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Realization of an ion trap quantum classifier

Tarun Dutta, Adrián Pérez-Salinas, Jasper Phua Sing Cheng, José Ignacio Latorre, Manas Mukherjee

Published Jun 26, 2021• 3 citations
OpenAlex

Abstract

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.

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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 kkk gates is as powerful as a neural network with one intermediate hidden layer of kkk 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.
Quantum machine learning has the potential to provide powerful algorithms for artificial intelligence. The pursuit of quantum advantage in quantum machine learning is an active area of research. For current noisy intermediate-scale quantum computers, various quantum-classical hybrid algorithms have been proposed. One such previously proposed hybrid algorithm is a gate-based variational embedding classifier, which is composed of a classical neural network and a parameterized gate-based quantum circuit. We propose a quantum variational embedding classifier based on an analog quantum computer, where control signals vary continuously in time: our particular focus is an implementation using quantum annealers. In our algorithm, the classical data are transformed into the parameters of the time-varying Hamiltonian of the analog quantum computer by a linear transformation. The nonlinearity needed for a nonlinear classification problem is purely provided by the analog quantum computer through the nonlinear dependence of the final quantum state on the control parameters of the Hamiltonian. We perform numerical simulations that demonstrate the effectiveness of our algorithm for performing binary and multiclass classification on linearly inseparable datasets such as concentric circles and MNIST digits. Our classifier can reach accuracy comparable with that of the best classical classifiers. We find that the performance of our classifier can be increased by increasing the number of qubits, until the performance saturates and fluctuates. Moreover, the number of optimization parameters of our classifier scales linearly with the number of qubits. The increase of the number of training parameters when the size of our model increases is therefore not as fast as that of a neural network. Our algorithm presents the possibility of using current quantum annealers for solving practical machine-learning problems, and it could also be useful to explore quantum advantage in quantum machine learning.
In this work, we investigate the use of a quantum circuit as a binary classification model in the context of quantum machine learning. We call this model, binary quantum classifier. First, we describe fundamental concepts of quantum computing and introduce the computational tool used: Qibo, an open-source framework for efficient quantum simulations and quantum hardware control. Then, we describe how to design a binary quantum classifier for the classification of images and small arrays of variables by showing how to input data in the circuit, defining a quantum circuit model Ansatz with trainable parameters and a loss function, and implementing multiple minimizers. We test our quantum classifier with two data sets. The first one is the MNIST data set which is composed of handwritten digits (reduced to only handwritten zeros and handwritten ones for binary classification). We study the behavior of different minimizers by increasing the number of layers of the Ansatz. The second data set represents two different high energy collisions that can occur at colliders such as LHC (CERN). Due to in-time proton-proton interactions known as pile-up, we distinguish two different data sets: "without pile-up" and "with pile-up". These collisions can be represented by images of size 32x32 or by six high-level variables that we call features. By increasing the size of the training data set and the number of layers of the Ansatz, we search for the best minimizer. Splitting the data set in training set and test set, we compute: ROC curve, AUC score, confusion matrices and test set accuracy. For "with pile-up" images, we compare the results obtained with the quantum classifier with a small convolutional neural network. We conclude that is possible to build a binary quantum classifier with a quantum circuit and we highlight its performances and limitations in comparison with classical technologies.
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.
Deep learning is one of the most successful and far-reaching strategies used in machine learning today. However, the scale and utility of neural networks is still greatly limited by the current hardware used to train them. These concerns have become increasingly pressing as conventional computers quickly approach physical limitations that will slow performance improvements in years to come. For these reasons, scientists have begun to explore alternative computing platforms, like quantum computers, for training neural networks. In recent years, variational quantum circuits have emerged as one of the most successful approaches to quantum deep learning on noisy intermediate scale quantum devices. We propose a hybrid quantum-classical neural network architecture where each neuron is a variational quantum circuit. We empirically analyze the performance of this hybrid neural network on a series of binary classification data sets using a simulated universal quantum computer and a state of the art universal quantum computer. On simulated hardware, we observe that the hybrid neural network achieves roughly 10% higher classification accuracy and 20% better minimization of cost than an individual variational quantum circuit. On quantum hardware, we observe that each model only performs well when the qubit and gate count is sufficiently small.
Classification, the computational process of categorizing an input into preexisting classes, is now a cornerstone in modern computation in the era of machine learning. Here, we propose an approach for a quantum physical computer; a quantum classifier, based on quantum transport of particles in a trained quantum network. The classifier is based on sending a quantum particle into a network and measuring the exit point of the particle, which serves as a ``class'' and can be determined by changing the network parameters, differing from standard quantum computers as no gate operations are required to perform the computation. Using this scheme, we demonstrate three examples of classification. In the first, wave functions are classified according to their overlap with predetermined (random) groups. In the second, we classify wave functions according to their level of localization. Both examples use small training sets and achieve over 95% precision and recall. The third classification scheme is a ``real-world problem,'' concerning classification of catalytic aromatic aldehyde substrates according to their reactivity. Using experimental data, the quantum classifier reaches an average 86% classification accuracy. We show that the quantum classifier outperforms its classical counterpart for these examples and demonstrates clear advantage, especially in the regime of ``small data.'' These results pave the way for a classification scheme that can be implemented as an algorithm and potentially realized experimentally on quantum hardware.