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Wang QQ, Dong S, Li XW, Xu XY, Wang C, Han S, Yung MH, Han YJ, Li CF, Guo GC. Efficient learning of mixed-state tomography for photonic quantum walk. SCIENCE ADVANCES 2024; 10:eadl4871. [PMID: 38489356 DOI: 10.1126/sciadv.adl4871] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Accepted: 02/11/2024] [Indexed: 03/17/2024]
Abstract
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.
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Affiliation(s)
- Qin-Qin Wang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Shaojun Dong
- Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei 230031, China
| | - Xiao-Wei Li
- Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
| | - Xiao-Ye Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Chao Wang
- Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei 230031, China
| | - Shuai Han
- Yangtze Delta Region Industrial Innovation Center of Quantum and Information Technology, Suzhou 215100, China
| | - Man-Hong Yung
- Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Yong-Jian Han
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei 230031, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
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Mao Y, Zhu Y, Hu H, Luo G, Wang J, Wang Y, Guo Y. Neural Network-Based Prediction for Secret Key Rate of Underwater Continuous-Variable Quantum Key Distribution through a Seawater Channel. ENTROPY (BASEL, SWITZERLAND) 2023; 25:937. [PMID: 37372281 DOI: 10.3390/e25060937] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Revised: 05/30/2023] [Accepted: 06/08/2023] [Indexed: 06/29/2023]
Abstract
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.
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Affiliation(s)
- Yun Mao
- School of Information Engineering, Shaoyang University, Shaoyang 422000, China
- School of Automation, Central South University, Changsha 410083, China
| | - Yiwu Zhu
- School of Automation, Central South University, Changsha 410083, China
| | - Hui Hu
- School of Automation, Central South University, Changsha 410083, China
| | - Gaofeng Luo
- School of Information Engineering, Shaoyang University, Shaoyang 422000, China
| | - Jinguang Wang
- School of Automation, Central South University, Changsha 410083, China
| | - Yijun Wang
- School of Automation, Central South University, Changsha 410083, China
| | - Ying Guo
- School of Information Engineering, Shaoyang University, Shaoyang 422000, China
- School of Computer Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
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3
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Entanglement detection with artificial neural networks. Sci Rep 2023; 13:1562. [PMID: 36709391 PMCID: PMC9884245 DOI: 10.1038/s41598-023-28745-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Accepted: 01/24/2023] [Indexed: 01/29/2023] Open
Abstract
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.
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Zhou MG, Liu ZP, Liu WB, Li CL, Bai JL, Xue YR, Fu Y, Yin HL, Chen ZB. Neural network-based prediction of the secret-key rate of quantum key distribution. Sci Rep 2022; 12:8879. [PMID: 35614090 PMCID: PMC9133163 DOI: 10.1038/s41598-022-12647-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Accepted: 05/13/2022] [Indexed: 11/25/2022] Open
Abstract
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.
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Affiliation(s)
- Min-Gang Zhou
- National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China
| | - Zhi-Ping Liu
- National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China
| | - Wen-Bo Liu
- National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China
| | - Chen-Long Li
- National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China.,MatricTime Digital Technology Co. Ltd., Nanjing, China
| | - Jun-Lin Bai
- National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China.,MatricTime Digital Technology Co. Ltd., Nanjing, China
| | - Yi-Ran Xue
- National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China.,MatricTime Digital Technology Co. Ltd., Nanjing, China
| | - Yao Fu
- MatricTime Digital Technology Co. Ltd., Nanjing, China
| | - Hua-Lei Yin
- National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China.
| | - Zeng-Bing Chen
- National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, China. .,MatricTime Digital Technology Co. Ltd., Nanjing, China.
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Liu ZP, Zhou MG, Liu WB, Li CL, Gu J, Yin HL, Chen ZB. Automated machine learning for secure key rate in discrete-modulated continuous-variable quantum key distribution. OPTICS EXPRESS 2022; 30:15024-15036. [PMID: 35473234 DOI: 10.1364/oe.455762] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2022] [Accepted: 04/12/2022] [Indexed: 06/14/2023]
Abstract
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.
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Yin XF, Du Y, Fei YY, Zhang R, Liu LZ, Mao Y, Liu T, Hsieh MH, Li L, Liu NL, Tao D, Chen YA, Pan JW. Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver. PHYSICAL REVIEW LETTERS 2022; 128:110501. [PMID: 35363009 DOI: 10.1103/physrevlett.128.110501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2021] [Revised: 12/28/2021] [Accepted: 02/11/2022] [Indexed: 06/14/2023]
Abstract
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.
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Affiliation(s)
- Xu-Fei Yin
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Yuxuan Du
- JD Explore Academy, Beijing 101111, China
- School of Computer Science, Faculty of Engineering, University of Sydney, Sydney 2006, Australia
| | - Yue-Yang Fei
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Rui Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Li-Zheng Liu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Yingqiu Mao
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Tongliang Liu
- School of Computer Science, Faculty of Engineering, University of Sydney, Sydney 2006, Australia
| | - Min-Hsiu Hsieh
- Hon Hai Quantum Computing Research Center, Taipei 114, Taiwan
| | - Li Li
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Nai-Le Liu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Dacheng Tao
- JD Explore Academy, Beijing 101111, China
- School of Computer Science, Faculty of Engineering, University of Sydney, Sydney 2006, Australia
| | - Yu-Ao Chen
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Jian-Wei Pan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
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Zhang X, Luo M, Wen Z, Feng Q, Pang S, Luo W, Zhou X. Direct Fidelity Estimation of Quantum States Using Machine Learning. PHYSICAL REVIEW LETTERS 2021; 127:130503. [PMID: 34623828 DOI: 10.1103/physrevlett.127.130503] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2021] [Revised: 08/04/2021] [Accepted: 08/17/2021] [Indexed: 06/13/2023]
Abstract
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.
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Affiliation(s)
- Xiaoqian Zhang
- School of Physics and State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510000, China
| | - Maolin Luo
- School of Physics and State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510000, China
| | - Zhaodi Wen
- College of Information Science and Technology, College of Cyber Security, Jinan University, Guangzhou 510632, China
| | - Qin Feng
- School of Physics and State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510000, China
| | - Shengshi Pang
- School of Physics and State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510000, China
| | - Weiqi Luo
- College of Information Science and Technology, College of Cyber Security, Jinan University, Guangzhou 510632, China
| | - Xiaoqi Zhou
- School of Physics and State Key Laboratory of Optoelectronic Materials and Technologies, Sun Yat-sen University, Guangzhou 510000, China
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