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.
