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arXiv 2025年

作者： Majidy, Shayan Hangleiter, Dominik Gullans, Michael J. Department of Physics Harvard University CambridgeMA02138 United States Simons Institute for the Theory of Computing University of California BerkeleyCA94720 United States Joint Center for Quantum Information and Computer Science University of Maryland NIST College ParkMD20742 United States

k-uniform states are valuable resources in quantum information, enabling tasks such as teleportation, error correction, and accelerated quantum simulations. The practical realization of k-uniform states, at scale, faces major obstacles: verifying k-uniformity is as difficult as measuring code distances, and devising fault-tolerant preparation protocols further adds to the complexity. To address these challenges, we present a scalable, fault-tolerant method for preparing encoded k-uniform states, and we illustrate our approach using surface and color codes. We first present a technique to determine k-uniformity of stabilizer states directly from their stabilizer tableau. We then identify a family of Clifford circuits that ensures both fault tolerance and scalability in preparing these states. Building on the encoded k-uniform states, we introduce a hybrid physical–logical strategy that retains some of the error-protection benefits of logical qubits while lowering the overhead for implementing arbitrary gates compared to fully logical algorithms. We show that this hybrid approach can outperform fully physical implementations for resource-state preparation, as demonstrated by explicit constructions of k-uniform states. Copyright © 2025, The Authors. All rights reserved.

关键词： Color codes

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Redundancy Is All You Need

arXiv

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arXiv 2024年

作者： Brakensiek, Joshua Guruswami, Venkatesan Department of Electrical Engineering and Computer Science University of California Berkeley United States Simons Institute for the Theory of Computing Departments of EECS and Mathematics University of California Berkeley United States

The seminal work of Benczúr and Karger demonstrated cut sparsifiers of near-linear size, with several applications throughout theoretical computer science. Subsequent extensions have yielded sparsifiers for hypergraph cuts and more recently linear codes over Abelian groups. A decade ago, Kogan and Krauthgamer asked about the sparsifiability of arbitrary constraint satisfaction problems (CSPs). For this question, a trivial lower bound is the size of a nonredundant CSP instance, which admits, for each constraint, an assignment satisfying only that constraint (so that no constraint can be dropped by the sparsifier). For instance, for graph cuts, spanning trees are non-redundant instances. Our main result is that redundant clauses are sufficient for sparsification: for any CSP predicate R, every unweighted instance of CSP(R) has a sparsifier of size at most its non-redundancy (up to polylog factors). For weighted instances, we similarly pin down the sparsifiability to the so-called chain length of the predicate. These results precisely determine the extent to which any CSP can be sparsified. A key technical ingredient in our work is a novel application of the entropy method from Gilmer's recent breakthrough on the union-closed sets conjecture. As an immediate consequence of our main theorem, a number of results in the non-redundancy literature immediately extend to CSP sparsification. We also contribute new techniques for understanding the non-redundancy of CSP predicates. In particular, we give an explicit family of predicates whose non-redundancy roughly corresponds to the structure of matching vector families in coding theory. By adapting methods from the matching vector codes literature, we are able to construct an explicit predicate whose non-redundancy lies between Ω(n1.5) and eO(n1.6), the first example with a provably non-integral exponent. © 2024, CC0.

关键词： Constraint satisfaction problems

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Retraction Note: High performance reconciliation for practical quantum key distribution systems

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Optical and quantum Electronics 2024年第12期56卷 1-2页

作者： Mao, ao-Kun Li, Qiong Hao, Peng-Lei Abd-El-Atty, Bassem Iliyasu, Abdullah M. Department of Computer Science and Technology Harbin Institute of Technology Harbin China CAS Key Laboratory of Quantum Information University of Science and Technology of China Hefei China CAS Center for Excellence in Quantum Information and Quantum Physics University of Science and Technology of China Hefei China Department of Computer Science Faculty of Computers and Information Luxor University Luxor Egypt Electrical Engineering Department College of Engineering Prince Sattam Bin Abdulaziz University Al- Kharj Saudi Arabia School of Computing Tokyo Institute of Technology Yokohama Japan School of Computer Science and Technology Changchun University of Science and Technology Changchun China

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quantum dynamical Hamiltonian Monte Carlo

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Physical Review Research 2024年第3期6卷 033142-033142页

作者： Owen Lockwood Peter Weiss Filip Aronshtein Guillaume Verdon Department of Computer Science Extropic Corp. San Francisco California 94111 USA Dirac Inc. New York New York 10001 USA Institute for Quantum Computing Department of Applied Mathematics

One of the open challenges in quantum computing is to find meaningful and practical methods to leverage quantum computation to accelerate classical machine-learning workflows. A ubiquitous problem in machine-learning workflows is sampling from probability distributions that we only have access to via their log probability. To this end, we extend the well-known Hamiltonian Monte Carlo (HMC) method for Markov chain Monte Carlo (MCMC) sampling to leverage quantum computation in a hybrid manner as a proposal function. Our new algorithm, quantum Dynamical Hamiltonian Monte Carlo (QD-HMC), replaces the classical symplectic integration proposal step with simulations of quantum-coherent continuous-space dynamics on digital or analog quantum computers. We show that QD-HMC maintains key characteristics of HMC, such as maintaining the detailed balanced condition with momentum inversion, while also having the potential for polynomial speedups over its classical counterpart in certain scenarios. As sampling is a core subroutine in many forms of probabilistic inference, and MCMC in continuously parametrized spaces covers a large class of potential applications, this work widens the areas of applicability of quantum devices.

关键词： Machine learning quantum algorithms quantum algorithms & computation quantum information processing with continuous variables

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Depth-Threshold Circuits vs. Depth-(+1) AND-OR Trees 55

Depth-Threshold Circuits vs. Depth-(+1) AND-OR Trees

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55th Annual ACM Symposium on theory of computing, STOC 2023

作者： Hatami, Pooya Hoza, William M. Tal, Avishay Tell, Roei Ohio State University Department of Computer Science and Engineering ColumbusOH United States University of California Simons Institute for the Theory of Computing BerkeleyCA United States University of California Department of Electrical Engineering and Computer Sciences BerkeleyCA United States Institute for Advanced Study School of Mathematics PrincetonNJ United States Rutgers University DIMACS PiscatawayNJ United States

ISBN: (纸本)9781450399135

For any n ,• and d = o(loglog(n)), we prove that there is a Boolean function F on n bits and a value γ= 2-(d) such that F can be computed by a uniform depth-(d + 1) AC0 circuit with O(n) wires, but F cannot be computed by any depth-d TC0 circuit with n1 +-3 wires. This bound matches the current state-of-the-art lower bounds for computing explicit functions by threshold circuits of depth d > 2, which were previously known only for functions outside AC0 such as the parity function. Furthermore, in our result, the AC0 circuit computing F is a monotone∗read-once formula∗(i.e., an AND-OR tree), and the lower bound holds even in the average-case setting with respect to advantage n-3. At a high level, our proof strategy combines two prominent approaches in circuit complexity from the last decade: The celebrated∗random projections∗method of Håstad, Rossman, Servedio, and Tan (J. ACM 2017), which was previously used to show a tight average-case depth hierarchy for AC0;and the line of works analyzing the effect of∗random restrictions∗on threshold circuits. We show that under a modified version of Håstad, Rossman, Servedio, and Tan's projection procedure, any depth-d threshold circuit with n1 +-3 wires simplifies to a near-trivial function, whereas an appropriately parameterized AND-OR tree of depth d + 1 maintains structure. © 2023 Owner/Author.

关键词： Wire

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Near-Tight Bounds for 3-Query Locally Correctable Binary Linear Codes via Rainbow Cycles

arXiv

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arXiv 2024年

作者： Alrabiah, Omar Guruswami, Venkatesan Department of Electrical Engineering and Computer Science UC Berkeley BerkeleyCA94709 United States Department of Electrical Engineering and Computer Science Department of Mathematics the Simons Institute the Theory of Computing UC Berkeley BerkeleyCA94709 United States

We prove that a binary linear code of block length n that is locally correctable with 3 queries against a fraction δ > 0 of adversarial errors must have dimension at most Oδ(log2 n · log log n). This is almost tight in view of quadratic Reed-Muller codes being a 3-query locally correctable code (LCC) with dimension Θ(log2 n). Our result improves, for the binary field case, the Oδ(log8 n) bound obtained in the recent breakthrough of [KM23a] (and the more recent improvement to Oδ(log4 n) for binary linear codes announced in [Yan24]). Previous bounds for 3-query linear LCCs proceed by constructing a 2-query locally decodable code (LDC) from the 3-query linear LCC/LDC and applying the strong bounds known for the former. Our approach is more direct and proceeds by bounding the covering radius of the dual code, borrowing inspiration from [IS20]. That is, we show that if x 7→ (v1·x, v2·x, . . ., vn·x) is an arbitrary encoding map Fk2 → Fn2 for the 3-query LCC, then all vectors in Fk2 can be written as a Oeδ(log n)-sparse linear combination of the vi’s, which immediately implies k 6 Oeδ((log n)2). The proof of this fact proceeds by iteratively reducing the size of any arbitrary linear combination of at least Ωeδ(log n) of the vi’s. We achieve this using the recent breakthrough result of [ABS+23] on the existence of rainbow cycles in properly edge-colored graphs, applied to graphs capturing the linear dependencies underlying the local correction property. © 2024, CC BY.

关键词： Forward error correction

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Small sets of genuinely nonlocal Greenberger-Horne-Zeilinger states in multipartite systems

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Physical Review A 2024年第2期109卷 022428-022428页

作者： Zong-Xing Xiong Yongli Zhang Mao-Sheng Li Lvzhou Li Institute of Quantum Computing and Software School of Computer Science and Engineering Sun Yat-Sen University Guangzhou 510006 China School of Mathematics and Systems Science Guangdong Polytechnic Normal University Guangzhou 510665 China School of Mathematics South China University of Technology Guangzhou 510641 China

A set of orthogonal multipartite quantum states are called (distinguishability-based) genuinely nonlocal if they are locally indistinguishable across any bipartition of the subsystems. In this work, we consider the problem of constructing small genuinely nonlocal sets consisting of generalized Greenberger-Horne-Zeilinger (GHZ) states in multipartite systems. For system (C2)⊗N where N is large, using the language of group theory, we show that a tiny proportion Θ(1/2N) of the states among the N-qubit GHZ basis suffice to exhibit genuine nonlocality. Similar arguments also hold for the canonical generalized GHZ bases in systems (Cd)⊗N, wherever d is even and N is large. What is more, moving to the condition that any fixed N is given, we show that d+1 genuinely nonlocal generalized GHZ states exist in (Cd)⊗N, provided the local dimension d is sufficiently large. As an additional merit, within and beyond an asymptotic sense, the latter result also indicates some evident limitations of the “trivial othogonality-preserving local measurements” (TOPLM) technique that has been utilized frequently for detecting genuine nonlocality.

关键词： Nonlocality quantum correlations in quantum information

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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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Design of a Secure Machine Learning-Based Malware Detection and Analysis Scheme

Design of a Secure Machine Learning-Based Malware Detection ...

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2023 IEEE International Conference on Communications, computing, Cybersecurity and Informatics, CCCI 2023

作者： Kumar, Pankaj Obaidat, Mohammad S. Pandey, Piyush Wazid, Mohammad Das, Ashok Kumar Singh, Devesh Pratap Graphic Era Deemed to Be University Department of Computer Science and Engineering Dehradun India King Abdullah Ii School of Information Technology The University of Jordan Amman11942 Jordan School of Computing Srm University Jordan University of Science and Technology Beijing Beijing100083 China School of Computing Srm University TN Kattankulathur603203 India Algorithmic Research International Institute of Information Technology Center for Security Theory Hyderabad India

ISBN: (纸本)9798350302561

Today's world is rapidly growing towards the advanced concept of technology. Technology nowadays is at its peak of development and has great advantages in all fields of work, whether it is in industrial automation, farming, weather forecasting, or disease detection and control. Despite its great advantages, it does have its negative side because a major population is using technology and general-purpose computing devices (i.e., desktops, laptops, smartphones, tablets, etc.). Therefore, most of their personal data is available online. The data is constantly in danger of getting stolen by malicious actors (i.e., hackers), who can find a way to get their hands on this data and then use it for their personal gain (i.e., money-making). The best-known technique to get this information is by using malware exploitation on the machine of the target. Malware is an executable or a binary that is malicious in nature. It may have various devastating effects, and in order to detect and make the system defensive, we need to propose a scheme to detect the malware in the system, analyze the particular file, and then mitigate it. In this paper, we propose a secure machine learning-based malware detection and analysis scheme (in short, SML-MDA). The conducted security analysis and formal security verification of the proposed SMLMDA prove its security against various types of potential attacks. The proposed SML-MDA is then compared with the other similar competing schemes, and its performance has been found to be better in terms of various performance metrics like accuracy and F1-score. © 2023 IEEE.

关键词： Machine learning

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Decidability for Sturmian Words 30

Decidability for Sturmian Words

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30th EACSL Annual Conference on computer science Logic, CSL 2022

作者： Hieronymi, Philipp Ma, Dun Oei, Reed Schaeffer, Luke Schulz, Christian Shallit, Jeffrey Department of Mathematics University of Illinois Urbana-ChampaignIL United States Mathematisches Institut Universität Bonn Germany Institute for Quantum Computing University of Waterloo Canada School of Computer Science University of Waterloo Canada

ISBN: (纸本)9783959772181

We show that the first-order theory of Sturmian words over Presburger arithmetic is decidable. Using a general adder recognizing addition in Ostrowski numeration systems by Baranwal, Schaeffer and Shallit, we prove that the first-order expansions of Presburger arithmetic by a single Sturmian word are uniformly ω-automatic, and then deduce the decidability of the theory of the class of such structures. Using an implementation of this decision algorithm called Pecan, we automatically reprove classical theorems about Sturmian words in seconds, and are able to obtain new results about antisquares and antipalindromes in characteristic Sturmian words. © Philipp Hieronymi, Dun Ma, Reed Oei, Luke Schaeffer, Christian Schulz, and Jeffrey Shallit.

关键词： Computability and decidability

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