A single qubit provides sufficient computational capabilities to construct a universal quantum classifier when assisted with a classical subroutine. This fact may be surprising since a single qubit only offers a simple superposition of two states and single-qubit gates only make a rotation in the Bloch sphere. The key ingredient to circumvent these limitations is to allow for multiple data re-uploading . A quantum circuit can then be organized as a series of data re-uploading and single-qubit processing units. Furthermore, both data re-uploading and measurements can accommodate multiple dimensions in the input and several categories in the output, to conform to a universal quantum classifier. The extension of this idea to several qubits enhances the efficiency of the strategy as entanglement expands the superpositions carried along with the classification. Extensive benchmarking on different examples of the single- and multi-qubit quantum classifier validates its ability to describe and classify complex data.
A single qubit provides sufficient computational capabilities to construct a universal quantum classifier when assisted with a classical subroutine. This fact may be surprising since a single qubit only offers a simple superposition of two states and single-qubit gates only make a rotation in the Bloch sphere. The key ingredient to circumvent these limitations is to allow for multiple data re-uploading . A quantum circuit can then be organized as a series of data re-uploading and single-qubit processing units. Furthermore, both data re-uploading and measurements can accommodate multiple dimensions in the input and several categories in the output, to conform to a universal quantum classifier. The extension of this idea to several qubits enhances the efficiency of the strategy as entanglement expands the superpositions carried along with the classification. Extensive benchmarking on different examples of the single- and multi-qubit quantum classifier validates its ability to describe and classify complex data.
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.
We report the realization of a versatile classifier based on the quantum mechanics of a single atom. The problem of classification has been extensively studied by the classical machine learning community, with plenty of proposed algorithms that have been refined over time. Quantum computation must necessarily develop quantum classifiers and benchmark them against their classical counterparts. It is not obvious how to make use of our increasing ability to precisely control and evolve a quantum state to solve this kind of problems, while there is only a limited number of strong theorems backing the quantum algorithms for classification. Here we show that both of these limitations can be successfully addressed by the implementation of a recently proposed data re-uploading algorithm in an ion trap based quantum processing unit. The quantum classifier is trained in two steps: first, the quantum circuit is fed with an optimal set of variational parameters found by classical simulation; then, the variational circuit is optimized by inspecting the parameter landscape with only the quantum processing unit. This second step provides a partial cancellation of the systematic errors inherent to the quantum device. The accuracy of our quantum supervised classifier is benchmarked on a variety of datasets, that imply, finding the separation of classes associated to regions in a plane in both binary and multi-class problems, as well as in higher-dimensional feature spaces. Our experiments show that a single-ion quantum classifier circuit made out of k gates is as powerful as a neural network with one intermediate hidden layer of k neurons.
Quantum computers can provide solutions to certain classically intractable problems. However, current devices have limited computational resources, and an effort is made to develop useful quantum algorithms under this constraint. This work demonstrates experimentally that a single-qubit processor can host a universal classifier based on the re-uploading scheme. The quantum processor used in this work is built with an ion trap, providing highly accurate control on a one-qubit system as required by the re-uploading scheme. A set of nontrivial classification tasks are completed successfully. The training procedure is performed in two steps combining simulation and experiment. Final results are benchmarked against exact simulations of the same method and also classical algorithms, showing a competitive performance of the ion-trap quantum classifier. This work constitutes the experimental implementation of a classification algorithm based on the re-uploading scheme.
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.
Quantum data re-uploading has proved powerful for classical inputs, where repeatedly encoding features into a small circuit yields universal function approximation. Extending this idea to quantum inputs remains underexplored, as the information contained in a quantum state is not directly accessible in classical form. We propose and analyze a quantum data re-uploading architecture in which a qubit interacts sequentially with fresh copies of an arbitrary input state. The circuit can approximate any bounded continuous function using only one ancilla qubit and single-qubit measurements, provided that sufficiently many copies of the input state and, in general, sufficiently many layers are available. By alternating entangling unitaries with mid-circuit resets of the input register, the architecture realizes a discrete cascade of completely positive and trace-preserving maps, analogous to collision models in open quantum system dynamics. Our framework provides a space-efficient and expressive approach to designing quantum machine learning models that operate directly on quantum data.
A single-qubit circuit can approximate any bounded complex function stored in the degrees of freedom defining its quantum gates. The single-qubit approximant presented in this work is operated through a series of gates that take as their parametrization the independent variable of the target function and an additional set of adjustable parameters. The independent variable is re-uploaded in every gate while the parameters are optimized for each target function. The output state of this quantum circuit becomes more accurate as the number of re-uploadings of the independent variable increases, i.e., as more layers of gates parameterized with the independent variable are applied. In this work, we provide two proofs of this claim related to both the Fourier series and the universal approximation theorem for neural networks, and we benchmark both methods against their classical counterparts. We further implement a single-qubit approximant in a real superconducting qubit device, demonstrating how the ability to describe a set of functions improves with the depth of the quantum circuit. This work shows the robustness of the re-uploading technique on quantum machine learning.