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Schrödinger's Catwalk

Brian Flynn

Published Jun 1, 2021• 0 citations
OpenAlex

Abstract

Quantum technologies exploit quantum mechanical processes to achieve outcomes beyond the reach of classical machinery.One of their most promising applications is quantum simulation, whereby particles, atoms and molecules can be examined thoroughly for the first time, having been beyond the scope of even the most powerful supercomputers.Models have been useful tools in understanding physical systems: these are mathematical structures encoding physical interactions, which allow us to predict how the system will behave under various conditions.Models of quantum systems are particularly difficult to design and test, owing to the huge computational resources required to represent them accurately.In this thesis, we introduce and develop an algorithm to characterise quantum systems efficiently, by inferring a model consistent with their observed dynamics.The Quantum Model Learning Agent (QMLA) is an extensible framework which permits the study of any quantum system of interest, by combining quantum simulation with state of the art machine learning.QMLA iteratively proposes candidate models and trains them against the target system, finally declaring a single model as the best representation for the system of interest.We describe QMLA and its implementation through open source software, before testing it under a series of physical scenarios.First, we consider idealised theoretical systems in simulation, verifying the core principles of QMLA.Next, we incorporate strategies for generating candidate models by exploiting the information QMLA has gathered to date; by incorporating a genetic algorithm within QMLA, we explore vast spaces of valid candidate models, with QMLA reliably identifying the precise target model.Finally, we apply QMLA to realistic quantum systems, including operating on experimental data measured from an electron spin in a nitrogen vacancy centre.QMLA is shown to be effective in all cases studied in this thesis; however, of greater interest is the platform it provides for examining quantum systems.QMLA can aid engineers in configuring experimental setups, facilitate calibration of near term quantum devices, and ultimately enable complete characterisation of natural quantum structures.This thesis marks the beginning of a new line of research, into automating the understanding of quantum mechanical systems.

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Quantum technologies exploit quantum mechanical processes to achieve outcomes beyond the reach of classical machinery.One of their most promising applications is quantum simulation, whereby particles, atoms and molecules can be examined thoroughly for the first time, having been beyond the scope of even the most powerful supercomputers.Models have been useful tools in understanding physical systems: these are mathematical structures encoding physical interactions, which allow us to predict how the system will behave under various conditions.Models of quantum systems are particularly difficult to design and test, owing to the huge computational resources required to represent them accurately.In this thesis, we introduce and develop an algorithm to characterise quantum systems efficiently, by inferring a model consistent with their observed dynamics.The Quantum Model Learning Agent (QMLA) is an extensible framework which permits the study of any quantum system of interest, by combining quantum simulation with state of the art machine learning.QMLA iteratively proposes candidate models and trains them against the target system, finally declaring a single model as the best representation for the system of interest.We describe QMLA and its implementation through open source software, before testing it under a series of physical scenarios.First, we consider idealised theoretical systems in simulation, verifying the core principles of QMLA.Next, we incorporate strategies for generating candidate models by exploiting the information QMLA has gathered to date; by incorporating a genetic algorithm within QMLA, we explore vast spaces of valid candidate models, with QMLA reliably identifying the precise target model.Finally, we apply QMLA to realistic quantum systems, including operating on experimental data measured from an electron spin in a nitrogen vacancy centre.QMLA is shown to be effective in all cases studied in this thesis; however, of greater interest is the platform it provides for examining quantum systems.QMLA can aid engineers in configuring experimental setups, facilitate calibration of near term quantum devices, and ultimately enable complete characterisation of natural quantum structures.This thesis marks the beginning of a new line of research, into automating the understanding of quantum mechanical systems.
Abstract Accurate models of real quantum systems are important for investigating their behaviour, yet are difficult to distil empirically. Here, we report an algorithm—the quantum model learning agent (QMLA)—to reverse engineer Hamiltonian descriptions of a target system. We test the performance of QMLA on a number of simulated experiments, demonstrating several mechanisms for the design of candidate Hamiltonian models and simultaneously entertaining numerous hypotheses about the nature of the physical interactions governing the system under study. QMLA is shown to identify the true model in the majority of instances, when provided with limited a priori information, and control of the experimental setup. Our protocol can explore Ising, Heisenberg and Hubbard families of models in parallel, reliably identifying the family which best describes the system dynamics. We demonstrate QMLA operating on large model spaces by incorporating a genetic algorithm to formulate new hypothetical models. The selection of models whose features propagate to the next generation is based upon an objective function inspired by the Elo rating scheme, typically used to rate competitors in games such as chess and football. In all instances, our protocol finds models that exhibit F 1 score ⩾ 0.88 when compared with the true model, and it precisely identifies the true model in 72% of cases, whilst exploring a space of over 250 000 potential models. By testing which interactions actually occur in the target system, QMLA is a viable tool for both the exploration of fundamental physics and the characterisation and calibration of quantum devices.
Characterizing quantum processes is crucial for the execution of quantum algorithms on available quantum devices. A powerful framework for this purpose is the Quantum Model Learning Agent (QMLA) which characterizes a given system by learning its Hamiltonian via adaptive generations of informative experiments and their validation against simulated models. Identifying the incoherent noise of a quantum device in addition to its coherent interactions is, however, as essential. Precise knowledge of such imperfections of a quantum device allows to devise strategies to mitigate detrimental effects, for example via quantum error correction. We introduce the open Quantum Model Learning Agent (oQMLA) framework to account for Markovian noise through the Liouvillian formalism. By simultaneously learning the Hamiltonian and jump operators, oQMLA independently captures both the coherent and incoherent dynamics of a system. The added complexity of open systems necessitates advanced algorithmic strategies. Among these, we implement regularization to steer the algorithm towards plausible models and an unbiased metric to evaluate the quality of the results. We validate our implementation in simulated scenarios of increasing complexity, demonstrating its robustness to hardware-induced measurement errors and its ability to characterize systems using only local operations. Additionally, we develop a scheme to interface oQMLA with a publicly available superconducting quantum computer, showcasing its practical utility. These advancements represent a significant step toward improving the performance of quantum hardware and contribute to the broader goal of advancing quantum technologies and their applications.
Quantum computing is one of the most exciting research areas of the last decades. At the same time, methods of machine learning have started to dominate science, industry and our everyday life. In this thesis we combine these two essential research topics of the 21st century and introduce dissipative quantum neural networks (DQNNs), which are designed for fully quantum learning tasks, are capable of universal quantum computation and have low memory requirements while training. We start the discussion of this interdisciplinary topic by introducing artificial neural networks, which are a very common tool in classical machine learning. Next, we give an overview on quantum information. Here we focus on quantum algorithms and circuits, which are used to implement quantum neural networks. Moreover, we explain the opportunities and challenges arising with today's quantum computers. The discussion of the architecture and training algorithm of the DQNNs forms the core of this work. These networks are optimised with training data pairs in form of input and desired output states and therefore can be used for characterising unknown or untrusted quantum devices. We not only demonstrate the generalisation behaviour of these quantum neural networks using classical simulations, but also implement them successfully on actual quantum computers. To understand the ultimate limits for such quantum machine learning methods, we discuss the quantum no free lunch theorem, which describes a bound on the probability that a quantum device, which can be modelled as a unitary process and is optimised with quantum examples, gives an incorrect output for a random input. This gives us a tool to review the learning behaviour of quantum neural networks in general and the DQNNs in particular. Moreover we expand the area of applications of DQNNs in two directions. In the first case, we include additional information beyond just the training data pairs: since quantum devices are always structured, the resulting data is always structured as well. We modify the DQNN's training algorithm such that knowledge about the graph-structure of the training data pairs is included in the training process and show that this can lead to better generalisation behaviour. Both the original DQNN and the DQNN including graph structure are trained with data pairs in order to characterise an underlying relation. However, in the second extension of the algorithm we aim to learn characteristics of a set of quantum states in order to extend it to quantum states which have similar properties. Therefore we build a generative adversarial model where two DQNNs, called the generator and discriminator, are trained in a competitive way. Overall, we observe that DQNNs can not only be trained efficiently but also, similar to their classical counterparts, modified to suit different applications.
Quantum machine learning (QML) is a computational paradigm that seeks to apply quantum-mechanical resources to solve learning problems. As such, the goal of this framework is to leverage quantum processors to tackle optimization, supervised, unsupervised and reinforcement learning, and generative modeling-among other tasks-more efficiently than classical models. Here we offer a high level overview of QML, focusing on settings where the quantum device is the primary learning or data generating unit. We outline the field's tensions between practicality and guarantees, access models and speedups, and classical baselines and claimed quantum advantages-flagging where evidence is strong, where it is conditional or still lacking, and where open questions remain. By shedding light on these nuances and debates, we aim to provide a friendly map of the QML landscape so that the reader can judge when-and under what assumptions-quantum approaches may offer real benefits.
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.
Abstract Despite the complexity of quantum systems in the real world, models with just a few effective many-body states often suffice to describe their quantum dynamics, provided decoherence is accounted for. We show that a machine learning algorithm is able to construct such models, given a straightforward set of quantum dynamics measurements. The effective Hilbert space can be a black box, with variations of the coupling to just one accessible output state being sufficient to generate the required training data. We demonstrate through simulations of a Markovian open quantum system that a neural network can automatically detect the number N of effective states and the most relevant Hamiltonian terms and state-dephasing processes and rates. For systems with N ⩽ 5 we find typical mean relative errors of predictions in the 10 % range. With more advanced networks and larger training sets, it is conceivable that a future single software can provide the automated first stop solution to model building for an unknown device or system, complementing and validating the conventional approach based on physical insight into the system.