Distributed quantum information processing is essential for building quantum networks and enabling more extensive quantum computations. In this regime, several spatially separated parties share a multipartite quantum system, and the most natural set of operations is Local Operations and Classical Communication (LOCC). As a pivotal part in quantum information theory and practice, LOCC has led to many vital protocols such as quantum teleportation. However, designing practical LOCC protocols is challenging due to LOCC's intractable structure and limitations set by near-term quantum devices. Here we introduce LOCCNet, a machine learning framework facilitating protocol design and optimization for distributed quantum information processing tasks. As applications, we explore various quantum information tasks such as entanglement distillation, quantum state discrimination, and quantum channel simulation. We discover protocols with evident improvements, in particular, for entanglement distillation with quantum states of interest in quantum information. Our approach opens up new opportunities for exploring entanglement and its applications with machine learning, which will potentially sharpen our understanding of the power and limitations of LOCC. An implementation of LOCCNet is available in Paddle Quantum, a quantum machine learning Python package based on PaddlePaddle deep learning platform.
Classification of quantum data is essential for quantum machine learning and near-term quantum technologies. In this paper, we propose a new hybrid quantum-classical framework for supervised quantum learning, which we call Variational Shadow Quantum Learning (VSQL). Our method in particular utilizes the classical shadows of quantum data, which fundamentally represent the side information of quantum data with respect to certain physical observables. Specifically, we first use variational shadow quantum circuits to extract classical features in a convolution way and then utilize a fully-connected neural network to complete the classification task. We show that this method could sharply reduce the number of parameters and thus better facilitate quantum circuit training. Simultaneously, less noise will be introduced since fewer quantum gates are employed in such shadow circuits. Moreover, we show that the Barren Plateau issue, a significant gradient vanishing problem in quantum machine learning, could be avoided in VSQL. Finally, we demonstrate the efficiency of VSQL in quantum classification via numerical experiments on the classification of quantum states and the recognition of multi-labeled handwritten digits. In particular, our VSQL approach outperforms existing variational quantum classifiers in the test accuracy in the binary case of handwritten digit recognition and notably requires much fewer parameters.
Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed to determine the singular values and their associated singular vectors of a given matrix. Although these algorithms are promising, the required quantum subroutines and resources are too costly on near-term quantum devices. In this work, we propose a variational quantum algorithm for singular value decomposition (VQSVD). By exploiting the variational principles for singular values and the Ky Fan Theorem, we design a novel loss function such that two quantum neural networks (or parameterized quantum circuits) could be trained to learn the singular vectors and output the corresponding singular values. Furthermore, we conduct numerical simulations of VQSVD for random matrices as well as its applications in image compression of handwritten digits. Finally, we discuss the applications of our algorithm in recommendation systems and polar decomposition. Our work explores new avenues for quantum information processing beyond the conventional protocols that only works for Hermitian data, and reveals the capability of matrix decomposition on near-term quantum devices.