The tasks of characterization and control of quantum systems are becoming more challenging with the advancement of quantum technology. Standard methods that were successful for simple quantum systems are becoming inadequate for more complex engineered systems. Modelling assumptions and approximations (such as Markovianity) are not justifiable anymore. As a result, the usual models fail to fit experimental measurements. In this thesis, we use state-of-the-art machine learning methods, assisted by tools from information theory as needed, to develop new frameworks that try to address these challenges. We focus on three directions. The first is developing an efficient online quantum state estimation algorithm with provable convergence properties. The second is developing a deep learning framework for characterizing and controlling closed quantum systems. The final direction is upgrading that framework to be suitable for characterization and control of open quantum systems. This thesis opens the door for a novel way of utilizing machine learning techniques for applications in quantum information specially and physics in general.
The tasks of characterization and control of quantum systems are becoming more challenging with the advancement of quantum technology. Standard methods that were successful for simple quantum systems are becoming inadequate for more complex engineered systems. Modelling assumptions and approximations (such as Markovianity) are not justifiable anymore. As a result, the usual models fail to fit experimental measurements. In this thesis, we use state-of-the-art machine learning methods, assisted by tools from information theory as needed, to develop new frameworks that try to address these challenges. We focus on three directions. The first is developing an efficient online quantum state estimation algorithm with provable convergence properties. The second is developing a deep learning framework for characterizing and controlling closed quantum systems. The final direction is upgrading that framework to be suitable for characterization and control of open quantum systems. This thesis opens the door for a novel way of utilizing machine learning techniques for applications in quantum information specially and physics in general.
The advancement of quantum technologies depends on the ability to create and manipulate increasingly complex quantum systems, with critical applications in quantum computation, quantum simulation and quantum sensing. These developments present substantial challenges in efficient control, calibration and verification of quantum systems. Machine learning methods have emerged as powerful tools owing to their remarkable capability to learn from data, and have thus been extensively utilized for various quantum tasks. This paper reviews several significant topics at the intersection of machine learning and quantum estimation and control. Specifically, we discuss neural network-based approaches for quantum state estimation, gradient-based methods for quantum optimal control, evolutionary computation for learning control of quantum systems, machine learning techniques for quantum robust control and reinforcement learning for adaptive quantum control.
In this thesis, we discuss applications of machine learning to quantum information science. The interface between these two fields has been the subject of much research, recently, driven by the many successes of machine learning for diverse pattern recognition tasks. The work reported in this Thesis addresses precisely the potential of such an interdisciplinary line of research and illustrates how machine learning provides a valuable add-on to standard techniques used in the context of quantum technologies. Specifically, we will first study the problem of devising time-independent dynamics implementing target quantum operations. This involves a challenging optimisation task, which is hard to tackle with standard numerical tools. We demonstrate how the use of supervised learning algorithms can dramatically speed-up this task. We then consider the tasks of engineering and characterising quantum states in large Hilbert spaces. Motivated by strong experimental reasons, we consider explicitly the embodiment of such multi-dimensional quantum systems provided by the orbital angular momentum and polarisation degrees of freedom of light. We devise a protocol involving quantum walks to implement arbitrary states by only making use of the possibility to couple polarisation and orbital angular momentum through relatively recent technological advances in the field of linear optics. This protocol relies solely on the properties of quantum walk dynamics, and is therefore applicable to different types of architectures. We then present an experimental demonstration of this engineering strategy, and consider the issue of assessing the quality of the states thus generated. We show how different machine learning algorithms, including supervised and unsupervised learning ones, are able to tackle this problem and provide useful information in realistic experimental conditions.
Understanding and controlling engineered quantum systems is key to developing practical quantum technology. However, given the current technological limitations, such as fabrication imperfections and environmental noise, this is not always possible. To address these issues, a great deal of theoretical and numerical methods for quantum system identification and control have been developed. These methods range from traditional curve fittings, which are limited by the accuracy of the model that describes the system, to machine learning methods, which provide efficient control solutions but no control beyond the output of the model, nor insights into the underlying physical process. Here we experimentally demonstrate a "graybox" approach to construct a physical model of a quantum system and use it to design optimal control. We report superior performance over model fitting, while generating unitaries and Hamiltonians, which are quantities not available from the structure of standard supervised machine learning models. Our approach combines physics principles with high-accuracy machine learning and is effective with any problem where the required controlled quantities cannot be directly measured in experiments. This method naturally extends to time-dependent and open quantum systems, with applications in quantum noise spectroscopy and cancellation.
Abstract Understanding and controlling engineered quantum systems is key to developing practical quantum technology. However, given the current technological limitations, such as fabrication imperfections and environmental noise, this is not always possible. To address these issues, a great deal of theoretical and numerical methods for quantum system identification and control have been developed. These methods range from traditional curve fittings, which are limited by the accuracy of the model that describes the system, to machine learning (ML) methods, which provide efficient control solutions but no control beyond the output of the model, nor insights into the underlying physical process. Here we experimentally demonstrate a ‘graybox’ approach to construct a physical model of a quantum system and use it to design optimal control. We report superior performance over model fitting, while generating unitaries and Hamiltonians, which are quantities not available from the structure of standard supervised ML models. Our approach combines physics principles with high-accuracy ML and is effective with any problem where the required controlled quantities cannot be directly measured in experiments. This method naturally extends to time-dependent and open quantum systems, with applications in quantum noise spectroscopy and cancellation.
Recent advances in Machine Learning have transformed numerous industrial sectors, yet classical paradigms face fundamental limitations: rapidly growing data volumes, rising computational costs, significant energy consumption, and the physical scaling limits of conventional hardware architectures. Quantum computing has emerged as a promising computational paradigm to address these challenges, giving rise to the field of Quantum Machine Learning (QML). In this thesis, the theoretical foundations of QML are investigated, with a focus on near-term and future practical applications. Three central challenges are addressed: the trainability of variational quantum circuits, their expressivity, and their resistance to efficient classical simulation. The trainability of Hamming-weight preserving variational quantum circuits is first studied, and theoretical guarantees are established that resolve an open conjecture on the absence of barren plateaus for this circuit family. Subspace-preserving QML algorithms are then introduced, including photonic circuits and quantum convolutional neural networks, and are designed to mimic classical ML subroutines while offering polynomial quantum advantage. Finally, variational quantum circuits are analyzed as quantum Fourier models, and a framework is derived to jointly characterize expressivity and trainability, from which conditions are obtained under which quantum models provably separate from their classical counterparts. These contributions are intended to advance the theoretical roadmap for harnessing near-term and future quantum technologies in real-world applications.
Quantum computation is a form of computation utilizing quantum mechanical phenomena.A formal formulation of quantum computer was proposed in 1985, leading to novel quantum algorithms whose computation time scales better, with respect to the problem size, than the classical counterparts.However, running these quantum algorithms requires fault-tolerant implementations, and hence, such engineering in quantum systems can be an overhead in utilizing quantum systems for information processing.This suggests, in addition to seeking faster quantum algorithms, the necessity of exploring how to harness quantum systems more naturally without extensive engineering, leading to another form of quantum information processing.Quantum machine learning (QML) is expected to be a promising approach for harnessing quantum systems for information processing.This is motivated by the fact that the success of neural networks has led to the possibility of solving ML tasks more efficiently with non-digital computer designs.Several QML algorithms that resemble neural networks utilize quantum systems in a manner distinct from digital quantum algorithms.However, training quantum systems is fundamentally challenging, suggesting that it still remains necessary to explore an alternative way of harnessing quantum systems for ML.Along with this direction, the quantum reservoir model harnesses quantum systems in a unique way: nontrivial outputs from an untrained quantum system are leveraged by a linear classical machine learning model to solve various tasks.Hence, the quantum part does not need to be programmable and can be analog quantum dynamics.Without extensive engineering in the quantum part, a quantum reservoir model was shown to be capable of performing nontrivial ML tasks using physical dynamics, which had already been realized experimentally.Therefore, the quantum reservoir model should be one of the promising directions for pursuing another form of quantum information processing.In this thesis, I will investigate the computational capability of natural quantum dynamics in the quantum reservoir model.I will tackle the following critical open questions in this context: (i) how well natural dynamics perform nontrivial ML tasks compared to engineered systems, and (ii) what kind of engineering in quantum dynamics is essential and appropriate for a given task.To tackle the first question (i), I will benchmark the learning performance of various natural quantum dynamics against random circuits that require complicated engineering, thereby revealing the computational power of natural dynamics.For the second question (ii), I will present a characterization method of quantum dynamics that has the potential to bridge quantum properties and their machine learning roles, providing concrete insights into essential and appropriate engineering to design quantum systems for ML.v