Time series prediction is essential for human activities in diverse areas. A common approach to this task is to harness Recurrent Neural Networks (RNNs). However, while their predictions are quite accurate, their learning process is complex and, thus, time and energy consuming. Here, we propose to extend the concept of RRNs by including continuous-variable quantum resources in it, and to use a quantum-enhanced RNN to overcome these obstacles. The design of the Continuous-Variable Quantum RNN (CV-QRNN) is rooted in the continuous-variable quantum computing paradigm. By performing extensive numerical simulations, we demonstrate that the quantum network is capable of learning-time dependence of several types of temporal data, and that it converges to the optimal weights in fewer epochs than a classical network. Furthermore, for a small number of trainable parameters, it can achieve lower losses than its classical counterpart. CV-QRNN can be implemented using commercially available quantum-photonic hardware.

Abstract: Machine learning is considered to be one of the most promising applications of quantum computing. Therefore, the search for quantum advantage of the quantum analogues of machine learning models is a key research goal. Here, we show that variational quantum classifiers (VQC) and support vector machines with quantum kernels (QSVM) can solve a classification problem based on the k-Forrelation problem, which is known to be PromiseBQP-complete. Because the PromiseBQP complexity class includes all Bounded-Error Quantum Polynomial-Time (BQP) decision problems, our results imply that there exists a feature map and a quantum kernel that make VQC and QSVM efficient solvers for any BQP problem. Abstract: In this paper, classical and continuous variable (CV) quantum neural network hybrid multiclassifiers are presented using the MNIST dataset.

In order to exploit quantum advantages, quantum algorithms are indispensable for operating machine learning with quantum computers. We here propose an intriguing hybrid approach of quantum information processing for quantum linear regression, which utilizes both discrete and continuous quantum variables, in contrast to existing wisdoms based solely upon discrete qubits. In our framework, data information is encoded in a qubit system, while information processing is tackled using auxiliary continuous qumodes via qubit-qumode interactions. Moreover, it is also elaborated that finite squeezing is quite helpful for efficiently running the quantum algorithms in realistic setup. Comparing with an all-qubit approach, the present hybrid approach is more efficient and feasible for implementing quantum algorithms, still retaining exponential quantum speed-up.