Experimental data reuploading with provable enhanced learning capabilities
Martin F. X. Mauser, Solène Four, Lena Marie Predl, Riccardo Albiero, Francesco Ceccarelli, Roberto Osellame, Philipp Petersen, Borivoje Dakić, Iris Agresti, Philip John Walther
The past decades have seen the development of quantum machine learning, stemming from the intersection of quantum computing and machine learning. This field is particularly promising for the design of alternative quantum (or quantum inspired) computation paradigms that could require fewer resources with respect to standard ones, e.g., in terms of energy consumption. In this context, we present the implementation of a data reuploading scheme on a photonic integrated processor, achieving high accuracies in several image classification tasks. We thoroughly investigate the capabilities of this apparently simple model, which relies on the evolution of one-qubit states, by providing an analytical proof that our implementation is a universal classifier and an effective learner, capable of generalizing to new, unknown data. Hence, our results not only demonstrate data reuploading in a potentially resource-efficient optical implementation but also provide theoretical insight into this algorithm, its trainability, and generalizability properties. This lays the groundwork for developing more resource-efficient machine learning algorithms, leveraging our scheme as a subroutine.
The past decades have seen the development of quantum machine learning, stemming from the intersection of quantum computing and machine learning. This field is particularly promising for the design of alternative quantum (or quantum inspired) computation paradigms that could require fewer resources with respect to standard ones, e.g., in terms of energy consumption. In this context, we present the implementation of a data reuploading scheme on a photonic integrated processor, achieving high accuracies in several image classification tasks. We thoroughly investigate the capabilities of this apparently simple model, which relies on the evolution of one-qubit states, by providing an analytical proof that our implementation is a universal classifier and an effective learner, capable of generalizing to new, unknown data. Hence, our results not only demonstrate data reuploading in a potentially resource-efficient optical implementation but also provide theoretical insight into this algorithm, its trainability, and generalizability properties. This lays the groundwork for developing more resource-efficient machine learning algorithms, leveraging our scheme as a subroutine.
In a single qubit system, a universal quantum classifier can be realized using the data reuploading technique. In this study, we propose a new quantum classifier applying this technique to bosonic systems and successfully demonstrate it using a silicon-based photonic integrated circuit. We established a theory of quantum machine learning algorithm applicable to bosonic systems and implemented a programmable optical circuit combined with an interferometer. Learning and classification using part of the implemented optical quantum circuit with uncorrelated two photons resulted in a classification with a success probability of 94±0.8% in the proof of principle experiment. As this method can be applied to an arbitrary two-mode N-photon system, further development of optical quantum classifiers, such as extensions to quantum entangled and multiphoton states, is expected in the future.
Abstract When applying quantum computing to machine learning tasks, one of the first considerations is the design of the quantum machine learning model itself. Conventionally, the design of quantum machine learning algorithms relies on the “quantisation” of classical learning algorithms, such as using quantum linear algebra to implement important subroutines of classical algorithms, if not the entire algorithm, seeking to achieve a quantum advantage through possible run-time accelerations brought by quantum computing. However, recent research has started questioning whether quantum advantage via speedup is the right goal for quantum machine learning (Schuld and Killoran 2022 PRX Quantum 3(3):030101.). Research also has been undertaken to exploit properties that are unique to quantum systems, such as quantum contextuality, to better design quantum machine learning models (Bowles et al. 2023). In this paper, we take an alternative approach by incorporating the heuristics and empirical evidences from the design of classical deep learning algorithms to the design of quantum neural networks. We first construct a model based on the data reuploading circuit (Pérez-Salinas et al. 2020 Quantum 4(226):226) with the quantum Hamiltonian data embedding unitary (Schuld and Petruccione 2021). Through numerical experiments on image datasets, including the famous MNIST and FashionMNIST datasets, we demonstrate that our model outperforms the quantum convolutional neural network (QCNN) (Cong et al. 2019 Nat Phys 15(12):1273–1278) by a large margin (up to over 40% on MNIST test set). Based on the model design process and numerical results, we then laid out six principles for designing quantum machine learning models, especially quantum neural networks.
Analyzing quantum systems is essential for quantum information processing, but can require exponentially many measurements without exploiting the structure of the system or task. Quantum machine learning offers a promising way to reduce this cost by learning from quantum data. Here, we theoretically establish a framework for efficient quantum-state classification and experimentally demonstrate the resulting scheme on a programmable photonic processor. Our analysis links learning efficiency to the structure of quantum data, without relying on a physical description tailored to each task. We derive sufficient conditions for accurate classification with a number of measurements polynomial in system size. We apply this guarantee to a resource problem in continuous-variable (CV) quantum computing: classifying stellar rank, a measure of non-Gaussianity. Experimentally, we implement the classification of single-mode CV quantum states with stellar rank zero and one. This is enabled by developing a programmable CV photonic processor capable of preparing and processing diverse Gaussian and non-Gaussian states and performing virtual projection onto such states, going beyond the Gaussian-only capabilities of most existing photonic platforms. The experiment demonstrates accurate classification despite experimental imperfections. Our results establish a theory-guided and experimentally validated framework for quantum-state classification that can be implemented on quantum devices available today.
Quantum machine learning integrates quantum computing with classical machine learning techniques to enhance computational power and efficiency. A major challenge in quantum machine learning is developing robust quantum classifiers capable of accurately processing and classifying complex datasets. In this work, we present an advanced approach leveraging data re-uploading, a strategy that cyclically encodes classical data into quantum states to improve classifier performance. We examine two cost functions, fidelity and trace distance, across various quantum classifier configurations, including single-qubit, two-qubit, and entangled two-qubit systems. Additionally, we evaluate four optimization techniques (L-BFGS-B, COBYLA, Nelder-Mead, and SLSQP) to determine their effectiveness in optimizing quantum circuits for both linear and non-linear classification tasks. Our results show that the choice of optimization method significantly impacts classifier performance, with L-BFGS-B and COBYLA often yielding superior accuracy. The two-qubit entangled classifier shows improved accuracy over its non-entangled counterpart, albeit with increased computational cost. Also, the two-qubit entangled classifier is the best option for real-world random datasets in terms of accuracy and computational cost. Linear classification tasks generally exhibit more stable performance across optimization techniques compared to non-linear tasks. Our findings highlight the potential of data re-uploading in quantum machine learning, outperforming existing quantum classifier models in terms of accuracy and robustness. This work contributes to the growing field of quantum machine learning by providing a comprehensive comparison of classification strategies and optimization techniques in quantum computing environments, offering a foundation for developing more efficient and accurate quantum classifiers.
Abstract Quantum machine learning integrates quantum computing with classical machine learning techniques to enhance computational power and efficiency. A major challenge in Quantum machine learning is developing robust quantum classifiers capable of accurately processing and classifying complex datasets. In this work, we present an advanced approach leveraging data re-uploading, a strategy that cyclically encodes classical data into quantum states to improve classifier performance. We examine two cost functions—fidelity and trace distance—across various quantum classifier configurations, including single-qubit, two-qubit, and entangled two-qubit systems. Additionally, we evaluate four optimization techniques (L-BFGS-B, COBYLA, Nelder-Mead, and SLSQP) to determine their effectiveness in optimizing quantum circuits for both linear and non-linear classification tasks. Our results show that the choice of optimization method significantly impacts classifier performance, with L-BFGS-B and COBYLA often yielding superior accuracy. The two-qubit entangled classifier shows improved accuracy over its non-entangled counterpart, albeit with increased computational cost. Also, the two-qubit entangled classifier are the best option for real word random dataset in order to accuracy and computational cost. Linear classification tasks generally exhibit more stable performance across optimization techniques compared to non-linear tasks. Our findings highlight the potential of data re-uploading in Quantum machine learning outperforming existing quantum classifier models in terms of accuracy and robustness. This work contributes to the growing field of Quantum machine learning by providing a comprehensive comparison of classification strategies and optimization techniques in quantum computing environments, offering a foundation for developing more efficient and accurate quantum classifiers.
As an emerging research direction in quantum computing, quantum convolutional neural networks provide a promising way to combine quantum feature processing with traditional machine learning algorithms; however, their development is constrained by the scarcity of quantum resources. In this work, we propose a quantum-classical hybrid convolutional neural network model based on quantum convolution kernels. This model employs a multi-data-per-qubit rotation-angle encoding scheme to embed multiple data points into a small number of qubits, aiming to reduce quantum resource consumption and enhance feature extraction for image classification tasks. Its compact structure is designed to extract multidimensional features with fewer qubits and reduced measurement overhead, thereby improving the utilization of limited quantum resources under the considered setting. To evaluate our method, we conducted several experiments to compare our model with existing approaches and to assess performance under varying numbers of qubits, different CNOT gate configurations, and diverse encoding schemes. Experimental results show that the proposed model achieves competitive performance and slightly higher average accuracy than the traditional convolution structure and three existing quantum convolution schemes under a Qiskit Aer noisy simulation environment. This investigation provides a compact design for the structural optimization and low-resource implementation of quantum convolutional neural networks, offering a potential scheme for quantum-assisted image feature extraction.