Quantum machine learning of graph-structured data

Abstract

Graph structures are ubiquitous throughout the natural sciences. Here we consider graph-structured quantum data and describe how to carry out its quantum machine learning via quantum neural networks. In particular, we consider training data in the form of pairs of input and output quantum states associated with the vertices of a graph, together with edges encoding correlations between the vertices. We explain how to systematically exploit this additional graph structure to improve quantum learning algorithms. These algorithms are numerically simulated and exhibit excellent learning behavior. Scalable quantum implementations of the learning procedures are likely feasible on the next generation of quantum computing devices.

From Quantum Graph Computing to Quantum Graph Learning: A Survey

“…of the measurements. An alternative approach devised by [Beer et al, 2021] uses qubits as neurons to characterize the graph as quantum states. They design a quantum neural network (QNN) trained on a well-designed loss evaluated by the fidelity of quantum representations of connected nodes.…”

Dissipative quantum generative adversarial networks

“…Many attempts on builing a QNN, the quantum analogue of the popular classical neural network, have been made [18,22,23,25,[46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. In the following we describe the architecture of so-called dissipative quantum neural networks (DQNNs) [17,18,20] as we will exploit this ansatz to form the DQGANs. We explain how their training algorithm can be simulated on a classical computer and how the DQNN can be implemented on a quantum computer [20].…”

“…In the following we describe the architecture of so-called dissipative quantum neural networks (DQNNs) [17,18,20] as we will exploit this ansatz to form the DQGANs. We explain how their training algorithm can be simulated on a classical computer and how the DQNN can be implemented on a quantum computer [20].…”

“…Here, we focus on the dissipative QNN (DQNN) [18] which features a unique set of qubits for each network layer. It is universal for quantum computation and has achieved remarkable results for various applications [19,20], including their application on actual NISQ devices [17]. The DQNN propagates the input state's information through the network in a feed-forward manner.…”

“…Most of the current QNN applications are limited to supervised learning of labeled training states [9]. This includes their use for classification [21][22][23], denoising quantum data [19,[24][25][26][27], learning unitary transformations [17,18,[28][29][30][31] and learning graphstructured quantum data [20,[30][31][32][33][34]. In these problems, the QNNs are trained with respect to a special family of loss functions.…”