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arXiv:1712.00456 · Physical Review Letters

Experimental Machine Learning of Quantum States

Jun Gao, Lu‐Feng Qiao, Zhi‐Qiang Jiao, Yuechi Ma, Cheng-Qiu Hu, Ruo-Jing Ren, Ai-Lin Yang, Hao Long Tang, Man‐Hong Yung, Xian‐Min Jin

Published Jun 11, 2018• 155 citations
arXivHTMLPDF

Abstract

Quantum information technologies provide promising applications in communication and computation, while machine learning has become a powerful technique for extracting meaningful structures in "big data." A crossover between quantum information and machine learning represents a new interdisciplinary area stimulating progress in both fields. Traditionally, a quantum state is characterized by quantum-state tomography, which is a resource-consuming process when scaled up. Here we experimentally demonstrate a machine-learning approach to construct a quantum-state classifier for identifying the separability of quantum states. We show that it is possible to experimentally train an artificial neural network to efficiently learn and classify quantum states, without the need of obtaining the full information of the states. We also show how adding a hidden layer of neurons to the neural network can significantly boost the performance of the state classifier. These results shed new light on how classification of quantum states can be achieved with limited resources, and represent a step towards machine-learning-based applications in quantum information processing.

DOI
10.1103/physrevlett.120.240501

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Quantum information technologies provide promising applications in communication and computation, while machine learning has become a powerful technique for extracting meaningful structures in "big data." A crossover between quantum information and machine learning represents a new interdisciplinary area stimulating progress in both fields. Traditionally, a quantum state is characterized by quantum-state tomography, which is a resource-consuming process when scaled up. Here we experimentally demonstrate a machine-learning approach to construct a quantum-state classifier for identifying the separability of quantum states. We show that it is possible to experimentally train an artificial neural network to efficiently learn and classify quantum states, without the need of obtaining the full information of the states. We also show how adding a hidden layer of neurons to the neural network can significantly boost the performance of the state classifier. These results shed new light on how classification of quantum states can be achieved with limited resources, and represent a step towards machine-learning-based applications in quantum information processing.
Quantum state classification and entanglement quantification are of significant importance in the fundamental research of quantum information science and various quantum applications. Traditional methods, such as quantum state tomography, face exponential measurement demands with increasing numbers of qubits, necessitating more efficient approaches. Recent work has shown promise in using artificial neural networks (ANNs) for quantum state analysis. However, existing ANNs may falter when confronted with states affected by dephasing noise, especially with limited data and computational resources. In this study, we employ a machine-learning approach to investigate the disentanglement process in two-qubit systems in the presence of dephasing noise. Our findings highlight the limitations of general state-trained ANNs in classifying states under dephasing noise. Specialized ANN algorithms, tailored for classifying states and quantifying entanglement in such noisy environments, demonstrate excellent performance using only a subset of tomographic features.
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In the last few years, quantum computing and machine learning fostered rapid developments in their respective areas of application, introducing new perspectives on how information processing systems can be realized and programmed. The rapidly growing field of Quantum Machine Learning aims at bringing together these two ongoing revolutions. Here we first review a series of recent works describing the implementation of artificial neurons and feed-forward neural networks on quantum processors. We then present an original realization of efficient individual quantum nodes based on variational unsampling protocols. While keeping full compatibility with the overall memory-efficient feed-forward architecture, such a construction effectively reduces the quantum circuit depth required to determine the activation probability of single neurons upon input of the relevant data-encoding quantum states. This suggests a viable approach towards the use of quantum neural networks for pattern classification on near-term quantum hardware.
Artificial neural networks (ANN) proved to be efficient in solving many problems for big data analytics using machine learning. The complex and non-linear features of the input data can be learned and generalized by ANN. In the big data era, enormous amounts of data arrive from multiple sources. A stage is expected to be reached where even supercomputers are likely inundated with the big data. Training an ANN in such a situation is a challenging task due to the size and dimension of the big data. Also, a large number of parameters are to be used and optimized in the network to learn the patterns and analyze such data. Quantum computing is emerging as a field that provides a solution to this problem as a quantum computer can represent data differently using qubits. Qubits on quantum computers can be used to detect the hidden patterns in data that are difficult for a classical computer to find. Hence, there exists a huge scope for application in the area of artificial neural networks. In this work, we primarily focused on training an artificial neural network using qubits as artificial neurons. The simulation results show that our quantum computing approach for ANN (QC ANN) is efficient when compared to classical ANN. The model with qubits as artificial neurons can learn the features of data using fewer parameters for a binary classification task. We demonstrate our experiment using a quantum simulator and optimization of the quantum parameters used in QC ANN is carried out on a classical computer.
Machine learning (ML) is often listed among the most potential applications for quantum computing. This is in reality a puzzling choice: Nowadays machine learning algorithms are extremely powerful in practice, but still theoretically challenging to understand. Quantum computing, in contrast, does not give actual benchmarks on practical scales. However, theory remains the main tool we have to determine if it may become important for a task. Although it is far from reaching its full potential, nevertheless, it presents several techniques to efficiently deal with the problem which are tough to solve traditionally. In this perspective we deploy the Quanvolutional Neural Networks (QNNs) on a quantum computer to recognize handwritten digits, and compare its performance with that of its classical counterpart namely the Convolutional Neural Networks (CNNs). We used a quanvolutional layer to separate the pixel data and demonstrate the advantage of applying QNN on a quantum computer. Finally, we implement the Variational Quantum Classifier (VQC) and several classical classifiers built on the Iris dataset, in order to compare their accuracies. We employed amplitude encoding to map data into the large Hilbert space of a quantum computer. The results revealed that the QNN model and VQC had high accuracy and low loss value compared to their purely classical counterparts.
Abstract In quantum information science, a major challenge is to look for an efficient means for classifying quantum states. An attractive proposal is to utilize Bell’s inequality as an entanglement witness, for classifying entangled state. The problem is that entanglement is necessary but not sufficient for violating Bell’s inequalities, making these inequalities unreliable in state classification. Furthermore, in general, classifying the separability of states, even for only few qubits, is resource-consuming. Here we look for alternative solutions with the methods of machine learning, by constructing neural networks that are capable of simultaneously encoding convex sets of multiple entanglement witness inequalities. The simulation results indicated that these transformed Bell-type classifiers can perform significantly better than the original Bell’s inequalities in classifying entangled states. We further extended our analysis to classify quantum states into multiple species through machine learning. These results not only provide an interpretation of neural network as quantum state classifier, but also confirm that neural networks can be a valuable tool for quantum information processing.