Abstract Recent advances in artificial intelligence have highlighted the remarkable capabilities of neural network (NN)-powered systems on classical computers. However, these systems face significant computational challenges that limit scalability and efficiency. Quantum computers, which replace bits with qubits, hold the potential to overcome these limitations and increase processing power beyond classical systems. Despite this, integrating quantum computing with NNs remains largely unrealized due to challenges such as noise, decoherence, and high error rates in current quantum hardware. In this work, we propose a novel quantum circuit design and implementation algorithm that results in a dynamic quantum echo-state network (QESN). We apply classical control-theoretic response analysis to characterize the QESN, emphasizing its rich nonlinear dynamics and memory. We demonstrate that despite incorporating sparser gate weights for computational efficiency, the QESN preserves its rich dynamicity while enabling system trajectory predictions on any digital quantum computer that can implement a universal gate set. We validate our approach through a comprehensive demonstration of QESNs functioning as quantum observers, applied in both high-fidelity simulations and hardware experiments utilizing data from a prototypical chaotic Lorenz system. Our results show that the QESN can predict long time-series with persistent memory, running over 100 times longer than the median T1 and T2 of the IBM Marrakesh QPU, achieving state-of-the-art performance on superconducting hardware.
Abstract Recent advances in artificial intelligence have highlighted the remarkable capabilities of neural network (NN)-powered systems on classical computers. However, these systems face significant computational challenges that limit scalability and efficiency. Quantum computers, which replace bits with qubits, hold the potential to overcome these limitations and increase processing power beyond classical systems. Despite this, integrating quantum computing with NNs remains largely unrealized due to challenges such as noise, decoherence, and high error rates in current quantum hardware. In this work, we propose a novel quantum circuit design and implementation algorithm that results in a dynamic quantum echo-state network (QESN). We apply classical control-theoretic response analysis to characterize the QESN, emphasizing its rich nonlinear dynamics and memory. We demonstrate that despite incorporating sparser gate weights for computational efficiency, the QESN preserves its rich dynamicity while enabling system trajectory predictions on any digital quantum computer that can implement a universal gate set. We validate our approach through a comprehensive demonstration of QESNs functioning as quantum observers, applied in both high-fidelity simulations and hardware experiments utilizing data from a prototypical chaotic Lorenz system. Our results show that the QESN can predict long time-series with persistent memory, running over 100 times longer than the median T1 and T2 of the IBM Marrakesh QPU, achieving state-of-the-art performance on superconducting hardware.
Recent advancements in artificial neural networks have enabled impressive tasks on classical computers, but they demand significant computational resources. While quantum computing offers potential beyond classical systems, the advantages of quantum neural networks (QNNs) remain largely unexplored. In this work, we present and examine a quantum circuit (QC) that implements and aims to improve upon the classical echo-state network (ESN), a type of reservoir-based recurrent neural networks (RNNs), using quantum computers. Typically, ESNs consist of an extremely large reservoir that learns high-dimensional embeddings, enabling prediction of complex system trajectories. Quantum echo-state networks (QESNs) aim to reduce this need for prohibitively large reservoirs by leveraging the unique capabilities of quantum computers, potentially allowing for more efficient and higher performing time-series prediction algorithms. The proposed QESN can be implemented on any digital quantum computer implementing a universal gate set, and does not require any sort of stopping or re-initialization of the circuit, allowing continuous evolution of the quantum state over long time horizons. We conducted simulated QC experiments on the chaotic Lorenz system, both with noisy and noiseless models, to demonstrate the circuit's performance and its potential for execution on noisy intermediate-scale quantum (NISQ) computers.
Abstract Recent advances in artificial intelligence have highlighted the remarkable capabilities of neural network (NN)-powered systems on classical computers. However, these systems face significant computational challenges that limit scalability and efficiency. Here, we propose a quantum reservoir network (QRN) algorithm for prediction and reconstruction of dynamical systems with current quantum hardware. This is developed from the recent NISQRC framework to imbue quantum circuits with a practical fading memory, and we demonstrate its effectiveness on an IBM quantum processor. We apply classical control-theoretic response analysis to characterize the QRN, emphasizing its rich nonlinear dynamics and memory, as well as its ability to be fine-tuned with sparsity and re-uploading blocks. Noisy and noiseless simulations, as well as IBM hardware experiments, demonstrate the capability of our QRN to reconstruct unknown latent variables of the Lorenz system at future timesteps. Our results show that the QRN can operate with persistent memory for over 100 times longer than the median T1 T 1 and T2 T 2 of the QPU, achieving state-of-the-art time-series performance on IBM hardware.
One of the most promising new directions in quantum computing and artificial intelligence convergence is the Quantum Neural Networks (QNNs) that can potentially revolutionize the manner in which intelligent systems are designed, trained, and implemented. Although traditional deep learning models have proven to be incredibly successful in fields like computer vision, natural language processing and autonomous systems, they are becoming limited by computational bottlenecks, energy use, and scalability constraints when operating on large high-dimensional data. The distinctive principles of quantum mechanics (superposition, entanglement, and quantum parallelism) may be applied to the QNNs to provide a distinct computational paradigm with the ability to execute exponentially complicated computations more effectively than his classical counterparts. This article gives an in-depth analysis of QNNs as the new frontier of artificial intelligence. We start with the description of the theoretical foundations of quantum computation and their realization in the form of neural networks. We then examine state-of-the-art QNN architectures, such as hybrid quantum-classical models that help overcome present quantum hardware limitations in relation to the capabilities of classical machine learning. Some of the upcoming applications are showcased including molecular simulation and drug discovery and financial modeling, optimization, cryptography and intelligent automation. Such applications reveal the revolutionary power of QNNs to tackle the issues that cannot be tackled by traditional systems. Nonetheless, there are also major obstacles on the way to a practical implementation of QNN. Problems that still remain a barrier to widespread adoption include quantum decoherence, noise in near-term quantum devices, and the inability to scale qubit architectures or to train large-scale quantum models. In order to overcome these obstacles, we speak about the current research work on the topic of error correction, variational algorithms, and hybrid system designs. Also we examine the ethical and societal ramifications of quantum-accelerated AI, such as security, data sovereignty, and technological equity globally.
The simulation of quantum matter with classical hardware plays a central role in the discovery and development of quantum many-body systems, with far-reaching implications in condensed matter physics and quantum technologies. In general, efficient and sophisticated algorithms are required to overcome the severe challenge posed by the exponential scaling of the Hilbert space of quantum systems. In contrast, hardware built with quantum bits of information are inherently capable of efficiently finding solutions of quantum many-body problems. While a universal and scalable quantum computer is still beyond the horizon, recent advances in qubit manufacturing and coherent control of synthetic quantum matter are leading to a new generation of intermediate scale quantum hardware. \n \nThe complexity underlying quantum many-body systems closely resembles the one encountered in many problems in the world of information and technology. In both contexts, the complexity stems from a large number of interacting degrees of freedom. A powerful strategy in the latter scenario is machine learning, a subfield of artificial intelligence where large amounts of data are used to extract relevant features and patterns. In particular, artificial neural networks have been demonstrated to be capable of discovering low-dimensional representations of complex objects from high-dimensional dataset, leading to the profound technological revolution we all witness in our daily life. \n \nIn this Thesis, we envision a new paradigm for scientific discovery in quantum physics. On the one hand, we have the essentially unlimited data generated with the increasing amount of highly controllable quantum hardware. On the other hand, we have a set of powerful algorithms that efficiently capture non-trivial correlations from high-dimensional data. Therefore, we fully embrace this data-driven approach to quantum mechanics, and anticipate new exciting possibilities in the field of quantum many-body physics and quantum information science. We revive a powerful stochastic neural network called a restricted Boltzmann machine, which slowly moved out of fashion after playing a central role in the machine learning revolution of the early 2010s. We introduce a neural-network representation of quantum states based on this generative model. We propose a set of algorithms to reconstruct unknown quantum states from measurement data and numerically demonstrate their potential, with important implications for current experiments. These include the reconstruction of experimentally inaccessible properties, such as entanglement, and diagnostics to determine sources of noise. Furthermore, we introduce a machine learning framework for quantum error correction, where a neural network learns the best decoding strategy directly from data. We expect that the full integration between quantum hardware and artificial intelligence will become the gold standard, and will drive the world into the era of fault-tolerant quantum computing and large-scale quantum simulations.
Abstract Artificial intelligence algorithms largely build on multi-layered neural networks. Coping with their increasing complexity and memory requirements calls for a paradigmatic change in the way these powerful algorithms are run. Quantum computing promises to solve certain tasks much more efficiently than any classical computing machine, and actual quantum processors are now becoming available through cloud access to perform experiments and testing also outside of research labs. Here we show in practice an experimental realization of an artificial feed-forward neural network implemented on a state-of-art superconducting quantum processor using up to 7 active qubits. The network is made of quantum artificial neurons, which individually display a potential advantage in storage capacity with respect to their classical counterpart, and it is able to carry out an elementary classification task which would be impossible to achieve with a single node. We demonstrate that this network can be equivalently operated either via classical control or in a completely coherent fashion, thus opening the way to hybrid as well as fully quantum solutions for artificial intelligence to be run on near-term intermediate-scale quantum hardware.
The integration of quantum computing (QC) into predictive modeling represents a transformative advancement in machine learning, providing substantial improvements over traditional methods. This study compares classical Echo State Networks (ESN) with quantum Echo State Networks (qESN) for time-series forecasting, emphasizing the concept of a metabolic avatar—a dynamic data-driven model of individual metabolic processes. Utilizing time-series data from six distinct users, we assessed both models’ precision and adaptability through Root Mean Squared Error (RMSE). Our results demonstrate consistent superiority of qESN over classical ESN, highlighted by a 30% RMSE reduction during cross-validation (CV). Notably, qESN showed remarkable stability and accuracy even with limited training data, underscoring its effectiveness in data-sparse scenarios. Furthermore, we examined model performance in datasets containing outliers. QESN significantly outperformed classical ESN, achieving approximately 76% lower RMSE in CV and about 55% lower RMSE in walk-forward validation (WFV). This demonstrates qESN’s enhanced robustness and reduced susceptibility to overfitting. Crucially, our findings highlight the Quantum Metabolic Avatar’s (QMA) profound potential for personalized predictive analytics, essential for applications in personalized healthcare and customized wellness programs. The study strongly supports integrating quantum algorithms into predictive modeling, marking a pivotal advancement towards highly personalized and dynamic metabolic avatars.