Experimental Simultaneous Learning of Multiple Nonclassical Correlations

Efficient learning of mixed-state tomography for photonic quantum walk

Noise-enhanced applications in open quantum walk (QW) has recently seen a surge due to their ability to improve performance. However, verifying the success of open QW is challenging, as mixed-state tomography is a resource-intensive process, and implementing all required measurements is almost impossible due to various physical constraints. To address this challenge, we present a neural-network-based method for reconstructing mixed states with a high fidelity (∼97.5%) while costing only 50% of the number of measurements typically required for open discrete-time QW in one dimension. Our method uses a neural density operator that models the system and environment, followed by a generalized natural gradient descent procedure that significantly speeds up the training process. Moreover, we introduce a compact interferometric measurement device, improving the scalability of our photonic QW setup that enables experimental learning of mixed states. Our results demonstrate that highly expressive neural networks can serve as powerful alternatives to traditional state tomography.

Neural Network-Based Prediction for Secret Key Rate of Underwater Continuous-Variable Quantum Key Distribution through a Seawater Channel

Continuous-variable quantum key distribution (CVQKD) plays an important role in quantum communications, because of its compatible setup for optical implementation with low cost. For this paper, we considered a neural network approach to predicting the secret key rate of CVQKD with discrete modulation (DM) through an underwater channel. A long-short-term-memory-(LSTM)-based neural network (NN) model was employed, in order to demonstrate performance improvement when taking into account the secret key rate. The numerical simulations showed that the lower bound of the secret key rate could be achieved for a finite-size analysis, where the LSTM-based neural network (NN) was much better than that of the backward-propagation-(BP)-based neural network (NN). This approach helped to realize the fast derivation of the secret key rate of CVQKD through an underwater channel, indicating that it can be used for improving performance in practical quantum communications.

Entanglement detection with artificial neural networks

Quantum entanglement is one of the essential resources involved in quantum information processing tasks. However, its detection for usage remains a challenge. The Bell-type inequality for relative entropy of coherence serves as an entanglement witness for pure entangled states. However, it does not perform reliably for mixed entangled states. This paper constructs a classifier by employing the relationship between coherence and entanglement for supervised machine learning methods. This method encodes multiple Bell-type inequalities for the relative entropy of coherence into an artificial neural network to detect the entangled and separable states in a quantum dataset.

Neural network-based prediction of the secret-key rate of quantum key distribution

Numerical methods are widely used to calculate the secure key rate of many quantum key distribution protocols in practice, but they consume many computing resources and are too time-consuming. In this work, we take the homodyne detection discrete-modulated continuous-variable quantum key distribution (CV-QKD) as an example, and construct a neural network that can quickly predict the secure key rate based on the experimental parameters and experimental results. Compared to traditional numerical methods, the speed of the neural network is improved by several orders of magnitude. Importantly, the predicted key rates are not only highly accurate but also highly likely to be secure. This allows the secure key rate of discrete-modulated CV-QKD to be extracted in real time on a low-power platform. Furthermore, our method is versatile and can be extended to quickly calculate the complex secure key rates of various other unstructured quantum key distribution protocols.

Automated machine learning for secure key rate in discrete-modulated continuous-variable quantum key distribution

Continuous-variable quantum key distribution (CV QKD) with discrete modulation has attracted increasing attention due to its experimental simplicity, lower-cost implementation and compatibility with classical optical communication. Correspondingly, some novel numerical methods have been proposed to analyze the security of these protocols against collective attacks, which promotes key rates over one hundred kilometers of fiber distance. However, numerical methods are limited by their calculation time and resource consumption, for which they cannot play more roles on mobile platforms in quantum networks. To improve this issue, a neural network model predicting key rates in nearly real time has been proposed previously. Here, we go further and show a neural network model combined with Bayesian optimization. This model automatically designs the best architecture of neural network computing key rates in real time. We demonstrate our model with two variants of CV QKD protocols with quaternary modulation. The results show high reliability with secure probability as high as 99.15% - 99.59%, considerable tightness and high efficiency with speedup of approximately 10⁷ in both cases. This inspiring model enables the real-time computation of unstructured quantum key distribution protocols' key rate more automatically and efficiently, which has met the growing needs of implementing QKD protocols on moving platforms.

Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver

The recognition of entanglement states is a notoriously difficult problem when no prior information is available. Here, we propose an efficient quantum adversarial bipartite entanglement detection scheme to address this issue. Our proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits, where a two-outcome measurement can be used to query a classical binary result about whether the input state is bipartite entangled or not. In principle, for an N-qubit quantum state, the runtime complexity of our proposal is O(poly(N)T) with T being the number of iterations. We experimentally implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states. Our work paves the way for using near-term quantum machines to tackle entanglement detection on multipartite entangled quantum systems.

Direct Fidelity Estimation of Quantum States Using Machine Learning

In almost all quantum applications, one of the key steps is to verify that the fidelity of the prepared quantum state meets expectations. In this Letter, we propose a new approach solving this problem using machine-learning techniques. Compared to other fidelity estimation methods, our method is applicable to arbitrary quantum states, the number of required measurement settings is small, and this number does not increase with the size of the system. For example, for a general five-qubit quantum state, only four measurement settings are required to predict its fidelity with ±1% precision in a nonadversarial scenario. This machine-learning-based approach for estimating quantum state fidelity has the potential to be widely used in the field of quantum information.