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Kernel Approximation on a Quantum Annealer for Remote Sensing Regression Tasks

Edoardo Pasetto, Morris Riedel, Kristel F. L. Michielsen, Gabriele Cavallaro

Published May 12, 2023• 0 citations
Publisher

Abstract

The increased development of quantum computing hardware in recent years has led to increased interest in its application to various areas. Finding effective ways to apply this technology to real-world use-cases is a current area of research in the Remote Sensing (RS) community. This paper proposes an Adiabatic Quantum Kitchen Sinks (AQKS) kernel approximation algorithm with parallel quantum annealing on the D-Wave Advantage quantum annealer. The proposed implementation is applied to Support Vector Regression (SVR) and Gaussian Process Regression (GPR) algorithms. To evaluate its performance, a regression problem related to estimating chlorophyll concentra-tion in water is considered. The proposed algorithm was tested on two real-world datasets and its results were compared with those obtained from a classical implementation of kernel-based algorithms and a Random Kitchen Sinks (RKS) implementation. On average, the parallel AQKS achieved comparable results to the benchmark methods, indicating its potential for future applications.

DOI
10.36227/techrxiv.22794146

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The increased development of quantum computing hardware in recent years has led to increased interest in its application to various areas. Finding effective ways to apply this technology to real-world use-cases is a current area of research in the Remote Sensing (RS) community. This paper proposes an Adiabatic Quantum Kitchen Sinks (AQKS) kernel approximation algorithm with parallel quantum annealing on the D-Wave Advantage quantum annealer. The proposed implementation is applied to Support Vector Regression (SVR) and Gaussian Process Regression (GPR) algorithms. To evaluate its performance, a regression problem related to estimating chlorophyll concentra-tion in water is considered. The proposed algorithm was tested on two real-world datasets and its results were compared with those obtained from a classical implementation of kernel-based algorithms and a Random Kitchen Sinks (RKS) implementation. On average, the parallel AQKS achieved comparable results to the benchmark methods, indicating its potential for future applications.
The increased development of quantum computing hardware in recent years has led to increased interest in its application to various areas. Finding effective ways to apply this technology to real-world use-cases is a current area of research in the Remote Sensing (RS) community. This paper proposes an Adiabatic Quantum Kitchen Sinks (AQKS) kernel approximation algorithm with parallel quantum annealing on the D-Wave Advantage quantum annealer. The proposed implementation is applied to Support Vector Regression (SVR) and Gaussian Process Regression (GPR) algorithms. To evaluate its performance, a regression problem related to estimating chlorophyll concentra-tion in water is considered. The proposed algorithm was tested on two real-world datasets and its results were compared with those obtained from a classical implementation of kernel-based algorithms and a Random Kitchen Sinks (RKS) implementation. On average, the parallel AQKS achieved comparable results to the benchmark methods, indicating its potential for future applications.
The increased development of quantum computing hardware in recent years has led to increased interest in its application to various areas. Finding effective ways to apply this technology to real-world use-cases is a current area of research in the (RS) community. This paper proposes an (AQKS) kernel approximation algorithm with parallel quantum annealing on the D-Wave Advantage quantum annealer. The proposed implementation is applied to (SVR) and (GPR) algorithms. To evaluate its performance, a regression problem related to estimating chlorophyll concentration in water is considered. The proposed algorithm was tested on two real-world datasets and its results were compared with those obtained by a classical implementation of kernel-based algorithms and a (RKS) implementation. On average, the parallel (AQKS) achieved comparable results to the benchmark methods, indicating its potential for future applications.
Kernel methods are class of Machine Learning (ML) models that have been widely employed in the literature for Earth Observation (EO) applications. The increasing development of quantum computing hardware motivates further research to improve the capabilities and the performances of data analysis algorithms. In this manuscript an implementation of Adiabatic Quantum Kitchen Sinks (AQKS) kernel estimation algorithm integrated with parallel quantum annealing is presented. Such combination with the concept of parallel quantum annealing allows for the solving of multiple problem instances in the same annealing cycle, thus reducing the number of rquired calls to the quantum annealing solver. The proposed workflow is then implemented using a D-Wave Advantage system and tested on a regression problem on a real Remote Sensing (RS) dataset. The obtained results are then analyzed and compared with those obtained by a classical kernel approximation algorithm based on Random Fourier Features.
The increasing availability of quantum computers motivates researching their potential capabilities in enhancing the performance of data analysis algorithms. Similarly, as in other research communities, also in Remote Sensing (RS) it is not yet defined how its applications can benefit from the usage of quantum computing. This paper proposes a formulation of the Support Vector Regression (SVR) algorithm that can be executed by D-Wave quantum computers. Specifically, the SVR is mapped to a Quadratic Unconstrained Binary Optimization (QUBO) problem that is solved with Quantum Annealing (QA). The algorithm is tested on two different types of computing environments offered by D-Wave: The Advantage system, which directly embeds the problem into the Quantum Processing Unit (QPU), and a Hybrid solver that employs both classical and quantum computing resources. For the evaluation, we considered a biophysical variable estimation problem with RS data. The experimental results show that the proposed quantum SVR implementation can achieve comparable or in some cases better results than the classical implementation. This work is one of the first attempts to provide insight into how QA could be exploited and integrated in future RS workflows based on Machine Learning (ML) algorithms.
Regression analysis has a crucial role in many Earth Ob-servation (EO) applications. The increasing availability and recent development of new computing technologies moti-vate further research to expand the capabilities and enhance the performance of data analysis algorithms. In this paper, the biophysical variable estimation problem is addressed. A novel approach is proposed, which consists in a reformulated Support Vector Regression (SVR) and leverages Quantum Annealing (QA). In particular, the SVR optimization prob-lem is reframed to a Quadratic Unconstrained Binary Opti-mization (QUBO) problem. The algorithm is then tested on the D-Wave Advantage quantum annealer. The experiments presented in this paper show good results, despite current hardware limitations, suggesting that this approach is viable and has great potential.
In recent years, the development of quantum annealers has enabled experimental demonstrations and has increased research interest in applications of quantum annealing, such as in quantum machine learning and in particular for the popular quantum Support Vector Machine (SVM). Several versions of the quantum SVM have been proposed, and quantum annealing has been shown to be effective in them. Extensions to multiclass problems have also been made, which consist of an ensemble of multiple binary classifiers. This work proposes a novel quantum SVM formulation for direct multiclass classification based on quantum annealing, called Quantum Multiclass SVM (QMSVM). The multiclass classification problem is formulated as a single quadratic unconstrained binary optimization problem solved with quantum annealing. The main objective of this work is to evaluate the feasibility, accuracy, and time performance of this approach. Experiments have been performed on the D-Wave Advantage quantum annealer for a classification problem on remote sensing data. Results indicate that, despite the memory demands of the quantum annealer, QMSVM can achieve an accuracy that is comparable to standard SVM methods, such as the one-versus-one (OVO), depending on the dataset (compared to OVO: 0.8663 vs 0.8598 on Toulouse, 0.8123 vs 0.8521 on Potsdam). More importantly, it scales much more efficiently with the number of training examples, resulting in nearly constant time (compared to OVO: 85.72s vs 248.02s on Toulouse, 58.89s vs 580.17s on Potsdam). This work shows an approach for bringing together classical and quantum computation, solving practical problems in remote sensing with current hardware.