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On the Computational Complexity of Schrödinger Operators

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arXiv 2024年

作者： Zheng, Yufan Leng, Jiaqi Liu, Yizhou Wu, Xiaodi Department of Computer Science University of Maryland United States Joint Center for Quantum Information and Computer Science University of Maryland United States Department of Mathematics University of Maryland United States Simons Institute for the Theory of Computing Department of Mathematics UC Berkeley United States Physics of Living Systems Department of Physics MIT United States Department of Mechanical Engineering MIT United States

We study computational problems related to the Schrödinger operator H = −∆ + V in the real space under the condition that (i) the potential function V is smooth and has its value and derivative bounded within some polynomial of n and (ii) V only consists of O(1)-body interactions. We prove that (i) simulating the dynamics generated by the Schrödinger operator implements universal quantum computation, i.e., it is BQP-hard, and (ii) estimating the ground energy of the Schrödinger operator is as hard as estimating that of local Hamiltonians with no sign problem (a.k.a. stoquastic Hamiltonians), i.e., it is StoqMA-complete. This result is particularly intriguing because the ground energy problem for general bosonic Hamiltonians is known to be QMA-hard and it is widely believed that StoqMA (Equation presented) QMA. Copyright © 2024, The Authors. All rights reserved.

关键词： Hamiltonians

Security boundaries of an optical-power limiter for protecting quantum-key-distribution systems

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Physical Review Applied 2024年第1期21卷 014026-014026页

作者： Qingquan Peng Binwu Gao Konstantin Zaitsev Dongyang Wang Jiangfang Ding Yingwen Liu Qin Liao Ying Guo Anqi Huang Junjie Wu Institute for Quantum Information and State Key Laboratory of High Performance Computing College of Computer Science and Technology National University of Defense Technology Changsha 410073 China School of Automation Central South University Changsha 410083 China China Greatwall Research Institute China Greatwall Technology Group Co. Ltd. Shenzhen 518057 China Russian Quantum Center Skolkovo Moscow 121205 Russia NTI Center for Quantum Communications National University of Science and Technology MISiS Moscow 119049 Russia Vigo Quantum Communication Center University of Vigo 36310 Vigo Spain Escuela de Ingeniería de Telecomunicación Department of Signal Theory and Communications University of Vigo 36310 Vigo Spain atlanTTic Research Center University of Vigo 36310 Vigo Spain College of Computer Science and Electronic Engineering Hunan University Changsha 410082 China School of Computer Science Beijing University of Posts and Telecommunications Beijing 100876 China

Unauthorized light injection has always been a vital threat to the practical security of a quantum-key-distribution (QKD) system. An optical-power limiter (OPL) based on the thermo-optical defocusing effect has been proposed and implemented, limiting the injected hacking light. As a hardware countermeasure, the performance of the OPL under various light-injection attacks will be tested to clarify the security boundary before it is widely deployed. To investigate the security boundary of the OPL in quantum cryptography, we comprehensively test and analyze the behavior of the OPL under continuous-wave (cw) light-injection attacks and pulse-illumination attacks with pulse repetition rates of 0.5 Hz, 40 MHz, and 1 GHz. The test results illuminate the security boundary of the OPL, which allows one to properly employ the OPL in use cases. The methodology of testing and analysis proposed here is applicable to other power-limitation components in a QKD system.

关键词： Optical quantum information processing Photonics quantum communication quantum cryptography Devices

An Automata-Theoretic Approach to Synthesizing Binarized Neural Networks 21st

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An Automata-Theoretic Approach to Synthesizing Binarized Ne...

21st International Symposium on Automated Technology for Verification and Analysis, ATVA 2023

作者： Tao, Ye Liu, Wanwei Song, Fu Liang, Zhen Wang, Ji Zhu, Hongxu College of Computer Science and Technology National University of Defense Technology Changsha China School of Information Science and Technology ShanghaiTech University Shanghai China Institute of Software Chinese Academy of Sciences and University of Chinese Academy of Sciences Beijing China Automotive Software Innovation Center Shanghai China Institute for Quantum Information and State Key Laboratory for High Performance Computing National University of Defense Technology Changsha China

ISBN: (纸本)9783031453281

Deep neural networks, (DNNs, a.k.a. NNs), have been widely used in various tasks and have been proven to be successful. However, the accompanied expensive computing and storage costs make the deployments in resource-constrained devices a significant concern. To solve this issue, quantization has emerged as an effective way to reduce the costs of DNNs with little accuracy degradation by quantizing floating-point numbers to low-width fixed-point representations. Quantized neural networks (QNNs) have been developed, with binarized neural networks (BNNs) restricted to binary values as a special case. Another concern about neural networks is their vulnerability and lack of interpretability. Despite the active research on trustworthy of DNNs, few approaches have been proposed to QNNs. To this end, this paper presents an automata-theoretic approach to synthesizing BNNs that meet designated properties. More specifically, we define a temporal logic, called BLTL, as the specification language. We show that each BLTL formula can be transformed into an automaton on finite words. To deal with the state-explosion problem, we provide a tableau-based approach in real implementation. For the synthesis procedure, we utilize SMT solvers to detect the existence of a model (i.e., a BNN) in the construction process. Notably, synthesis provides a way to determine the hyper-parameters of the network before training. Moreover, we experimentally evaluate our approach and demonstrate its effectiveness in improving the individual fairness and local robustness of BNNs while maintaining accuracy to a great extent. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Deep neural networks

Experimental quantum natural gradient optimization in photonics

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arXiv 2023年

作者： Wang, Yizhi Xue, Shichuan Wang, Yaxuan Ding, Jiangfang Shi, Weixu Wang, Dongyang Liu, Yong Liu, Yingwen Fu, Xiang Huang, Guangyao Huang, Anqi Deng, Mingtang Wu, Junjie Institute for Quantum Information State Key Laboratory of High Performance Computing College of Computer Science and Technology National University of Defense Technology Changsha410073 China

Variational quantum algorithms (VQAs) combining the advantages of parameterized quantum circuits and classical optimizers, promise practical quantum applications in the Noisy Intermediate-Scale quantum era. The performance of VQAs heavily depends on the optimization method. Compared with gradient-free and ordinary gradient descent methods, the quantum natural gradient (QNG), which mirrors the geometric structure of the parameter space, can achieve faster convergence and avoid local minima more easily, thereby reducing the cost of circuit executions. We utilized a fully programmable photonic chip to experimentally estimate the QNG in photonics for the first time. We obtained the dissociation curve of the He-H+ cation and achieved chemical accuracy, verifying the outperformance of QNG optimization on a photonic device. Our work opens up a vista of utilizing QNG in photonics to implement practical near-term quantum applications. © 2023, CC BY.

关键词： Photonic devices

quantum generative adversarial learning in photonics

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arXiv 2023年

作者： Wang, Yizhi Xue, Shichuan Wang, Yaxuan Liu, Yong Ding, Jiangfang Shi, Weixu Wang, Dongyang Liu, Yingwen Fu, Xiang Huang, Guangyao Huang, Anqi Deng, Mingtang Wu, Junjie Institute for Quantum Information State Key Laboratory of High Performance Computing College of Computer Science and Technology National University of Defense Technology Changsha410073 China

quantum Generative Adversarial Networks (QGANs), an intersection of quantum computing and machine learning, have attracted widespread attention due to their potential advantages over classical analogs. However, in the current era of Noisy Intermediate-Scale quantum (NISQ) computing, it is essential to investigate whether QGANs can perform learning tasks on near-term quantum devices usually affected by noise and even defects. In this Letter, using a programmable silicon quantum photonic chip, we experimentally demonstrate the QGAN model in photonics for the first time, and investigate the effects of noise and defects on its performance. Our results show that QGANs can generate high-quality quantum data with a fidelity higher than 90%, even under conditions where up to half of the generator’s phase shifters are damaged, or all of the generator and discriminator’s phase shifters are subjected to phase noise up to 0.04π. Our work sheds light on the feasibility of implementing QGANs on NISQ-era quantum hardware. © 2023, CC BY.

关键词： Phase shifters

Verifiable blind quantum computation with identity authentication for different types of clients

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arXiv 2022年

作者： Quan, Junyu Li, Qin Li, Lvzhou School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China School of Computer Science Xiangtan University Xiangtan411105 China Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-sen University Guangzhou510006 China

quantum computing has considerable advantages in solving some problems over its classical counterpart. Currently various physical systems are developed to construct quantum computers but it is still challenging and the first use of quantum computers may adopt the cloud style. Blind quantum computing (BQC) provides a solution for clients with limited quantum capabilities to delegate their quantum computation to remote quantum servers while keeping input, output, and even algorithm private. In this paper, we propose three multi-party verifiable blind quantum computing (VBQC) protocols with identity authentication to handle clients with varying quantum capabilities in quantum networks, such as those who can just make measurements, prepare single qubits, or perform a few single-qubit gates. They are client-friendly and flexible since the clients can achieve BQC depending on their own quantum devices and resist both insider outsider attacks in quantum networks. Furthermore, all the three proposed protocols are verifiable, namely that the clients can verify the correctness of their calculations. Copyright © 2022, The Authors. All rights reserved.

关键词： Qubits

Entirety of quantum Uncertainty and Its Experimental Verification

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Chinese Physics Letters 2021年第7期38卷 11-16页

作者： Jie Xie Li Zhou Aonan Zhang Huichao Xu Man-Hong Yung Ping Xu Nengkun Yu Lijian Zhang National Laboratory of Solid State Microstructures College of Engineering and Applied Sciences and School of PhysicsNanjing UniversityNanjing 210093China Collaborative Innovation Center of Advanced Microstructures Nanjing UniversityNanjing 210093China Department of Computer Science and Technology Tsinghua UniversityBeijing 100084China Shenzhen Institute for Quantum Science and Engineering and Department of Physics Southern University of Science and TechnologyShenzhen 518055China Shenzhen Key Laboratory of Quantum Science and Engineering Southern University of Science and TechnologyShenzhen 518055China Institute for Quantum Information&State Key Laboratory of High Performance Computing College of ComputerNational University of Defense TechnologyChangsha 410073China Centre for Quantum Software and Information School of SoftwareFaculty of Engineering and Information TechnologyUniversity of Technology SydneyNSWAustralia

As a foundation of quantum physics,uncertainty relations describe ultimate limit for the measurement uncertainty of incompatible ***,uncertainty relations are formulated by mathematical bounds for a specific *** we present a method for geometrically characterizing uncertainty relations as an entire area of variances of the observables,ranging over all possible input *** find that for the pair of position and momentum operators,Heisenberg's uncertainty principle points exactly to the attainable area of the variances of position and ***,for finite-dimensional systems,we prove that the corresponding area is necessarily semialgebraic;in other words,this set can be represented via finite polynomial equations and inequalities,or any finite union of such *** particular,we give the analytical characterization of the areas of variances of(a)a pair of one-qubit observables and(b)a pair of projective observables for arbitrary dimension,and give the first experimental observation of such areas in a photonic system.

关键词： observable union operators

Using Data Mining Techniques to Analyze Facial Expression Motion Vectors 6th

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Using Data Mining Techniques to Analyze Facial Expression Mo...

6th International Conference on Dynamics of Information Systems, DIS 2023

作者： Roshanzamir, Mohamad Alizadehsani, Roohallah Roshanzamir, Mahdi Shoeibi, Afshin Gorriz, Juan M. Khosravi, Abbas Nahavandi, Saeid Acharya, U. Rajendra Department of Computer Engineering Faculty of Engineering Fasa University Fasa74617-81189 Iran Deakin University GeelongVIC Australia Department of Electrical and Computer Engineering University of Tabriz Tabriz Iran Data Science and Computational Intelligence Institute University of Granada Granada Spain Department of Signal Theory Networking and Communications Universidad de Granada Granada Spain Swinburne University of Technology HawthornVIC3122 Australia School of Mathematics Physics and Computing University of Southern Queensland Springfield Australia

ISBN: (纸本)9783031503191

Automatic recognition of facial expressions is a common problem in human-computer interaction. While humans can recognize facial expressions very easily, machines cannot do it as easily as humans. Analyzing facial changes during facial expressions is one of the methods used for this purpose by the machines. In this research, facial deformation caused by facial expressions is considered for automatic facial expression recognition by machines. To achieve this goal, the motion vectors of facial deformations are captured during facial expression using an optical flow algorithm. These motion vectors are then used to analyze facial expressions using some data mining algorithms. This analysis not only determined how changes in the face occur during facial expressions but can also be used for facial expression recognition. The facial expressions investigated in this research are happiness, sadness, surprise, fear, anger, and disgust. According to our research, these facial expressions were classified into 12 classes of facial motion vectors. We applied our proposed analysis mechanism to the extended Cohen-Kanade facial expression dataset. Our developed automatic facial expression system achieved 95.3%, 92.8%, and 90.2% accuracy using Deep Learning (DL), Support Vector Machine (SVM), and C5.0 classifiers, respectively. In addition, based on this research, it was determined which parts of the face have a greater impact on facial expression recognition. © 2024, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Data mining

Deterministic Algorithms for the Hidden Subgroup Problem

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SSRN

SSRN 2022年

作者： Ye, Zekun Li, Lvzhou Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-sen University Guangzhou510006 China Ministry of Education Key Laboratory of Machine Intelligence and Advanced Computing Sun Yat-sen University Guangzhou510006 China

We consider deterministic algorithms for the well-known hidden subgroup problem (HSP): for a finite group G and a finite set X, given a function f : G → X and the promise that for any (Formula Presented) for a subgroup H ≤ G, the goal of the decision version is to determine whether H is trivial, and the goal of the search version is to find H. An algorithm for the problem should query f(g) for g ∈ G at least as possible. Nayak [? ] asked whether there exist deterministic algorithms with (Formula Presented) query complexity for HSP. We answer this problem completely by proving the following results, which also extend the main results of Ref. [? ], since here the algorithms do not rely on any prior knowledge of H. (i) When G is a general finite Abelian group, there exists an algorithm with (Formula Presented) queries to decide the triviality of H and an algorithm to find H with (Formula Presented) queries.(ii) In general, there is no deterministic algorithm for the search version of HSP with query complexity of (Formula Presented), since there exists an instance of HSP that needs (Formula Presented) queries to find H. f(x) is said to be (Formula Presented) if for every positive constant C, there exists a positive constant N such that for (Formula Presented), which means g is a strict lower bound for f.} On the other hand, there exist instances of HSP with query complexity far smaller than (Formula Presented), whose query complexity is (Formula Presented) and even O(1). © 2022, The Authors. All rights reserved.

关键词： Computational complexity