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Machine Learning Algorithms Using Classical and Quantum Photonics

Bhawani Shankar Leelar

Published Apr 30, 2020• 1 citation
OpenAlex

Abstract

ABSTRACT In the modern day , we are witnessing two complementary trends, exponential growth in data and shrinking of chip size. The Data is approaching to 44 zettabytes by 2020 and the chips are now available with 10nm technology. The hyperconnectivity between machine-to-machine and humanto- machine creates multi-dimensional data which is more complex. Our thesis addresses the quantum meta layer abstraction which provides the interface to the Application layer to design quantum and classical algorithms. The first part of the thesis addresses the quantum algorithms and second part address classical algorithms running on top of quantum meta layer. In the first part of our thesis we explored quantum stochastic algorithm for ranking Quantum Webpages, analogous to the classical Google PageRank. The architecture is a six-waveguide photonic lattice that runs finely-tuned quantum stochastic walk. The evolution of density matrix solves the ranking of quantum webpages. We force the photon stochastic walk for quantum PageRank by matching the entries of Google matrix with parameters of the Kossakowski-Lindblad master equation. We have done extensive simulation to observe the density matrix evolution with different parameter settings. We have used noise in the Kossakowski-Lindblad master equation to break the symmetry (reciprocity) property of quantum system, which helps in distinguishable measurement of the quantum PageRank. We next propose a new quantum deep learning with photonic lattice waveguide as a feedforward neural network. The proposed deep photonic neural network uses the quantum properties for learning. The hidden layers of our deep photonic neural network can be designed to learn object representation and mentains the quantum quantum properties for longer time for optimal learning. The second part of the thesis discusses the data based learning. We have used data graph method which captures the system representation. The proposed data graph model captures and encodes the data efficiently and then the data graph is updated and trained with new data to provide efficient predictions. The model retains the previously learned knowledge by transfer learning and improves it with new training. The proposed method is highly adaptive and scalable for different real-time scenarios. Data graph models the system where every node (object) is associated with data and if two objects are related then they are linked with a data edge. The proposed algorithm is an incremental algorithm which learns hidden objects and hidden relationships through the data pattern over time and updates the model accordingly. We have used algebraic graph transformation methods to trigger the mutation of the Data Graph. This new updated Data Graph behaves differently for the data it observes. We explore more into machine learning algorithms and have proposed a complete framework to predict the state of the system based on the system parameters. We have proposed the discretization of the data points using the symbol algebra and used Bayesian machine…

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ABSTRACT
In the modern day , we are witnessing two complementary trends, exponential growth in data and shrinking of chip size. The Data is approaching to 44 zettabytes by 2020 and the chips are now available with 10nm technology. The hyperconnectivity between machine-to-machine and humanto- machine creates multi-dimensional data which is more complex. Our thesis addresses the quantum meta layer abstraction which provides the interface to the Application layer to design quantum and classical algorithms. The first part of the thesis addresses the quantum algorithms and second part address classical algorithms running on top of quantum meta layer. In the first part of our thesis we explored quantum stochastic algorithm for ranking Quantum Webpages, analogous to the classical Google PageRank. The architecture is a six-waveguide photonic lattice that runs finely-tuned quantum stochastic walk. The evolution of density matrix
solves the ranking of quantum webpages. We force the photon stochastic walk for quantum PageRank by matching the entries of Google matrix with parameters of the Kossakowski-Lindblad master equation. We have done extensive simulation to observe the density matrix evolution with different parameter settings. We have used noise in the Kossakowski-Lindblad master equation to break the symmetry (reciprocity) property of quantum system, which helps in distinguishable measurement of the quantum PageRank. We next propose a new quantum deep learning with photonic lattice waveguide as a feedforward neural network. The proposed deep photonic neural network uses the quantum properties for learning. The hidden layers of our deep photonic neural network can be designed to learn object representation and mentains the quantum quantum properties for longer time for optimal learning.
The second part of the thesis discusses the data based learning. We have used data graph method which captures the system representation. The proposed data graph model captures and encodes the data efficiently and then the data graph is updated and trained with new data to provide efficient predictions. The model retains the previously learned knowledge by transfer learning and improves it with new training. The proposed method is highly adaptive and scalable for different real-time scenarios. Data graph models the system where every node (object) is associated with data and if two objects are related then they are linked with a data edge. The proposed algorithm is an incremental algorithm which learns hidden objects and hidden relationships through the data pattern over time and updates the model accordingly. We have used algebraic graph transformation methods to trigger the mutation of the Data Graph. This new updated Data Graph behaves differently for the data it observes. We explore more into machine learning algorithms and have proposed a complete framework to predict the state of the system based on the system parameters. We have proposed the discretization of the data points using the symbol algebra and used Bayesian machine…
Artificial Neural Networks (ANNs) are computational models used in Machine Learning (ML), based on a large collection of connected simple units called artificial neurons, loosely analogous to axons in a biological brain. Most of the Neural Networks (NNs) work in classical architecture and a few hardware implementations with optical components have been proposed, which facilitates real-time parallel processing of massive data sets. While these Optical Neural Networks (ONNs) are faster and comparable in efficiency with the classical NNs, they lack in scalability and flexibility. We have proposed a scalable and reconfigurable photonic lattice based NN, similar to feedforward neural network, where photonic lattice represents the layer of the network. The superposition property of quantum computations allows photons to process massive data sets faster than electronic circuits. We explicitly tried to exploit quantum coherence for learning. Hardware implementations put restrictions on the weight space of photon as negative weights are not possible, therefore we have modified the Backpropagation algorithm for optimizing the weights of the network to manipulate the quantum states. The proposed architecture is theoretically scalable as any number of photonic lattice can be included and provides a platform to get benefit of photonic lattices with different properties. It can be used in understanding the learning behaviour of NNs in a constrained environment.
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then describe more precisely how to link them through linear algebra: we introduce quantum algorithms to efficiently solve tasks such as matrix product or distance estimation. These results are then used to develop new quantum algorithms for unsupervised machine learning, such as k-means and spectral clustering. This allows us to define many fundamental procedures, in particular in vector and graph analysis. We will also present new quantum algorithms for neural networks, or deep learning. For this, we introduce an algorithm to perform a quantum convolution product on images, as well as a new way to perform a fast tomography on quantum states. We prove that these quantum algorithms are faster versions of equivalent classical algorithms, but exhibit random effects due to the quantum nature of the computation. Many simulations have been carried out to study these effects and measure their learning accuracy on real data. Finally, we will present a quantum orthogonal neural network circuit adapted to the currently available small and imperfect quantum computers. This allows us to perform real experiments to test our theory.
The quantum version of Google PageRank has recently been investigated by various groups and shown to be quadratically faster in time than the classical PageRank algorithm. In this paper we propose the implementation of Quantum PageRank by a stochastic quantum walk of correlated photons in a photonic waveguide lattice, where we allow the density matrix to evolve according to the Lindblad-Kossakowski master equation. This yields a stationary state, the diagonal of whose density matrix gives the page ranking.
In recent years, quantum computing, as a potential way to break the bottleneck of Moore's Law, has gradually shown its unique advantages in the field of machine learning. Not only can it bring exponential or polynomial acceleration in some specific tasks, it also provides entirely new ways of representing and processing information. Focusing on the core theme of application and method innovation of quantum machine learning in structured data, this thesis systematically studies the theoretical models and practical applications of quantum computing in many sub-fields such as agricultural remote sensing, graph neural networks, and hyperdimensional computing, and explores the adaptability, scalability, and effectiveness of quantum models in real-world tasks. Firstly, in the cropland classification and yield prediction task, this study identifies that traditional neural networks tend to underperform when facing imbalanced and small-sample remote sensing data, often misclassifying minority crop types. To address this, we propose a quantum-classical hybrid recognition framework that integrates quantum feature mapping with classical neural networks. After incorporating quantum feature encoding, we observe a significant improvement in classification performance, especially in cases involving subtle field boundaries and heterogeneous textures. The quantum-enhanced model demonstrates superior accuracy, robustness, and generalization compared to its classical counterpart, validating the advantage of leveraging quantum representations in real-world agricultural datasets. The second part focuses on the learning of graph structure data and proposes to embed the Continuous Time Quantum Walk (CTQW) into the Graph Neural Network (GNN) architecture. This method not only preserves the global interference characteristic of quantum states but also realizes the efficient modeling of graph topology through the spectral graph methods. Experiments show that the proposed method is superior to many classical graph learning models in tasks such as node classification and graph structure inference. The third and fourth components of this thesis collectively explore quantum approaches to hyperdimensional computing (HDC), establishing a progressive transition from native quantum-state-based implementation to quantum-enhanced HDC strategies. Initially, we investigate the intrinsic mathematical correspondence between quantum states and high-dimensional hypervectors, and propose a novel quantum-state-based high-dimensional encoding method. This method is realized through quantum circuits capable of generating hypervectors with controllable entropy, thereby implementing essential HDC operations, such as classification and memory reconstruction, on real quantum hardware. This marks the first successful migration of core HDC mechanisms into a fully quantum-native framework. Building upon this foundation, we further propose the first quantum-enhanced HDC strategy, which does not rely solely on quantum-native implementations but rather utilizes key quantum features to boost the efficiency and expressivity of conventional HDC systems. Specifically, we introduce mechanisms such as quantum-reference-state-based binding, using density matrices to represent superclass states, and quantum state tomography for robust feature extraction. These innovations significantly enhance the resilience and performance of HDC under high-noise and high-dimensional sensing environments. The resulting models achieve superior accuracy and robustness across a variety of multi-class classification tasks, demonstrating the practical benefits of integrating quantum computation into the broader HDC paradigm. In this thesis, experimental validation is carried out in multiple real and simulation environments, including Qiskit and Paddle Quantum platforms, and a complete closed loop was achieved from theoretical derivation, quantum circuit design to end-to-end experimental evaluation. The results show that quantum methods can expand the expressive power of classical models and become an important tool to deal with large-scale, structured data problems in the future. The work in this thesis provides methodological support for quantum machine learning from theory to application, and also expands the research boundaries of high-dimensional computation and graph learning in the quantum background.
This thesis investigates the interplay between machine learning (ML) and quantum mechanics to advance quantum machine learning (QML) and quantum calculations, addressing computational challenges in quantum machine learning, materials science, and condensed matter physics. The high dimensionality of quantum systems often renders traditional methods computationally intensive. By integrating classical and quantum ML techniques, innovative algorithms are developed to enhance efficiency and accuracy. The first part investigates the design and optimization of quantum circuit architectures for quantum machine learning, with a focus on quantum support vector machines (QSVM). I develop a Bayesian algorithm that adaptively constructs quantum kernels, achieving superior performance over classical kernels in small-data classification tasks. I also establish an isomorphism between quantum circuits and polyatomic molecules, which enables the restriction of the search space for compositional optimization of quantum circuits. Additionally, I introduce a flexible scheme that maps quantum circuits into graph representations compatible with the neutral atom quantum hardware. Using this circuit-graph mapping scheme, I develop a Gaussian process regression model with quantum evolution kernels and a classical graph neural network to interpolate QSVM accuracy on graph-structured data. The second part applies ML to accelerate quantum calculations. I develop a variational algorithm based on eigenvector continuation to compute ground state energies of particle-phonon systems. This algorithm constructs the lowest eigenvalue and eigenvector for extended lattices by solving eigenvalue problems for small, independent lattice segments, with a lower computational cost. This enables the application of variational quantum eigensolvers to particle-phonon interactions in large and disordered lattices, reducing the demands on quantum resources. I also developed Gaussian process models to accelerate Green’s function calculations for electron-phonon systems, achieving high accuracy by extrapolating from restricted Hilbert spaces to larger systems with lower computational cost. Ultimately, this thesis demonstrates that these advancements pave the way for applications, including the design of materials, enhanced drug discovery, and the development of scalable quantum computing technologies, thereby positioning the integration of ML and quantum physics as a promising approach for future scientific breakthroughs.
This thesis investigates the interplay between machine learning (ML) and quantum mechanics to advance quantum machine learning (QML) and quantum calculations, addressing computational challenges in quantum machine learning, materials science, and condensed matter physics. The high dimensionality of quantum systems often renders traditional methods computationally intensive. By integrating classical and quantum ML techniques, innovative algorithms are developed to enhance efficiency and accuracy. The first part investigates the design and optimization of quantum circuit architectures for quantum machine learning, with a focus on quantum support vector machines (QSVM). I develop a Bayesian algorithm that adaptively constructs quantum kernels, achieving superior performance over classical kernels in small-data classification tasks. I also establish an isomorphism between quantum circuits and polyatomic molecules, which enables the restriction of the search space for compositional optimization of quantum circuits. Additionally, I introduce a flexible scheme that maps quantum circuits into graph representations compatible with the neutral atom quantum hardware. Using this circuit-graph mapping scheme, I develop a Gaussian process regression model with quantum evolution kernels and a classical graph neural network to interpolate QSVM accuracy on graph-structured data. The second part applies ML to accelerate quantum calculations. I develop a variational algorithm based on eigenvector continuation to compute ground state energies of particle-phonon systems. This algorithm constructs the lowest eigenvalue and eigenvector for extended lattices by solving eigenvalue problems for small, independent lattice segments, with a lower computational cost. This enables the application of variational quantum eigensolvers to particle-phonon interactions in large and disordered lattices, reducing the demands on quantum resources. I also developed Gaussian process models to accelerate Green’s function calculations for electron-phonon systems, achieving high accuracy by extrapolating from restricted Hilbert spaces to larger systems with lower computational cost. Ultimately, this thesis demonstrates that these advancements pave the way for applications, including the design of materials, enhanced drug discovery, and the development of scalable quantum computing technologies, thereby positioning the integration of ML and quantum physics as a promising approach for future scientific breakthroughs.