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Learning Many-Body Hamiltonians with Heisenberg-Limited Scaling

Physical Review Letters 2023年第20期130卷 200403-200403页

作者： Hsin-Yuan Huang Yu Tong Di Fang Yuan Su Institute for Quantum Information and Matter California Institute of Technology Pasadena California 91125 USA Department of Mathematics University of California Berkeley California 94720 USA Simons Institute for the Theory of Computing University of California Berkeley California 94720 USA Microsoft Quantum Redmond Washington 98052 USA

Learning a many-body Hamiltonian from its dynamics is a fundamental problem in physics. In this Letter, we propose the first algorithm to achieve the Heisenberg limit for learning an interacting N-qubit local Hamiltonian. After a total evolution time of O(ε−1), the proposed algorithm can efficiently estimate any parameter in the N-qubit Hamiltonian to ε error with high probability. Our algorithm uses ideas from quantum simulation to decouple the unknown N-qubit Hamiltonian H into noninteracting patches and learns H using a quantum-enhanced divide-and-conquer approach. The proposed algorithm is robust against state preparation and measurement error, does not require eigenstates or thermal states, and only uses polylog(ε−1) experiments. In contrast, the best existing algorithms require O(ε−2) experiments and total evolution time. We prove a matching lower bound to establish the asymptotic optimality of our algorithm.

关键词： Machine learning Quantum algorithms Quantum information theory Quantum metrology Quantum sensing

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Using Experience Classification for Training Non-Markovian Tasks

SSRN

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SSRN 2023年

作者： Miao, Ruixuan Lu, Xu Tian, Cong Yu, Bin Cui, Jin Duan, Zhenhua Institute of Computing Theory and Technology State Key Laboratory of Integrated Services Networks Xidian University China School of Computer Science Xi’an Shiyou University China

Unlike the standard Reinforcement Learning (RL) model, many real-world tasks are non-Markovian, whose rewards are predicated on state history rather than solely on the current state. Solving a non-Markovian task, frequently applied in practical applications such as autonomous driving, financial trading, and medical diagnosis, can be quite challenging. We propose a novel RL approach to achieve non-Markovian rewards expressed in temporal logic LTLf (Linear Temporal Logic over Finite Traces). To this end, an encoding of linear complexity from LTLf into MDPs (Markov Decision Processes) is introduced to take advantage of advanced RL algorithms. Then, a prioritized experience replay technique based on the automata structure (semantics equivalent to LTLf specification) is utilized to improve the training process. We empirically evaluate several benchmark problems augmented with non-Markovian tasks to demonstrate the feasibility and effectiveness of our approach. © 2023, The Authors. All rights reserved.

关键词： Reinforcement learning

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A Provably Secure and Lightweight Access Control Protocol for EI-Based Vehicle to Grid Environment

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IEEE Internet of Things Journal 2023年第18期10卷 16650-16657页

作者： Shamshad, Salman Mahmood, Khalid Shamshad, Usman Hussain, Ibrar Hussain, Shafiq Das, Ashok Kumar The University of Lahore Department of Software Engineering Lahore54590 Pakistan National Yunlin University of Science and Technology Graduate School of Intelligent Data Science Douliu64002 Taiwan Riphah International University Riphah School of Computing and Innovation Lahore54000 Pakistan University of Sahiwal Department of Computer Science Sahiwal57000 Pakistan International Institute of Information Technology Hyderabad Center for Security Theory and Algorithmic Research Hyderabad500032 India Old Dominion University Virginia Modeling Analysis and Simulation Center SuffolkVA23435 United States

The energy Internet (EI) presents a novel paradigm for renewable energy distribution that utilizes communication and computing technologies to revolutionize the conventional intelligent transportation systems (ITSs) and power grid into a structure that provides assistance to open innovation. The EI offers sustainable and bidirectional transmission for the improvement and analysis of energy convention among electric vehicles (EVs) and service providers. To ensure efficient, reliable, and secure operation, EI must be safe from security attacks. Therefore, efficient and secure key negotiation is a significant issue for the EI-based Vehicle-to-Grid (V2G) architecture. Thus, to ensure the system's security, we have devised a robust scheme to facilitate a secure key agreement between the entities involved for the secure and efficient renewable energy distribution for the EI-based energy vehicles in V2G. The devised scheme's robustness is solicited through the widely accepted formal random or real (RoR) model. In addition, the informal security analysis is conducted on the devised scheme, which is evident that the designed scheme achieves all the required security features of EI-based ITS. Moreover, the performance evaluation results endorse that the designed scheme achieves the desired security and minimizes the communication, computation, and energy overhead by 29.33%, 27.94%, and 28.08% in comparison to the existing competitive schemes. © 2014 IEEE.

关键词： Vehicle-to-grid

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An MSVL-Based Modeling Framework for Back Propagation Neural Networks 10th

An MSVL-Based Modeling Framework for Back Propagation Neural...

引用

International Workshop on Structured Object-Oriented Formal Language and Method, SOFL+MSVL 2020

作者： Zhao, Liang Feng, Zhe Wang, Xiaobing Shu, Xinfeng Institute of Computing Theory and Technology ISN Laboratory Xidian University Xi’an710071 China School of Computer Science and Technology Xi’an University of Posts and Telecommunications Xi’an710061 China

ISBN: (纸本)9783030774738

With the rapid development and wide application of artificial neural networks, formal modeling and verification of their security become more and more significant. As a basic step towards the direction, this work proposes a comprehensive modeling framework for back propagation (BP) neural networks based on the formal language MSVL. In this framework, the structure and behavior of a BP neural network are formalized as specifications of data structures and operations, and they are in turn implemented as MSVL structs and functions, respectively. Based on the formalization, models of BP neural networks can be constructed and trained according to the requirements of users. Experimental results show that these models have good performance in terms of metrics concerning training and prediction such as loss and accuracy. © 2021, Springer Nature Switzerland AG.

关键词： Formal verification

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Automatic Generation of Specification from Natural Language Based on Temporal Logic 10th

Automatic Generation of Specification from Natural Language ...

引用

International Workshop on Structured Object-Oriented Formal Language and Method, SOFL+MSVL 2020

作者： Wang, Xiaobing Li, Ge Li, Chunyi Zhao, Liang Shu, Xinfeng Institute of Computing Theory and Technology and ISN Laboratory Xidian University Xi’an710071 China School of Computer Science and Technology Xi’an University of Posts and Communications Xi’an710061 China

ISBN: (纸本)9783030774738

Formal specifications are usually used for describing safety system properties and play an important role in formal verification. In order to improve the effectiveness of formal specification generation and formal verification, this paper proposes a framework for automatic conversion from natural language describing properties to temporal logic formulas, and implements a tool PPTLGenerator (Propositional Projection Temporal Logic formula Generator) for the conversion. First, PPTLGenerator is developed based on JavaCC for automatic conversion from natural language to PPTL. Then, the satisfiability of a PPTL formula generated by PPTLGenerator is checked by a tool PPTLSAT. Finally, to illustrate the principle and effectiveness of the framework, a case study of the safety property of Level 3 autonomous car is provided. © 2021, Springer Nature Switzerland AG.

关键词： Formal specification

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Deconfined classical criticality in the anisotropic quantum spin-12 XY model on the square lattice

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Physical Review B 2025年第10期111卷 104402-104402页

作者： Christopher Mudry Ömer M. Aksoy Claudio Chamon Akira Furusaki Condensed Matter Theory Group PSI Center for Scientific Computing Theory and Data 5232 Villigen PSI Switzerland Institut de Physique EPF Lausanne CH-1015 Lausanne Switzerland Department of Physics Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Department of Physics Boston University Boston Massachusetts 02215 USA RIKEN Center for Emergent Matter Science Wako Saitama 351-0198 Japan Condensed Matter Theory Laboratory RIKEN Wako Saitama 351-0198 Japan

The anisotropic quantum spin-12 XY model on a linear chain was solved by Lieb, Schultz, and Mattis [Ann. Phys. 16, 407 (1961)] and shown to display a continuous quantum phase transition at the O(2) symmetric point separating two gapped phases with competing Ising long-range order. For the square lattice, the following is known. The two competing Ising ordered phases extend to finite temperatures, up to a boundary where a transition to the paramagnetic phase occurs, and meet at the O(2) symmetric critical line along the temperature axis that ends at a tricritical point at the Berezinskii-Kosterlitz-Thouless transition temperature where the two competing phases meet the paramagnetic phase. We show that the first-order zero-temperature (quantum) phase transition that separates the competing phases as a function of the anisotropy parameter is smoothed by thermal fluctuations into deconfined classical criticality.

关键词： Paramagnetism

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Bypassing the Exponential Dependency: Looped Transformers Efficiently Learn In-context by Multi-step Gradient Descent

arXiv

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arXiv 2024年

作者： Chen, Bo Li, Xiaoyu Liang, Yingyu Shi, Zhenmei Song, Zhao Middle Tennessee State University United States Stevens Institute of Technology United States The University of Hong Kong Hong Kong University of Wisconsin-Madison United States The Simons Institute for the Theory of Computing The University of California Berkeley United States

In-context learning has been recognized as a key factor in the success of Large Language Models (LLMs). It refers to the model’s ability to learn patterns on the fly from provided in-context examples in the prompt during inference. Previous studies have demonstrated that the Transformer architecture used in LLMs can implement a single-step gradient descent update by processing in-context examples in a single forward pass. Recent work has further shown that, during in-context learning, a looped Transformer can implement multi-step gradient descent updates in forward passes. However, their theoretical results require an exponential number of in-context examples, n = exp(Ω(T)), where T is the number of loops or passes, to achieve a reasonably low error. In this paper, we study linear looped Transformers in-context learning on linear vector generation tasks. We show that linear looped Transformers can implement multi-step gradient descent efficiently for in-context learning. Our results demonstrate that as long as the input data has a constant condition number, e.g., n = O(d), the linear looped Transformers can achieve a small error by multi-step gradient descent during in-context learning. Furthermore, our preliminary experiments validate our theoretical analysis. Our findings reveal that the Transformer architecture possesses a stronger in-context learning capability than previously understood, offering new insights into the mechanisms behind LLMs and potentially guiding the better design of efficient inference algorithms for LLMs. © 2024, CC BY.

关键词： Contrastive Learning

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Preparing a commercial quantum key distribution system for certification against implementation loopholes

引用

Physical Review Applied 2024年第4期22卷 044076页

作者： Vadim Makarov Alexey Abrikosov Poompong Chaiwongkhot Aleksey K. Fedorov Anqi Huang Evgeny Kiktenko Mikhail Petrov Anastasiya Ponosova Daria Ruzhitskaya Andrey Tayduganov Daniil Trefilov Konstantin Zaitsev Skolkovo Moscow 121205 Russia Vigo Quantum Communication Center NTI Center for Quantum Communications Department of Physics Faculty of Science Institute for Quantum Computing Department of Physics and Astronomy Quantum technology foundation (Thailand) Bangkok 10110 Thailand QRate Skolkovo Moscow 143026 Russia Institute for Quantum Information & State Key Laboratory of High Performance Computing College of Computer Science and Technology Moscow 119991 Russia atlanTTic Research Center School of Telecommunication Engineering Department of Signal Theory and Communications Moscow 101000 Russia

A commercial quantum key distribution (QKD) system needs to be formally certified to enable its wide deployment. The certification should include the system’s robustness against known implementation loopholes and attacks that exploit them. Here we ready a fiber-optic QKD system for this procedure. The system has a prepare-and-measure scheme with decoy-state BB84 protocol, polarization encoding, a qubit source rate of 312.5 MHz, and is manufactured by QRate. We detail its hardware and postprocessing. We analyze the hardware for known implementation loopholes, search for possible new loopholes, and discuss countermeasures. We then amend the system design to address the highest-risk loopholes identified. We also work out technical requirements on the certification lab and outline its possible structure.

关键词： Quantum communication Quantum cryptography Quantum protocols

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SELF-ADHESIVITY IN LATTICES OF ABSTRACT CONDITIONAL INDEPENDENCE MODELS

arXiv

引用

arXiv 2024年

作者： Boege, Tobias Bolt, Janneke H. Studený, Milan Department of Mathematics KTH Royal Institute of Technology Stockholm Sweden Department of Information and Computing Sciences Utrecht University The Netherlands & Faculty of Science Open University of the Netherlands Heerlen Netherlands Institute of Information Theory and Automation of the CAS Prague Czech Republic

We introduce an algebraic concept of the frame for abstract conditional independence (CI) models, together with basic operations with respect to which such a frame should be closed: copying and marginalization. Three standard examples of such frames are (discrete) probabilistic CI structures, semi-graphoids and structural semi-graphoids. We concentrate on those frames which are closed under the operation of set-theoretical intersection because, for these, the respective families of CI models are lattices. This allows one to apply the results from lattice theory and formal concept analysis to describe such families in terms of implications among CI statements. The central concept of this paper is that of self-adhesivity defined in algebraic terms, which is a combinatorial reflection of the self-adhesivity concept studied earlier in context of polymatroids and information theory. The generalization also leads to a self-adhesivity operator defined on the meta-level of CI frames. We answer some of the questions related to this approach and raise other open questions. The core of the paper is in computations. The combinatorial approach to computation might overcome some memory and space limitation of software packages based on polyhedral geometry, in particular, if SAT solvers are utilized. We characterize some basic CI families over 4 variables in terms of canonical implications among CI statements. We apply our method in information-theoretical context to the task of entropic region demarcation over 5 *** Codes 62B10 (primary) 06A15, 68T27, 68V05, 05B35 (secondary) Copyright © 2024, The Authors. All rights reserved.

关键词： Lattice theory

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Fast Second-order Method for Neural Networks under Small Treewidth Setting

Fast Second-order Method for Neural Networks under Small Tre...

引用

IEEE International Conference on Big Data

作者： Xiaoyu Li Jiangxuan Long Zhao Song Tianyi Zhou Department of Computer Science Stevens Institute of Technology Hoboken NJ School of Software Engineering South China University of Technology Guangzhou China The Simons Institute for the Theory of Computing University of California Berkeley Berkeley CA Department of Computer Science University of Southern California Los Angeles CA

ISBN: (数字)9798350362480

ISBN: (纸本)9798350362497

Training neural networks is a fundamental problem in theoretical machine learning. Second-order methods are rarely used in practice due to their high computational cost, even they converge much faster than first-order methods. The state-of-the-art result for the second-order method to train an over-parameterized neural network can run in O(log(1/ϵ)) iterations and each iteration has O(mnd + n 3 ) running time, where n represent the number of data points, d is the dimension of the feature space of each data and m is the width of the neural network [Brand, Peng, Song and Weinstein ITCS 2021]. In this work, we further improve the convergence rate and the running time for each iteration to O(loglog(1/ϵ)) and O(mdτ 2 ) respectively, where m = Ω(n 4 ) and τ is the treewidth of the data matrix and usually very small. Our algorithm has a quadratic convergence rate, so it can be regarded as a truly second-order algorithm. To the best of our knowledge, our algorithm is the first to achieve a quadratic convergence rate for neural network training, with a per-iteration running time of O(mdτ 2 ).

关键词： Training Knowledge engineering Costs Neural networks Machine learning Big Data Computational efficiency Matrix decomposition Optimization Convergence

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