Quantum feature maps for graph machine learning on a neutral atom quantum processor
Boris Albrecht, Constantin Dalyac, Lucas Leclerc, Luis Ortiz-Gutiérrez, Slimane Thabet, Mauro D'Arcangelo, Julia Cline, Vincent E. Elfving, Lucas Lassablière, Henrique Silvério, B. X. R. Alves, Louis-Paul Henry, Adrien Signoles, Loïc Henriet
Using a Rydberg quantum processor with up to 32 qubits, the authors implement machine learning tasks on data structured into graphs and show that their platform can distinguish two different graph connectivities. To illustrate the potential of such a method, they show that it can classify the toxicity of a given molecule based on a real-world biochemistry dataset.
Using a Rydberg quantum processor with up to 32 qubits, the authors implement machine learning tasks on data structured into graphs and show that their platform can distinguish two different graph connectivities. To illustrate the potential of such a method, they show that it can classify the toxicity of a given molecule based on a real-world biochemistry dataset.
Neutral atom platforms are analogue quantum simulators that offer the possibility to map graphs onto a 2D qubit register using programmable Rubidium atoms arrays, whose valence electrons' energy state is used as qubits, using optical tweezers. This makes it possible to implement algorithms for solving graph combinatorial optimization and Quantum Machine Learning (QML) tasks, such as graph classification. However, the restrictions of real hardware, as well as the very low number of publicly available machines, make such implementation non-trivial. In this work, we manage to compute the Quantum Evolution Kernel (QEK) to extract the features from graphs of the PROTEINS dataset using the 256-qubits Aquila platform (available through AWS) and then we apply classical Machine Learning (ML) techniques for the final classification. The method is benchmarked against classical kernels, resulting in slightly better performance, proving the effectiveness of the method, even in the case of a noisy quantum simulator.
The rapid development of reliable quantum processing units opens up novel computational opportunities for machine learning. Here, we introduce a procedure for measuring the similarity between graph-structured data, based on the time evolution of a quantum system. By encoding the topology of the input graph in the Hamiltonian of the system, the evolution produces measurement samples that retain key features of the data. We study analytically the procedure and illustrate its versatility in providing links to standard classical approaches. We then show numerically that this scheme performs well compared to standard graph kernels on typical benchmark datasets. Finally, we study the possibility of a concrete implementation on a realistic neutral-atom quantum processor.
Quantum processors may enhance machine learning by mapping high-dimensional data onto quantum systems for processing. Conventional feature maps, for encoding data onto a quantum circuit are currently impractical, as the number of entangling gates scales quadratically with the dimension of the dataset and the number of qubits. In this work, we introduce a quantum feature map designed to handle high-dimensional data with a significantly reduced number of qubits and entangling operations. Our approach preserves essential data characteristics while promoting computational efficiency, as evidenced by extensive experiments on benchmark datasets that demonstrate a marked improvement in both accuracy and resource utilization when using our feature map as a kernel for characterization, as compared to state-of-the-art quantum feature maps. Our noisy simulation results, combined with lower resource requirements, highlight our map's ability to function within the constraints of noisy intermediate-scale quantum devices. Through numerical simulations and small-scale implementation on a superconducting circuit quantum computing platform, we demonstrate that our scheme performs on par or better than a set of classical algorithms for classification. While quantum kernels are typically stymied by exponential concentration, our approach is affected with a slower rate with respect to both the number of qubits and features, which allows practical applications to remain within reach. Our findings herald a promising avenue for the practical implementation of quantum machine learning algorithms on near future quantum computing platforms.
Quantum machine learning sits at the intersection of quantum computing and artificial intelligence, seeking to exploitquantum mechanical phenomena -- superposition, entanglement, and interference -- to achieve computationaladvantages for learning tasks. This study presents a systematic evaluation of five quantum ML approaches -- variationalquantum classifiers (VQC), quantum kernel methods, quantum reservoir computing, quantum Boltzmann machines, andhybrid quantum-classical neural networks -- benchmarked against classical counterparts on both simulated quantumhardware (up to 30 qubits) and real NISQ devices (IBM Quantum, 27 qubits). Evaluations spanned four task categories:binary classification on structured datasets (6 UCI benchmarks), quantum chemistry property prediction (QM9 molecularenergies), generative modelling (learning probability distributions), and optimisation (Max-Cut on random graphs). A totalof 1,920 experiments were conducted. On classical structured datasets, no quantum method outperformed the bestclassical baseline (XGBoost or SVM) at any problem size accessible to current quantum hardware (up to 30 features),with quantum kernel methods achieving parity at 0.4 +- 0.8% accuracy difference but at 100-1000x higher computationalcost. On quantum chemistry, variational quantum eigensolvers showed a genuine advantage for small molecules (H2,LiH, BeH2): achieving chemical accuracy (1 kcal/mol) with 4-12 qubits where classical methods required exponentiallymore compute for equivalent accuracy. Noise on real NISQ devices degraded all quantum ML methods by 8.4-22.6%relative to noiseless simulation, with error mitigation recovering 42-68% of the noise-induced loss. The quantumadvantage threshold -- the problem size at which quantum methods become faster than classical for equivalent accuracy-- was estimated at 50-100 logical qubits for quantum chemistry and 200+ logical qubits for general ML tasks, placingpractical quantum ML advantage beyond current NISQ capabilities but within plausible reach of fault-tolerant devices. Apractical assessment framework mapping task type, problem structure, and available quantum hardware to expectedquantum advantage is proposed.
Quantum machine learning is a fast-emerging field that aims to tackle machine learning using quantum algorithms and quantum computing. Due to the lack of physical qubits and an effective means to map real-world data from Euclidean space to Hilbert space, most of these methods focus on quantum analogies or process simulations rather than devising concrete architectures based on qubits. In this paper, we propose a novel hybrid quantum-classical algorithm for graph-structured data, which we refer to as the Ego-graph based Quantum Graph Neural Network (egoQGNN). egoQGNN implements the GNN theoretical framework using the tensor product and unity matrix representation, which greatly reduces the number of model parameters required. When controlled by a classical computer, egoQGNN can accommodate arbitrarily sized graphs by processing ego-graphs from the input graph using a modestly-sized quantum device. The architecture is based on a novel mapping from real-world data to Hilbert space. This mapping maintains the distance relations present in the data and reduces information loss. Experimental results show that the proposed method outperforms competitive state-of-the-art models with only 1.68\% parameters compared to those models.
Quantum information processing is likely to have a far-reaching impact in the field of artificial intelligence. Noisy, intermediate-scale quantum devices provide a platform for exploring the possibility of attaining a quantum advantage through hybrid quantum-classical machine-learning algorithms. One example of such a hybrid algorithm is ``quantum kitchen sinks,'' which builds upon a classical algorithm known as ``random kitchen sinks'' to leverage a gate model quantum computer for machine-learning applications. We propose an alternative algorithm called ``analog-quantum kitchen sinks'' (AQKSs), which employs an analog-quantum computer for mapping data features into new features in a nonlinear manner. The new features can then be used by a classical algorithm to perform machine-learning tasks. We show the effectiveness of our algorithm for performing binary classification on both a synthetic dataset and a real-world dataset by simulating the operations of a quantum annealer. We demonstrate that the AQKS algorithm reduces the classification error of a linear classifier from $50\mathrm{%}$ to $0.6\mathrm{%}$ for the synthetic dataset and from $4.4\mathrm{%}$ to $1.6\mathrm{%}$ for the other dataset. Our proposed AQKS algorithm presents the possibility to use current quantum annealers for solving practical machine-learning problems.