Recurrent neural networks play an important role in both research and industry. With the advent of quantum machine learning, the quantisation of recurrent neural networks has become recently relevant. We propose fully quantum recurrent neural networks, based on dissipative quantum neural networks, capable of learning general causal quantum automata. A quantum training algorithm is proposed and classical simulations for the case of product outputs with the fidelity as cost function are carried out. We thereby demonstrate the potential of these algorithms to learn complex quantum processes with memory in terms of the exemplary delay channel, the time evolution of quantum states governed by a time-dependent Hamiltonian, and high- and low-frequency noise mitigation. Numerical simulations indicate that our quantum recurrent neural networks exhibit a striking ability to generalise from small training sets.
Recurrent neural networks play an important role in both research and industry. With the advent of quantum machine learning, the quantisation of recurrent neural networks has become recently relevant. We propose fully quantum recurrent neural networks, based on dissipative quantum neural networks, capable of learning general causal quantum automata. A quantum training algorithm is proposed and classical simulations for the case of product outputs with the fidelity as cost function are carried out. We thereby demonstrate the potential of these algorithms to learn complex quantum processes with memory in terms of the exemplary delay channel, the time evolution of quantum states governed by a time-dependent Hamiltonian, and high- and low-frequency noise mitigation. Numerical simulations indicate that our quantum recurrent neural networks exhibit a striking ability to generalise from small training sets.
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.
Neural networks enjoy widespread success in both research and industry and, with the advent of quantum technology, it is a crucial challenge to design quantum neural networks for fully quantum learning tasks. Here we propose a truly quantum analogue of classical neurons, which form quantum feedforward neural networks capable of universal quantum computation. We describe the efficient training of these networks using the fidelity as a cost function, providing both classical and efficient quantum implementations. Our method allows for fast optimisation with reduced memory requirements: the number of qudits required scales with only the width, allowing deep-network optimisation. We benchmark our proposal for the quantum task of learning an unknown unitary and find remarkable generalisation behaviour and a striking robustness to noisy training data.
Quantum neural network (QNN) is one of the promising areas in which noisy medium-scale quantum devices (MCD) can find advantageous applications in the short term compared to classical resources. Recurrent neural networks are the most fundamental networks for sequential learning, but there is still no canonical model of a quantum recurrent neural network (QRNN), which certainly limits research in the field of quantum deep learning. In the present paper, a new type of QRNS is proposed that would be a good candidate as a canonical QRNN model, where quantum recurrent blocks (QRB) are built in a hardware-efficient way, and QRNN are constructed by stacking QRB in a checkerboard pattern, which can significantly reduce the algorithm’s requirements with respect to coherent time of quantum devices. That is, QRNN is much more accessible on MCD devices. Numerical experiments show that our QRNN provides much better performance in prediction (classification) accuracy compared to classical RNN and state-of-the-art QNN models for sequential training and can predict changing details of time series data.
Abstract Quantum Recurrent Neural Networks are receiving an increased attention thanks to their enhanced generalization capabilities in time series analysis. However, their performances were bottlenecked by long training times and unscalable architectures. In this paper, we propose a novel Quantum Recurrent Neural Network model based on Quantum Gated Recurrent Units. It uses a learnable Variational Quantum Layer to process temporal data, interspersed with two classical layers to properly match the dimensionality of the input and output vectors. Such an architecture has fewer quantum parameters than existing Quantum Long Short-Term Memory models. Both the quantum networks were evaluated on periodic and real-world time series datasets, together with the classical counterparts. The quantum models exhibited superior performances compared to the classical ones in all the test cases. The Quantum Gated Recurrent Units outperformed the Quantum Long Short-Term Memory network despite having a simpler internal configuration. Moreover, the Quantum Gated Recurrent Units network demonstrated to be about 25% faster during the training and inference procedure over the Quantum Long Short-Term Memory. This improvement in speed comes with one less quantum circuit to be executed, suggesting that our model may offer a more efficient alternative for implementing Quantum Recurrent Neural Networks on both simulated and real quantum hardware.
Quantum neural network (QNN) is one of the promising directions where the near-term noisy intermediate-scale quantum (NISQ) devices could find advantageous applications against classical resources. Recurrent neural networks are the most fundamental networks for sequential learning, but up to now there is still a lack of canonical model of quantum recurrent neural network (QRNN), which certainly restricts the research in the field of quantum deep learning. In the present work, we propose a new kind of QRNN which would be a good candidate as the canonical QRNN model, where, the quantum recurrent blocks (QRBs) are constructed in the hardware-efficient way, and the QRNN is built by stacking the QRBs in a staggered way that can greatly reduce the algorithm's requirement with regard to the coherent time of quantum devices. That is, our QRNN is much more accessible on NISQ devices. Furthermore, the performance of the present QRNN model is verified concretely using three different kinds of classical sequential data, i.e., meteorological indicators, stock price, and text categorization. The numerical experiments show that our QRNN achieves much better performance in prediction (classification) accuracy against the classical RNN and state-of-the-art QNN models for sequential learning, and can predict the changing details of temporal sequence data. The practical circuit structure and superior performance indicate that the present QRNN is a promising learning model to find quantum advantageous applications in the near term.
Abstract Modeling temporal dependencies within quantum systems remains a key challenge for quantum machine learning. Current quantum neural networks largely depend on classical recurrent modules, which introduce optimization bottlenecks and coherence loss during sequence processing. To address this, we propose a fully quantum-native recurrent neural network (QRNN) for end-to-end sequential learning. Our architecture captures temporal dynamics through coherent unitary operations, avoiding external classical recurrence and mid-circuit state collapse. The proposed model was benchmarked against a classical recurrent neural network (RNN), quantum tensor networks, and state-of-the-art hybrid QRNN using the Origin Quantum superconducting platform. Experimental evaluations on nonlinear functions, complex dynamical systems, and meteorological datasets demonstrate that our quantum-native QRNN achieves improved prediction accuracy and exhibits enhanced capability in forecasting complex temporal features. For instance, on the relative humidity forecasting task, the proposed QRNN achieves a 73.5% reduction in Root mean square error compared to the hybrid VQRNN. This work establishes a robust framework for preserving coherence in pure quantum sequential processing, offering a scalable path for time-series forecasting on near-term quantum hardware.