Periodic Reporting for period 2 - QNets (Open Quantum Neural Networks: from Fundamental Concepts to Implementations with Atoms and Photons)
Periodo di rendicontazione: 2021-04-01 al 2022-09-30
Classical neural networks, originally inspired by the neural structure of the brain, have become a powerful and ubiquitous information processing paradigm in our every day’s life. Neural-network-based algorithms and software are used with impressive success for tasks as diverse as image and speech recognition and classification, machine learning or the analysis of ‘big data’. At the same time, we witness enormous progress in developing quantum technologies, as highlighted by increasingly larger and more powerful quantum computers being built by both academic research teams as well as some of the world’s leading tech companies. Driven by the hope of combining properties such as massive parallel information processing in neural networks with advantages like the computational speedup promised by quantum computers, there have been efforts in several directions to develop quantum-mechanical generalisations of neural networks. If successful, this could fundamentally enhance the power of information processors, which form the backbone of our information-driven modern society. Most attempts to tackle this challenge so far have focussed on developing quantum neural networks in the form of quantum algorithms, i.e. developing quantum software that can be run on current prototype or future quantum computers - very much like classical neural network algorithms that are executed on our digital computing devices. In this project, we take a complementary approach and aim to establish and explore quantum neural networks by following an approach of quantum neuromorphic engineering: here, the idea is that the actual quantum neural networks are realised by the real-time dynamics of interacting many-particle quantum systems coupled to a surrounding environment - so-called open many-body quantum systems.
Here, our goal is on the one hand to understand which quantum neural architectures can be formulated in a meaningful way, for instance in the form of coupled layers of quantum neurons, or in the form of quantum networks where quantum neurons are connected to all other constituents of the quantum network. We will then explore if and how these quantum networks can provide advantages over their classical counterparts, for instance with respect to their computational power, in the form of enhanced information storage capacities, or by increased speed of the required training to teach the quantum networks to perform their tasks with high accuracy. Based on this conceptual basis, we will also identify physical building blocks for the practical implementation of such a new quantum processor paradigm in state-of-the-art quantum technological platforms: these include trapped ions, neutral Rydberg atom systems and hybrid light-matter platforms, which offer unique opportunities for quantum engineering the required building blocks with an exquisite level of control. Thereby, the project aims at laying the foundation for quantum neuromorphic engineering of quantum neural hardware in state-of-the-art and newly emerging experimental systems.
Here, our goal is on the one hand to understand which quantum neural architectures can be formulated in a meaningful way, for instance in the form of coupled layers of quantum neurons, or in the form of quantum networks where quantum neurons are connected to all other constituents of the quantum network. We will then explore if and how these quantum networks can provide advantages over their classical counterparts, for instance with respect to their computational power, in the form of enhanced information storage capacities, or by increased speed of the required training to teach the quantum networks to perform their tasks with high accuracy. Based on this conceptual basis, we will also identify physical building blocks for the practical implementation of such a new quantum processor paradigm in state-of-the-art quantum technological platforms: these include trapped ions, neutral Rydberg atom systems and hybrid light-matter platforms, which offer unique opportunities for quantum engineering the required building blocks with an exquisite level of control. Thereby, the project aims at laying the foundation for quantum neuromorphic engineering of quantum neural hardware in state-of-the-art and newly emerging experimental systems.
Along one line of research, we have been able to show how classical neural networks can be used for the task of assisting the process of correcting errors in quantum computers. Here, the main idea is that a classical neural network is fed and trained with measurement information that is obtained from periodically extracting so-called error syndrome information from quantum processors. The neural network can then be trained to identify the types of errors that might have happened on the quantum hardware and come up with suitable suggestions for corrections to remove these errors and restore the original quantum states.
Complementary, we have formulated and studied quantum mechanical generalisations of classical neural networks, such as the Hopfield model, which constitute paradigmatic model systems for the storage and retrieval of information, such as patterns or images. Here, we studied the non-equilibrium dynamics of these interacting open-system quantum neural networks, to investigate under which conditions a robust storage and retrieval of information in these quantum systems is possible: here, we have for example examined what happens if they are exposed to finite temperatures or competing dynamical processes, both being effects which can affect the information storage capabilities of the quantum networks. An important question concerns the amount of information that can be stored in a network - the storage capacity. Recently, we have been able to develop a new method that allows one to determine the maximum information storage capacity of open quantum neural networks - this is a first enabling step towards further studies to understand the potential storage capacity of various models of quantum neural networks.
Furthermore, we explored the performance of a special type of layered quantum neural networks, so-called quantum autoencoders. In the classical realm, autoencoder networks can be used for information compressing and also for denoising of data - for example to restore clear pictures starting from blurry images as inputs of the network. Here, we have for the quantum case constructed quantum neural networks, which are able to autonomously - that means without external intervention - correct computational errors or even the loss of qubits in the quantum registers. This successful cleaning up noisy quantum states by quantum neural networks provides a promising step towards autonomous quantum error correction, thereby opening a potential alternative avenue to realise robust and eventually error-corrected quantum processors.
Complementary, we have formulated and studied quantum mechanical generalisations of classical neural networks, such as the Hopfield model, which constitute paradigmatic model systems for the storage and retrieval of information, such as patterns or images. Here, we studied the non-equilibrium dynamics of these interacting open-system quantum neural networks, to investigate under which conditions a robust storage and retrieval of information in these quantum systems is possible: here, we have for example examined what happens if they are exposed to finite temperatures or competing dynamical processes, both being effects which can affect the information storage capabilities of the quantum networks. An important question concerns the amount of information that can be stored in a network - the storage capacity. Recently, we have been able to develop a new method that allows one to determine the maximum information storage capacity of open quantum neural networks - this is a first enabling step towards further studies to understand the potential storage capacity of various models of quantum neural networks.
Furthermore, we explored the performance of a special type of layered quantum neural networks, so-called quantum autoencoders. In the classical realm, autoencoder networks can be used for information compressing and also for denoising of data - for example to restore clear pictures starting from blurry images as inputs of the network. Here, we have for the quantum case constructed quantum neural networks, which are able to autonomously - that means without external intervention - correct computational errors or even the loss of qubits in the quantum registers. This successful cleaning up noisy quantum states by quantum neural networks provides a promising step towards autonomous quantum error correction, thereby opening a potential alternative avenue to realise robust and eventually error-corrected quantum processors.
In the upcoming phase of the project, we will on the one hand focus on further exploring the potential computational power of the open quantum neural networks. On the other hand, we will use the insights gained so far to develop proposals for realistic implementations of the open quantum neural network frameworks in state-of-the-art quantum technology labs. We expect that these results will help lay the conceptual foundation and provide a viable practical route towards experimental realisations of engineered quantum neural networks in the lab.