Continuous Variable Quantum Computing: Quantum Machine Learning

Quantum Machine Learning is the synergy between quantum computing devices and Machine/Deep Learning techniques. It refers to a field of study for analysing data and for optimization problems. There exists distinct quantum computing devices such as superconducting, quantum annealer, or photonics quantum computing. Here we use a photonic-based quantum computing device so-called Continuous Variable Quantum Computing (CV-QC) for a regression task and analyse its use for practical problems (Remote Sensing and earth observation image classification, optimization problems, or satellite-based quantum radar)

Exploiting the Quantum Advantage for Satellite Image Processing: Review and Assessment

This article examines the current status of quantum computing in Earth observation (EO) and satellite imagery. We analyze the potential limitations and applications of quantum learning models when dealing with satellite data, considering the persistent challenges of profiting from quantum advantage and finding the optimal sharing between high-performance computing (HPC) and quantum computing (QC). We then assess some parameterized quantum circuit models transpiled into a Clifford+T universal gate set. The T-gates shed light on the quantum resources required to deploy quantum models, either on an HPC system or several QC systems. In particular, if the T-gates cannot be simulated efficiently on an HPC system, we can apply a quantum computer and its computational power over conventional techniques. Our quantum resource estimation showed that quantum machine learning (QML) models, with a sufficient number of T-gates, provide the quantum advantage if and only if they generalize on unseen data points better than their classical counterparts deployed on the HPC system and they break the symmetry in their weights at each learning iteration like in conventional deep neural networks. We also estimated the quantum resources required for some QML models as an initial innovation. Lastly, we defined the optimal sharing between an HPC+QC system for executing QML models for hyperspectral satellite images. These are a unique dataset compared to other satellite images since they have a limited number of input qubits and a small number of labeled benchmark images, making them less challenging to deploy on quantum computers.Comment: It could be withdrawn if accepted in IEEE Transaction on Quantum Engineerin

Exploiting the Quantum Advantage for Satellite Image Processing: Review and Assessment

This article examines the current status of quantum computing in Earth observation (EO) and satellite imagery. We analyze the potential limitations and applications of quantum learning models when dealing with satellite data, considering the persistent challenges of profiting from quantum advantage and finding the optimal sharing between high-performance computing (HPC) and quantum computing (QC). We then assess some parameterized quantum circuit models transpiled into a Clifford+T universal gate set. The T-gates shed light on the quantum resources required to deploy quantum models, either on an HPC system or several QC systems. In particular, if the T-gates cannot be simulated efficiently on an HPC system, we can apply a quantum computer and its computational power over conventional techniques. Our quantum resource estimation showed that quantum machine learning (QML) models, with a sufficient number of T-gates, provide the quantum advantage if and only if they generalize on unseen data points better than their classical counterparts deployed on the HPC system and they break the symmetry in their weights at each learning iteration like in conventional deep neural networks. We also estimated the quantum resources required for some QML models as an initial innovation. Lastly, we defined the optimal sharing between an HPC+QC system for executing QML models for hyperspectral satellite images. These are a unique dataset compared to other satellite images since they have a limited number of input qubits and a small number of labeled benchmark images, making them less challenging to deploy on quantum computers

Natural Embedding of the Stokes Parameters of Polarimetric Synthetic Aperture Radar Images in a Gate-Based Quantum Computer

Quantum algorithms are designed to process quantum data (quantum bits) in a gate-based quantum computer. They are proven rigorously that they reveal quantum advantages over conventional algorithms when their inputs are certain quantum data or some classical data mapped to quantum data. However, in a practical domain, data are classical in nature, and they are very big in dimension, size, and so on. Hence, there is a challenge to map (embed) classical data to quantum data, and even no quantum advantages of quantum algorithms are demonstrated over conventional ones when one processes the mapped classical data in a gate-based quantum computer. For the practical domain of earth observation (EO), due to the different sensors on remotesensing platforms, we can map directly some types of EO data to quantum data. In particular, we have polarimetric synthetic aperture radar (PolSAR) images characterized by polarized beams. A polarized state of the polarized beam and a quantum bit are the Doppelganger of a physical state. We map them to each other, and we name this direct mapping a natural embedding, otherwise an artificial embedding. Furthermore, we process our naturally embedded data in a gate-based quantum computer by using a quantum algorithm regardless of its quantum advantages over conventional techniques; namely, we use the QML network as a quantum algorithm to prove that we naturally embedded our data in input qubits of a gate-based quantum computer. Therefore, we employed and directly processed PolSAR images in a QML network. Furthermore, we designed and provided a QML network with an additional layer of a neural network, namely, a hybrid quantum-classical network, and demonstrate how to program (via optimization and backpropagation) this hybrid quantum-classical network when employing and processing PolSAR images. In this work, we used a gate-based quantum computer offered by an IBM Quantum and a classical simulator for a gate-based quantum computer. Our contribution is that we provided very specific EO data with a natural embedding feature, the Doppelganger of quantum bits, and processed them in a hybrid quantum-classical network. More importantly, in the future, these PolSAR data can be processed by future quantum algorithms and future quantum computing platforms to obtain (or demonstrate) some quantum advantages over conventional techniques for EO problems

Advancing of Earth Observation Methodologies by using a Quantum Computer

Remotely-sensed images obtained from aircraft and satellite platforms are used for Earth observation tasks. The remotely-sensed images are available in digital format and contain information on the number of spectral bands, radiometric resolution, and spatial resolution. We performed the first exploratory studies for applying quantum computers to remotely-sensed images and problems. Parametrized quantum circuits solve optimization problems and can be utilized as a learning model exploiting different mechanisms and techniques of quantum physics. As a case example, we present therefore the result that parametrized quantum circuits are very competitive in contrast with its classical neural networks

Quantum Annealer for Subset Feature Selection and the Classification of Hyperspectral Images

Hyperspectral images showing objects belonging to several distinct target classes are characterized by dozens of spectral bands being available. However, some of these spectral bands are redundant and/or noisy, and hence, selecting highly informative and trustworthy bands for each class is a vital step for classification and for saving internal storage space; then the selected bands are termed a highly-informative spectral band subset. We use a Mutual Information (MI)-based method to select the spectral band subset of a given class and two additional binary quantum classifiers, namely a quantum boost (Qboost) and a quantum boost plus (Qboost-Plus) classifier, to classify a two-label dataset characterized by the selected band subset. We pose both our MI-based band subset selection problem and the binary quantum classifiers as a quadratic unconstrained binary optimization (QUBO) problem. Thus, we adapted our MI-based optimization problem for selecting highly-informative bands for each class of a given hyperspectral image to be run on a D-Wave quantum annealer. After the selection of these highly-informative bands for each class, we employ our binary quantum classifiers to a two-label dataset on the D-Wave quantum annealer. In addition, we provide a novel multi-label classifier exploiting an Error-Encoding Output Code (ECOC) when using our binary quantum classifiers. As a real-world dataset in Earth observation, we used the well known AVIRIS hyperspectral image (HSI) of Indian Pine, northwestern Indiana, USA

AI4EO: from physics guided paradigms to quantum machine learning

Earth Observation (EO) Data Intelligence is addressing the entire value chain: data processing to extract information, the information analysis to gather knowledge, and knowledge transformation in value. EO technologies have immensely evolved the state of the art sensors deliver a broad variety of images, and have made considerable progress in spatial and radiometric resolution, target acquisition strategies, imaging modes, geographical coverage and data rates. Generally imaging sensors generate an isomorphic representation of the observed scene. This is not the case for EO, the observations are a doppelgänger of the scattered field, an indirect signature of the imaged object. EO images are instrument records, i.e. in addition to the spatial information, they are sensing physical parameters, and they are mainly sensing outside of the visual spectrum. This positions the load of EO image understanding, and the outmost challenge of Big EO Data Science, as new and particular challenge of Machine Learning (ML) and Artificial Intelligence (AI). The presentation introduces specific solutions for the EO Data Intelligence, as methods for physically meaningful features extraction to enable high accuracy characterization of any structure in large volumes of EO images. The theoretical background is introduced, discussing the advancement of the paradigms from Bayesian inference, machine learning, and evolving to the methods of Deep Learning and Quantum Machine Learning. The applications are demonstrated for: alleviation of atmospheric effects and retrieval of Sentinel 2 data, enhancing the opportunistic bi-static images with Sentinel 1, explainable data mining and discovery of physical scattering properties for SAR observations, and natural embedding of the PolSAR Stokes parameters in a gate-based quantum computer

Assembly of a Coreset of Earth Observation Images on a Small Quantum Computer

Satellite instruments monitor the Earth's surface day and night, and, as a result, the size of Earth observation (EO) data is dramatically increasing. Machine Learning (ML) techniques are employed routinely to analyze and process these big EO data, and one well-known ML technique is a Support Vector Machine (SVM). An SVM poses a quadratic programming problem, and quantum computers including quantum annealers (QA) as well as gate-based quantum computers promise to solve an SVM more efficiently than a conventional computer; training the SVM by employing a quantum computer/conventional computer represents a quantum SVM (qSVM)/classical SVM (cSVM) application. However, quantum computers cannot tackle many practical EO problems by using a qSVM due to their very low number of input qubits. Hence, we assembled a coreset (core of a dataset) of given EO data for training a weighted SVM on a small quantum computer, a D-Wave quantum annealer with around 5000 input quantum bits. The coreset is a small, representative weighted subset of an original dataset, and its performance can be analyzed by using the proposed weighted SVM on a small quantum computer in contrast to the original dataset. As practical data, we use synthetic data, Iris data, a Hyperspectral Image (HSI) of Indian Pine, and a Polarimetric Synthetic Aperture Radar (PolSAR) image of San Francisco. We measured the closeness between an original dataset and its coreset by employing a Kullback–Leibler (KL) divergence test, and, in addition, we trained a weighted SVM on our coreset data by using both a D-Wave quantum annealer (D-Wave QA) and a conventional computer. Our findings show that the coreset approximates the original dataset with very small KL divergence (smaller is better), and the weighted qSVM even outperforms the weighted cSVM on the coresets for a few instances of our experiments. As a side result (or a by-product result), we also present our KL divergence findings for demonstrating the closeness between our original data (i.e., our synthetic data, Iris data, hyperspectral image, and PolSAR image) and the assembled coreset

Quantum Transfer Learning for Real-World, Small, and High-Dimensional Datasets

Quantum machine learning (QML) networks promise to have some computational (or quantum) advantage for classifying supervised datasets (e.g., satellite images) over some conventional deep learning (DL) techniques due to their expressive power via their local effective dimension. There are, however, two main challenges regardless of the promised quantum advantage: 1) Currently available quantum bits (qubits) are very small in number, while real-world datasets are characterized by hundreds of high-dimensional elements (i.e., features). Additionally, there is not a single unified approach for embedding real-world high-dimensional datasets in a limited number of qubits. 2) Some real-world datasets are too small for training intricate QML networks. Hence, to tackle these two challenges for benchmarking and validating QML networks on real-world, small, and high-dimensional datasets in one-go, we employ quantum transfer learning composed of a multi-qubit QML network, and a very deep convolutional network (a with VGG16 architecture) extracting informative features from any small, high-dimensional dataset. We use real-amplitude and strongly-entangling N-layer QML networks with and without data re-uploading layers as a multi-qubit QML network, and evaluate their expressive power quantified by using their local effective dimension; the lower the local effective dimension of a QML network, the better its performance on unseen data. Our numerical results show that the strongly-entangling N-layer QML network has a lower local effective dimension than the real-amplitude QML network and outperforms it on the hard-to-classify three-class labelling problem. In addition, quantum transfer learning helps tackle the two challenges mentioned above for benchmarking and validating QML networks on real-world, small, and high-dimensional datasets.Comment: This article is submitted to IEEE TGRS. Hence, this version will be removed from ArXiv after published in this IEEE journa

Coreset of Hyperspectral Images on Small Quantum Computer

Machine Learning (ML) techniques are employed to analyze and process big Remote Sensing (RS) data, and one well-known ML technique is a Support Vector Machine (SVM). An SVM is a quadratic programming (QP) problem, and a D-Wave quantum annealer (D-Wave QA) promises to solve this QP problem more efficiently than a conventional computer. However, the D-Wave QA cannot solve directly the SVM due to its very few input qubits. Hence, we use a coreset ("core of a dataset") of given EO data for training an SVM on this small D-Wave QA. The coreset is a small, representative weighted subset of an original dataset, and any training models generate competitive classes by using the coreset in contrast to by using its original dataset. We measured the closeness between an original dataset and its coreset by employing a Kullback-Leibler (KL) divergence measure. Moreover, we trained the SVM on the coreset data by using both a D-Wave QA and a conventional method. We conclude that the coreset characterizes the original dataset with very small KL divergence measure. In addition, we present our KL divergence results for demonstrating the closeness between our original data and its coreset. As practical RS data, we use Hyperspectral Image (HSI) of Indian Pine, US