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arXiv:2311.02442

Quantum transport on networks for supervised classification

Shmuel Lorber, Oded Zimron, Inbal L. Zak, Anat Milo, Yonatan Dubi

Published Nov 4, 2023• 0 citations
arXivHTMLPDF

Abstract

Classification, the computational process of categorizing an input into pre-existing classes, is now a cornerstone in modern computation in the era of machine learning. Here we propose a new type of 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 particle's exit point, which serves as a "class" and can be determined by changing the network parameters. 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 90\% 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, thus demonstrating quantum advantage, especially in the regime of "small data". These results pave the way for a novel classification scheme, which can be implemented as an algorithm, and potentially realized experimentally on quantum hardware such as photonic networks.

DOI
10.48550/arxiv.2311.02442

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Classification, the computational process of categorizing an input into pre-existing classes, is now a cornerstone in modern computation in the era of machine learning. Here we propose a new type of 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 particle's exit point, which serves as a "class" and can be determined by changing the network parameters. 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 90% 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, thus demonstrating quantum advantage, especially in the regime of "small data". These results pave the way for a novel classification scheme, which can be implemented as an algorithm, and potentially realized experimentally on quantum hardware such as photonic networks.
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.
Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are implementations of quantum classifiers, or models for the classification of data inputs with a quantum computer. Following the success of collective decision making with ensembles in classical machine learning, this paper introduces the concept of quantum ensembles of quantum classifiers. Creating the ensemble corresponds to a state preparation routine, after which the quantum classifiers are evaluated in parallel and their combined decision is accessed by a single-qubit measurement. This framework naturally allows for exponentially large ensembles in which - similar to Bayesian learning - the individual classifiers do not have to be trained. As an example, we analyse an exponentially large quantum ensemble in which each classifier is weighed according to its performance in classifying the training data, leading to new results for quantum as well as classical 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.
Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are implementations of quantum classifiers, or models for the classification of data inputs with a quantum computer. Following the success of collective decision making with ensembles in classical machine learning, this paper introduces the concept of quantum ensembles of quantum classifiers. Creating the ensemble corresponds to a state preparation routine, after which the quantum classifiers are evaluated in parallel and their combined decision is accessed by a single-qubit measurement. This framework naturally allows for exponentially large ensembles in which -- similar to Bayesian learning -- the individual classifiers do not have to be trained. As an example, we analyse an exponentially large quantum ensemble in which each classifier is weighed according to its performance in classifying the training data, leading to new results for quantum as well as classical machine learning.
Quantum machine learning, an important element of quantum computing, recently has gained research attention around the world. In this paper, we have proposed a quantum machine learning model to classify images using a quantum classifier. We exhibit the results of a comprehensive quantum classifier with transfer learning applied to image datasets in particular. The work uses hybrid transfer learning technique along with the classical pre-trained network and variational quantum circuits as their final layers on a small scale of dataset. The implementation is carried out in a quantum processor of a chosen set of highly informative functions using PennyLane a cross-platform software package for using quantum computers to evaluate the high-resolution image classifier. The performance of the model proved to be more accurate than its counterpart and outperforms all other existing classical models in terms of time and competence.
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.