Abstract The application of machine learning techniques to solve problems in quantum control together with established geometric methods for solving optimisation problems leads naturally to an exploration of how machine learning approaches can be used to enhance geometric approaches for solving problems in quantum information processing. In this work, we review and extend the application of deep learning to quantum geometric control problems. Specifically, we demonstrate enhancements in time-optimal control in the context of quantum circuit synthesis problems by applying novel deep learning algorithms in order to approximate geodesics (and thus minimal circuits) along Lie group manifolds relevant to low-dimensional multi-qubit systems, such as SU(2), SU(4) and SU(8). We demonstrate the superior performance of greybox models, which combine traditional blackbox algorithms with whitebox models (which encode prior domain knowledge of quantum mechanics), as means of learning underlying quantum circuit distributions of interest. Our results demonstrate how geometric control techniques can be used to both (a) verify the extent to which geometrically synthesised quantum circuits lie along geodesic, and thus time-optimal, routes and (b) synthesise those circuits. Our results are of interest to researchers in quantum control and quantum information theory seeking to combine machine learning and geometric techniques for time-optimal control problems.
Abstract The application of machine learning techniques to solve problems in quantum control together with established geometric methods for solving optimisation problems leads naturally to an exploration of how machine learning approaches can be used to enhance geometric approaches for solving problems in quantum information processing. In this work, we review and extend the application of deep learning to quantum geometric control problems. Specifically, we demonstrate enhancements in time-optimal control in the context of quantum circuit synthesis problems by applying novel deep learning algorithms in order to approximate geodesics (and thus minimal circuits) along Lie group manifolds relevant to low-dimensional multi-qubit systems, such as SU(2), SU(4) and SU(8). We demonstrate the superior performance of greybox models, which combine traditional blackbox algorithms with whitebox models (which encode prior domain knowledge of quantum mechanics), as means of learning underlying quantum circuit distributions of interest. Our results demonstrate how geometric control techniques can be used to both (a) verify the extent to which geometrically synthesised quantum circuits lie along geodesic, and thus time-optimal, routes and (b) synthesise those circuits. Our results are of interest to researchers in quantum control and quantum information theory seeking to combine machine learning and geometric techniques for time-optimal control problems.
The use of geometric and symmetry techniques in quantum and classical information processing has a long tradition across the physical sciences as a means of theoretical discovery and applied problem solving. In the modern era, the emergent combination of such geometric and symmetry-based methods with quantum machine learning (QML) has provided a rich opportunity to contribute to solving a number of persistent challenges in fields such as QML parametrisation, quantum control, quantum unitary synthesis and quantum proof generation. In this thesis, we combine state-of-the-art machine learning methods with techniques from differential geometry and topology to address these challenges. We present a large-scale simulated dataset of open quantum systems to facilitate the development of quantum machine learning as a field. We demonstrate the use of deep learning greybox machine learning techniques for estimating approximate time-optimal unitary sequences as geodesics on subRiemannian symmetric space manifolds. Finally, we present novel techniques utilising Cartan decompositions and variational methods for analytically solving quantum control problems for certain classes of Riemannian symmetric space. Owing to its multidisciplinary nature, this work contains extensive supplementary background information in the form of Appendices. Each supplementary Appendix is tailored to provide additional background material in a relatively contained way for readers whom may be familiar with some, but not all, of these diverse scientific disciplines. The Appendices reproduce or paraphrase standard results in the literature with source material identified at the beginning of each Appendix. Proofs are omitted for brevity but can be found in the cited sources and other standard texts.
In this Research Paper we have highlighted about the Study on Machine Learning Application in Quantum Circuit Synthesis. Quantum circuit synthesis, a fundamental task in quantum computing, involves designing efficient circuits to execute quantum algorithms on quantum computers. Machine learning techniques have been increasingly applied to enhance this process. One key area where machine learning excels is in optimizing quantum circuits for specific tasks. Quantum circuit synthesis often involves a large search space of possible circuit configurations, making it computationally intensive to find optimal solutions. Machine learning algorithms, such as reinforcement learning or genetic algorithms, can efficiently navigate this search space to identify high-performing circuit configurations. These algorithms learn from past experiences and iteratively improve their performance, gradually converging towards optimal solutions. Machine learning can aid in automating the design process by predicting the performance of quantum circuits based on their characteristics. By analyzing large datasets of quantum circuits and their corresponding performance metrics, machine learning models can identify patterns and correlations, enabling the prediction of circuit performance without the need for exhaustive simulations. Additionally, machine learning techniques can assist in error mitigation in quantum circuits. Quantum computers are susceptible to various types of errors, which can degrade the performance of quantum algorithms. Machine learning algorithms can analyze error patterns and devise strategies to mitigate them, leading to more reliable quantum circuits.
The convergence of machine learning (ML) and quantum computing is quickly becoming a game-changing new frontier in computational science. The most intriguing area of overlap may be quantum optimization, which seeks to reduce the exponentially increasing complexity and computational cost of ML algorithms. As they grow larger and more complicated, traditional optimization methods, particularly in high-dimensional and non-convex space, will inevitably hit performance limits. Quantum optimization is the whole new paradigm that leverages quantum mechanical effects like superposition, entanglement, and tunnelling to explore solution spaces more efficiently. The chapter outlines the theory, practice, and potential of hybrid quantum-classical optimization algorithms for machine learning. The most brilliant research direction in the current NISQ (noisy intermediate-scale quantum) era is mixed systems leveraging classical computing capability augmented by quantum capacity. In such designs, computationally intensive subroutines like optimization for global optima or escape from local minima are left to quantum processors and data preprocessing, iterative refinement, and model testing are performed by classical processors. We start by defining the fundamental principles of quantum computing and acquainting readers with the fundamentals like qubits, quantum gates, and quantum circuits. These are the building blocks for quantum algorithms, which hopefully can be utilized for optimization, for example, the QAOA (quantum approximate optimization algorithm), the VQE (variational quantum Eigensolver), and quantum annealing. They all build to optimize the problems in some way differently: QAOA through parameterized quantum circuits, VQE through approximations of ground states of the Hamiltonians, and quantum annealing through quantum evolution to low-energy solutions. We then form a loop between these quantum algorithms and regular machine learning tasks. Optimization impacts virtually all ML phases, from training neural networks, where one reduces loss functions; feature selection, where one aims to discover the most relevant subset of input variables; and hyperparameter optimization, which often involves expensive search procedures over extremely large combinatorial spaces. Quantum optimization techniques can therefore, in principle, accelerate such procedures through computational complexity reduction and enhancing solutions over challenging landscapes. Realistic simulations and case studies emphasize the degree to which hybrid quantum-classical algorithms have been employed in solving ML problems, that is, QSVMs, quantum-enhanced clustering, and quantum reinforcement learning. Despite their experimental nature, these applications already show encouraging results in terms of improved performance metrics as well as reduction in time-to-solution compared to classical-only solutions. Notwithstanding that, this new field is not bereft of real challenges. Quantum hardware suffers from hard limits on qubit fidelity, decoherence, and scalability in the current times. Furthermore, quantum circuit integration into broad ML pipelines requires novel architectures and software platforms. As a counter to those issues, this chapter surveys recent advances in quantum programming languages, simulators, and hybrid platforms like PennyLane, Qiskit, and TensorFlow Quantum. We conclude by looking to the future possibility that quantum optimization will revolutionize the machine learning landscape. As hardware improves and algorithmic complexity increases, the possibility of quantum-powered learning systems solving hard problems becomes increasingly accessible. From speeding up deep network training to enabling new types of unsupervised learning, quantum optimization holds the potential to recast computational tractability in machine learning. This chapter is an all-encompassing introduction and state-of-the-art work for students, researchers, and practitioners interested in using quantum optimization for practical ML applications. It sets the foundation for understanding how to pursue hybrid approaches (how they may be applied today in the real world and bracing oneself for disruption in the future).
Quantum Machine Learningby Jordi RIU This project applies reinforcement learning techniques to optimize a quantum algorithm.The upcoming quantum computers are capable of optimization tasks in an exponentially large parameter space.Having access to such a large optimization space potentially allows an advantage of Quantum methods over classical algorithms, but at the price of problems in the optimization process -just to name a few, the presence of local minima and the low convergence speeds-.This project explores the application of reinforcement learning techniques to control and optimize the operation of a quantum computer solving a hard combinatorial problem, namely the MaxCut problem.Our methods use a collection of quantum observables to feed the state of the agent, inspired on a similar classical approach to the problem applied to the antiferromagnetic Ising model lattice.Our results show how an agent using these observables can optimally control the operation of a quantum device to obtain quasi-optimal solutions when in combination with the Quantum Approximate Optimization Algorithm (QAOA).v
Quantum Machine Learning (QML) offers a paradigm shift in computation, potentially unlocking unprecedented capabilities in areas like drug discovery, materials science, and optimization. This paper investigates the application of geometric mapping to QML, specifically focusing on optimizing quantum model parameters through the application of geometric transformations. We propose a novel framework that utilizes geometric properties to guide the parameter search process, leading to improved model accuracy and efficiency. This research explores the benefits of this approach compared to traditional machine learning techniques, particularly in the context of quantum systems. The core mechanism involves mapping a quantum system's state space to a geometric space, leveraging geometric properties to enhance the optimization process. The paper concludes with a discussion of the potential impact of this geometric mapping technique on the future of QML.
This paper explores the application of deep learning techniques to optimize quantum circuits. The core challenge in quantum computing lies in the intricate design and manipulation of quantum circuits to achieve desired computational outcomes. Traditional methods of quantum circuit optimization are often computationally expensive and require significant domain expertise. This research proposes a novel approach leveraging deep learning algorithms to automatically generate optimal quantum circuits. The system learns the underlying structure and characteristics of quantum circuits through training, effectively reducing the complexity associated with quantum computation. This work presents a framework for automated quantum circuit optimization, paving the way for more accessible and efficient quantum computing solutions. The key contribution is the integration of deep learning with quantum circuit optimization, offering an automated process for circuit design and potentially unlocking the full potential of quantum computers.