Periodic Reporting for period 4 - QNets (Open Quantum Neural Networks: from Fundamental Concepts to Implementations with Atoms and Photons)
Okres sprawozdawczy: 2024-04-01 do 2025-09-30
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. In this project, we aim to establish and explore quantum neural networks which 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. 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.
During this project, we have been able to achieve significant progress towards these goals. Specific achievements include:
- The development of a formalism to evaluate the maximal storage capacity of quantum neural networks;
- The formulation and exploration of quantum generalisations of auto-encoder type neural networks;
- Development and exploration of quantum cellular automata with emergent quantum error correction capabilities;
- The development and benchmarking of an interpretability framework for (classical) neural network based decoders for quantum error correction;
- The theoretical and experimental development and implementation of new protocols for autonomous, measurement-free quantum error correction and quantum computing in state-of-the-art quantum processors.
Overall, these results demonstrate the conceptual potential and practical feasibility of (quantum) neural-network based information processing methods as a promising alternative approach for scalable quantum information processing.
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. 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.
During this project, we have been able to achieve significant progress towards these goals. Specific achievements include:
- The development of a formalism to evaluate the maximal storage capacity of quantum neural networks;
- The formulation and exploration of quantum generalisations of auto-encoder type neural networks;
- Development and exploration of quantum cellular automata with emergent quantum error correction capabilities;
- The development and benchmarking of an interpretability framework for (classical) neural network based decoders for quantum error correction;
- The theoretical and experimental development and implementation of new protocols for autonomous, measurement-free quantum error correction and quantum computing in state-of-the-art quantum processors.
Overall, these results demonstrate the conceptual potential and practical feasibility of (quantum) neural-network based information processing methods as a promising alternative approach for scalable quantum information processing.
Completing the work within the last reporting period, a series of main results have been achieved in the project:
- The development of a formalism to evaluate the maximal storage capacity of quantum neural networks, which act as associative memories, for the storage of patterns. Here, we have successfully applied this new methodology to study the storage capacity of quantum generalisations of paradigmatic classical Hopfield neural networks under thermal and coherent perturbations.
- The formulation of quantum generalisations of auto-encoder type neural networks with emergent quantum error correction capabilities that allow them to autonomously "clean up" noisy quantum states that have suffered from computational errors or the loss of quantum neurons.
- Development and exploration of quantum cellular automata: Here, we have been able to combine different classes of classical cellular automata dynamics and lift those to quantum dynamics, which realise multi-layer QNNs and which we showed can have emergent quantum error correction behavior. Interestingly, such QCAs even work if the quantum dynamics is noisy itself, and these QCAs are ideally suited for implementations in state-of-the-art neutral-atom or trapped-ion quantum processors.
- Motivated by the success of neural network-based decoders for quantum error correction (QEC), we have developed and successfully benchmarked a framework that allows for interpretability of neural network decoders. In the spirit of interpretatible AI, this toolbox allows one to determine via a quantitative Shapley value analysis how a NN comes to its QEC decoding decision.
- We have also explored conceptual and practical ways to engineer measurement-free, yet fully-fault-tolerant quantum error correction and quantum computing protocols. These new protocols can be viewed as realizing coupled qubit networks, whose dynamics through quantum circuits is not learned from training but rather crafted in a careful way. Our new schemes work without mid-circuit measurements with feed-forward control, which are often slow, and susceptible to relatively high error rates. We have shown in a series of theory works that this allows for a scalable, universal measurement-free quantum computing, and in a collaboration realised a first experimental demonstration of mid-circuit measurement-free fault-tolerant universal quantum computation.
- Furthermore, we have established a new theoretical method to evaluate the maximum error-correcting capacity of QEC codes, which is based on the coherent information as an order parameter. This technique allows one to determine critical error thresholds for quantum information processing for a wide family of QEC codes and noise models, including computational errors and loss of qubits.
The results obtained have been presented at national and international invited talks and seminars. With regard to exploitation, they have already given rise to follow-up research projects building on them, as well as to follow-up third-party funded research grants.
- The development of a formalism to evaluate the maximal storage capacity of quantum neural networks, which act as associative memories, for the storage of patterns. Here, we have successfully applied this new methodology to study the storage capacity of quantum generalisations of paradigmatic classical Hopfield neural networks under thermal and coherent perturbations.
- The formulation of quantum generalisations of auto-encoder type neural networks with emergent quantum error correction capabilities that allow them to autonomously "clean up" noisy quantum states that have suffered from computational errors or the loss of quantum neurons.
- Development and exploration of quantum cellular automata: Here, we have been able to combine different classes of classical cellular automata dynamics and lift those to quantum dynamics, which realise multi-layer QNNs and which we showed can have emergent quantum error correction behavior. Interestingly, such QCAs even work if the quantum dynamics is noisy itself, and these QCAs are ideally suited for implementations in state-of-the-art neutral-atom or trapped-ion quantum processors.
- Motivated by the success of neural network-based decoders for quantum error correction (QEC), we have developed and successfully benchmarked a framework that allows for interpretability of neural network decoders. In the spirit of interpretatible AI, this toolbox allows one to determine via a quantitative Shapley value analysis how a NN comes to its QEC decoding decision.
- We have also explored conceptual and practical ways to engineer measurement-free, yet fully-fault-tolerant quantum error correction and quantum computing protocols. These new protocols can be viewed as realizing coupled qubit networks, whose dynamics through quantum circuits is not learned from training but rather crafted in a careful way. Our new schemes work without mid-circuit measurements with feed-forward control, which are often slow, and susceptible to relatively high error rates. We have shown in a series of theory works that this allows for a scalable, universal measurement-free quantum computing, and in a collaboration realised a first experimental demonstration of mid-circuit measurement-free fault-tolerant universal quantum computation.
- Furthermore, we have established a new theoretical method to evaluate the maximum error-correcting capacity of QEC codes, which is based on the coherent information as an order parameter. This technique allows one to determine critical error thresholds for quantum information processing for a wide family of QEC codes and noise models, including computational errors and loss of qubits.
The results obtained have been presented at national and international invited talks and seminars. With regard to exploitation, they have already given rise to follow-up research projects building on them, as well as to follow-up third-party funded research grants.
The project has gone beyond the state-of-the-art in a number of directions, as outlined above.
Particularly worth highlighting are the following achievements:
- Demonstration that quantum auto-encoder neural networks as well as quantum cellular automata can be trained or constructed in a way so that they have emergent quantum error correction capabilities.
- Comprehensive exploration of schemes for autonomous quantum dynamics that realise measurement-free, yet fully fault-tolerant and scalable universal quantum computing, as well as a world's first experimental demonstration of mid-circuit measurement-free fault-tolerant universal quantum computation.
- Development of new theoretical methodology to (i) calculate the maximal storage capacity of quantum neural networks, and (ii) to analyze in the spirit of interpretable AI the functioning principle of neural-network-based decoders for fault-tolerant quantum error correction.
Particularly worth highlighting are the following achievements:
- Demonstration that quantum auto-encoder neural networks as well as quantum cellular automata can be trained or constructed in a way so that they have emergent quantum error correction capabilities.
- Comprehensive exploration of schemes for autonomous quantum dynamics that realise measurement-free, yet fully fault-tolerant and scalable universal quantum computing, as well as a world's first experimental demonstration of mid-circuit measurement-free fault-tolerant universal quantum computation.
- Development of new theoretical methodology to (i) calculate the maximal storage capacity of quantum neural networks, and (ii) to analyze in the spirit of interpretable AI the functioning principle of neural-network-based decoders for fault-tolerant quantum error correction.