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Methods for Quantum Dynamics, Localization and Quantum Machine Learning

Nicola Pancotti

Published Jan 1, 2020• 0 citations
OpenAlex

Abstract

The thesis is divided into three parts. In the first part, we explore scenarios where quantum dynamics is slow and information is localized. In the second part, we design thermodynamic protocols by engineering time-dependent Hamiltonians of a system interacting with its bath. Finally, in the third part, we examine the intersections between tensor-network methods for quantum mechanics and machine learning methods.

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The thesis is divided into three parts. In the first part, we explore scenarios where quantum dynamics is slow and information is localized. In the second part, we design thermodynamic protocols by engineering time-dependent Hamiltonians of a system interacting with its bath. Finally, in the third part, we examine the intersections between tensor-network methods for quantum mechanics and machine learning methods.
These brief lecture notes cover the basics of neural networks and deep learning as well as their applications in the quantum domain, for physicists without prior knowledge. In the first part, we describe training using backpropagation, image classification, convolutional networks and autoencoders. The second part is about advanced techniques like reinforce-ment learning (for discovering control strategies), recurrent neural networks (for analyz-ing time traces), and Boltzmann machines (for learning probability distributions). In the third lecture, we discuss first recent applications to quantum physics, with an emphasis on quantum information processing machines. Finally, the fourth lecture is devoted to the promise of using quantum effects to accelerate machine learning.
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
These brief lecture notes cover the basics of neural networks and deep learning as well as their applications in the quantum domain, for physicists without prior knowledge. In the first part, we describe training using back-propagation, image classification, convolutional networks and autoencoders.The second part is about advanced techniques like reinforcement learning (for discovering control strategies), recurrent neural networks (for analyzing timetraces), and Boltzmann machines (for learning probability distributions). In the third lecture, we discuss first recent applications to quantum physics, with an emphasis on quantum information processing machines. Finally, the fourth lecture is devoted to the promise of using quantum effects to accelerate machine learning.
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.