Research in quantum machine learning has recently proliferated due to the potential of quantum computing to accelerate machine learning. An area of machine learning that has not yet been explored is neural ordinary differential equation (neural ODE) based residual neural networks (ResNets), which aim to improve the effectiveness of neural networks using the principles of ordinary differential equations. In this work, we present our insights about why analog Rydberg atom quantum computers are especially well-suited for ResNets. We also introduce ResQ, a novel framework to optimize the dynamics of Rydberg atom quantum computers to solve classification problems in machine learning using analog quantum neural ODEs.
Research in quantum machine learning has recently proliferated due to the potential of quantum computing to accelerate machine learning. An area of machine learning that has not yet been explored is neural ordinary differential equation (neural ODE) based residual neural networks (ResNets), which aim to improve the effectiveness of neural networks using the principles of ordinary differential equations. In this work, we present our insights about why analog Rydberg atom quantum computers are especially well-suited for ResNets. We also introduce ResQ, a novel framework to optimize the dynamics of Rydberg atom quantum computers to solve classification problems in machine learning using analog quantum neural ODEs.
Quantum computing has shown theoretical promise for accelerating machine learning, including both generative and discriminative tasks. Recent advances in analog Rydberg atom quantum computers have opened new opportunities for near-term quantum machine learning applications, due to uniquely reconfigurable qubit positions and global multi-qubit operations. In this work, we present two complementary contributions that leverage the unique properties of this technology. First, we propose ReCon, the first implementation of quantum generative adversarialnetworks (GANs) on analog Rydberg atom quantum computers, achieving a 33% improvement in image generation quality (measured via Frechet Inception Distance) compared to state-of-the-art superconducting-qubit techniques. Second, we introduce ResQ, a novel framework that optimizes the dynamics of Rydberg atom quantum computers for discriminative tasks, specifically neural ordinary differential equation (neural ODE) based residual neural network (ResNets) classifiers. ResQ demonstrates how analog quantum computing can be tailored to solve classification problems in machine learning, achieving a 36% improvement over classical neural ODE classifiers. Together, these works highlight the versatility and scalability of analog Rydberg atom quantum computing for both generative and discriminative quantum machine learning, advancing the feasibility and versatility of near-term hardware implementations for QML tasks.
The research evaluates the traditional numerical algorithms and neural network-based methods for solving ordinary differential equations. The evaluation covers both mathematical and machine learning perspectives. Practical experiments are carried out by implementing neural networks and the necessary algorithms using the Julia programming language. These experiments highlight significant advancements in the realm of quantum computing. Additionally, analyzing the efficiency metrics of solving differential equations with numerical methods versus neural networks uncovers intriguing results, which vary based on the chosen architecture and network parameters.
Configurable arrays of optically trapped Rydberg atoms are a versatile platform for quantum computation and quantum simulation, also allowing controllable decoherence. We demonstrate theoretically that they also enable proof-of-principle demonstrations for a technique to build models for open quantum dynamics using machine learning with artificial neural networks, recently proposed by Mukherjee et al. [Quantum Sci. Technol. 10, 02LT01 (2025)]. Using the outcome of quantum transport through a network of sites that correspond to excited Rydberg atoms, the multistage neural-network algorithm successfully identifies the number of atoms (or nodes in the network) and, subsequently, their location. It further extracts an effective interaction Hamiltonian and decoherence operators induced by the environment. To probe the Rydberg array, one initiates dynamics repeatedly from the same initial state and then measures the transport probability to an output atom. Large datasets are generated by varying the position of the latter. Measurements are required in only one single basis, making the approach complementary to, e.g., quantum process tomography. Due to steeply increasing requirements for training data size, the present implementation appears best suited for networks of just a few sites. The cold-atom platform discussed in this article can be used to explore the performance of the proposed protocol when training the neural network with simulation data but then applying it to construct models based on experimental data.
Quantum machine learning promises to deliver near-term practical quantum computation applications using machine learning tools to optimize quantum hardware for scientific applications. Studies in this direction often propose using variational quantum circuits as the underlying hardware. However, these so-called VQCs exhibit flat landscapes with narrow and concentrated local minima, making their optimization inefficient and thwarting their advantage. This dissertation proposes using quantum many-body systems' dynamics for computation instead of circuits. This Analog quantum machine learning approach (AQML) uses tools from optimal control to deliver more manageable optimization landscapes and helps explain what types of computation are suitable for different hardware. Concretely, I show that arrays of Rydberg atoms can be leveraged to implement reservoir computers with enhanced memory storage and retrieval. I also show that two atom-species Rydberg arrays can reproduce the dynamics of the basic building blocks of artificial neural networks and be used for quantum-enhanced sensing and entanglement detection. This study shows that AQML algorithms are theoretically more expressive than their classical counterparts. Lastly, I show that while AQML algorithms can still exhibit problematic optimization landscapes, flatness can be mitigated, and local minima can be circumvented by co-designing the underlying hardware with the desired task. We exemplify this co-design in the context of quantum chemistry calculations. This dissertation shows that AQML algorithms can be used for various scientific and small-scale applications such as sensing, chemical design, entanglement witnessing, and time-series prediction. However, we still have a way to go before seeing full-scale applications. Instead, this dissertation focuses on theoretical studies and answers the question of what we can compute with quantum hardware's analog dynamics.
I present a simple hybrid framework that combines physics informed neural networks (PINNs) with features generated from small quantum circuits. As a proof of concept, a first-order equation is solved by feeding quantum measurement probabilities into the neural model. The architecture enforces the initial condition exactly, and training is guided by the ODE residual loss. Numerical results show that the hybrid model reproduces the analytical solution, illustrating the potential of quantum-enhanced PINNs for differential equation solving.
Recently, a novel type of Neural Network (NNs): the Physics-Informed Neural Networks (PINNs), was discovered to have many applications in computational physics. By integrating knowledge of physical laws and processes in Partial Differential Equations (PDEs), fast convergence and effective solutions are obtained. Since training modern Machine Learning (ML) systems is a computationally intensive endeavour, using Quantum Computing (QC) in the ML pipeline attracts increasing interest. Indeed, since several Quantum Machine Learning (QML) algorithms have already been implemented on present-day noisy intermediate-scale quantum devices, experts expect that ML on reliable, large-scale quantum computers will soon become a reality. However, after potential benefits from quantum speedup, QML may also entail reliability, trustworthiness, safety, and security risks. To solve the challenges of QML, we combine classical information processing, quantum manipulation, and processing with PINNs to accomplish a hybrid QML model named quantum based PINNs.