspired by kernels, graphs neural networks, and transformers with the intention to be ran on current hardware. I performed numerical experiments on large scale datasets, and described the results of an experimental implementation on the hardware of Pasqal.

Quantum Machine Learning: theory, applications and implementations on the Pasqal quantum processors

Mon, 12 May 2025 00:00:00 +0000

Félicitations Dr.Thabet !

Constrained and Vanishing Expressivity of Quantum Fourier Models

Sun, 24 Nov 2024 00:00:00 +0000

In this work, we highlight an unforeseen behavior of the expressivity of Parameterized Quantum Circuits (PQC) for machine learning. A large class of these models, seen as Fourier Series which frequencies are derived from the encoding gates, were thought to have their Fourier coefficients mostly determined by the trainable gates. Here, we demonstrate a new correlation between the Fourier coefficients of the quantum model and its encoding gates. In addition, we display a phenomenon of vanishing expressivity in certain settings, where some Fourier coefficients vanish exponentially when the number of qubits grows. These two behaviors imply novel forms of constraints which limit the expressivity of PQCs, and therefore imply a new inductive bias for Quantum models. The key concept in this work is the notion of a frequency redundancy in the Fourier series spectrum, which determines its importance. Those theoretical behaviours are observed in numerical simulations.

Slimane Thabet - is Quantum Positional Encodings for Graph Neural Networks

Wed, 26 Jun 2024 00:00:00 +0000

is Quantum Positional Encodings for Graph Neural Networks

Ce séminaire, donné par Slimane Thabet, aura lieu le 26 June 2024, à 9:0. Il aura lieu en salle Not specified.

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Résumé

In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the topology of a graph onto interactions between qubits in a quantum computer. Our inspiration stems from the recent advancements in quantum processing units, which offer computational capabilities beyond the reach of classical hardware. We prove that some of these quantum features are theoretically more expressive for certain graphs than the commonly used relative random walk probabilities. Empirically, we show that the performance of state-of-the-art models can be improved on standard benchmarks and large-scale datasets by computing tractable versions of quantum features. Our findings highlight the potential of leveraging quantum computing capabilities to enhance the performance of transformers in handling graph data.

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.