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Discrimination of quantum States Under Locality Constraints in the Many-Copy Setting

Communications in Mathematical Physics 2023年第1期404卷 151-183页

作者： Cheng, Hao-Chung Winter, Andreas Yu, Nengkun Department of Electrical Engineering and Graduate Institute of Communication Engineering National Taiwan University Tapei 106 Taiwan Department of Mathematics National Taiwan University Tapei 106 Taiwan Center for Quantum Science and Engineering National Taiwan University Tapei 106 Taiwan Physics Division National Center for Theoretical Sciences Taipei 10617 Taiwan Hon Hai (Foxconn) Quantum Computing Center New Taipei City 236 Taiwan ICREA-Institució Catalana de Recerca i Estudis Avançats Barcelona 08010 Spain Departament de Física Física Teòrica: Informaciò i Fenòmens Quàntics Universitat Autònoma de Barcelona Barcelona 08193 Spain Computer Science Department Stony Brook University New York NY United States Centre for Quantum Software and Information and Faculty of Engineering and Information Technology University of Technology Sydney Ultimo 2007 NSW Australia

We study quantum hypothesis testing between orthogonal states under restricted local measurements in the many-copy scenario. For testing arbitrary multipartite entangled pure state against its orthogonal complement state via the local operation and classical communication (LOCC) operation, we prove that the optimal average error probability always decays exponentially in the number of copies. Second, we provide a sufficient condition for the LOCC operations to achieve the same performance as the positive-partial-transpose (PPT) operations. We further show that testing a maximally entangled state against its orthogonal complement and testing extremal Werner states both fulfill the above-mentioned condition. Hence, we determine the explicit expressions for the optimal average error probability, the optimal trade-off between the type-I and type-II errors, and the associated Chernoff, Stein, Hoeffding, and strong converse exponents. Then, we show an infinite asymptotic separation between the separable (SEP) and PPT operations by providing a pair of states constructed from an unextendible product basis (UPB). The quantum states can be distinguished perfectly by PPT operations, while the optimal error probability, with SEP operations, admits an exponential lower bound. On the technical side, we prove this result by providing a quantitative version of the well-known statement that the tensor product of UPBs is a UPB. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

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Parameterized Inapproximability Hypothesis under ETH

arXiv

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arXiv 2023年

作者： Guruswami, Venkatesan Lin, Bingkai Ren, Xuandi Sun, Yican Wu, Kewen Simons Institute for the Theory of Computing Departments of EECS and Mathematics UC Berkeley United States State Key Laboratory for Novel Software Technology Nanjing University China Department of EECS UC Berkeley United States School of Computer Science Peking University China

The Parameterized Inapproximability Hypothesis (PIH) asserts that no fixed parameter tractable (FPT) algorithm can distinguish a satisfiable CSP instance, parameterized by the number of variables, from one where every assignment fails to satisfy an ϵ fraction of constraints for some absolute constant ϵ > 0. PIH plays the role of the PCP theorem in parameterized complexity. However, PIH has only been established under Gap-ETH, a very strong assumption with an inherent gap. In this work, we prove PIH under the Exponential Time Hypothesis (ETH). This is the first proof of PIH from a gap-free assumption. Our proof is self-contained and elementary. We identify an ETH-hard CSP whose variables take vector values, and constraints are either linear or of a special parallel structure. Both kinds of constraints can be checked with constant soundness via a "parallel PCP of proximity" based on the Walsh-Hadamard code. © 2023, CC BY.

关键词： Parameterization

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quantum Self-Attention Neural Networks for Text Classification

arXiv

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arXiv 2022年

作者： Li, Guangxi Zhao, Xuanqiang Wang, Xin Institute for Quantum Computing Baidu Research Beijing100193 China Centre for Quantum Software and Information University of Technology SydneyNSW2007 Australia QICI Department of Computer Science The University of Hong Kong Hong Kong Nansha China

An emerging direction of quantum computing is to establish meaningful quantum applications in various fields of artificial intelligence, including natural language processing (NLP). Although some efforts based on syntactic analysis have opened the door to research in quantum NLP (QNLP), limitations such as heavy syntactic preprocessing and syntax-dependent network architecture make them impracticable on larger and real-world data sets. In this paper, we propose a new simple network architecture, called the quantum self-attention neural network (QSANN), which can compensate for these limitations. Specifically, we introduce the self-attention mechanism into quantum neural networks and then utilize a Gaussian projected quantum self-attention serving as a sensible quantum version of self-attention. As a result, QSANN is effective and scalable on larger data sets and has the desirable property of being implementable on near-term quantum devices. In particular, our QSANN outperforms the best existing QNLP model based on syntactic analysis as well as a simple classical self-attention neural network in numerical experiments of text classification tasks on public data sets. We further show that our method exhibits robustness to low-level quantum noises and showcases resilience to quantum neural network architectures. © 2022, CC BY.

关键词： Network architecture

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Upper Bounds on Device-Independent quantum Key Distribution Rates in Static and Dynamic Scenarios

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Physical Review Applied 2022年第5期18卷 054033-054033页

作者： Eneet Kaur Karol Horodecki Siddhartha Das Institute for Quantum Computing and Department of Physics and Astronomy University of Waterloo Waterloo Ontario N2L 3G1 Canada Institute of Informatics National Quantum Information Centre in Gdańsk Faculty of Mathematics Physics and Informatics University of Gdańsk 80-952 Gdańsk Poland International Centre for Theory of Quantum Technologies University of Gdańsk Wita Stwosza 63 Gdansk 80-308 Poland Centre for Quantum Information & Communication (QuIC) École polytechnique de Bruxelles Université libre de Bruxelles Brussels B-1050 Belgium Center for Security Theory and Algorithmic Research (CSTAR) Centre for Quantum Science and Technology (CQST) International Institute of Information Technology Hyderabad Gachibowli Telangana 500032 India

In this work, we develop upper bounds on key rates for device-independent quantum key distribution (DI-QKD) protocols and devices. We study the reduced cc-squashed entanglement and show that it is a convex functional. As a result, we show that the convex hull of the currently known bounds is a tighter upper bound on the device-independent key rates of the standard Clauser-Horne-Shimony-Holt (CHSH)-based protocol. We further provide tighter bounds for DI-QKD key rates achievable by any protocol applied to the CHSH-based device. This bound is based on reduced relative entropy of entanglement optimized over decompositions into local and nonlocal parts. In the dynamical scenario of quantum channels, we obtain upper bounds for device-independent private capacity for the CHSH-based protocols. We show that the device-independent private capacity for the CHSH-based protocols on depolarizing and erasure channels is limited by the secret key capacity of dephasing channels.

关键词： Optical quantum information processing quantum communication quantum cryptography quantum entanglement quantum protocols Devices

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Backaction-evading receivers with magnetomechanical and electromechanical sensors

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Physical Review Research 2024年第2期6卷 023141-023141页

作者： Brittany Richman Sohitri Ghosh Daniel Carney Gerard Higgins Peter Shawhan C. J. Lobb Jacob M. Taylor Joint Quantum Institute (JQI) College Park Maryland 20742 USA Department of Physics University of Maryland College Park Maryland 20742 USA Joint Center for Quantum Information and Computer Science (QuICS) College Park Maryland 20742 USA Theory Division Fermi National Accelerator Laboratory Batavia Illinois 60510 USA Physics Division Lawrence Berkeley National Laboratory Berkeley California 94720-8153 USA Institute for Quantum Optics and Quantum Information (IQOQI) Austrian Academy of Sciences A-1090 Vienna Austria Department of Microtechnology and Nanoscience (MC2) Chalmers University of Technology SE-412 96 Gothenburg Sweden Maryland Quantum Materials Center (QMC) College Park Maryland 20742 USA National Institute of Standards and Technology (NIST) Gaithersburg Maryland 20899 USA

Today's mechanical sensors are capable of detecting extremely weak perturbations while operating near the standard quantum limit. However, further improvements can be made in both sensitivity and bandwidth when we reduce the noise originating from the process of measurement itself—the quantum-mechanical backaction of measurement—and go below this ‘standard’ limit, possibly approaching the Heisenberg limit. One of the ways to eliminate this noise is by measuring a quantum nondemolition variable such as the momentum in a free-particle system. Here, we propose and characterize theoretical models for direct velocity measurement that utilize traditional electric and magnetic transducer designs to generate a signal while enabling this backaction evasion. We consider the general readout of this signal via electric or magnetic field sensing by creating toy models analogous to the standard optomechanical position-sensing problem, thereby facilitating the assessment of measurement-added noise. Using simple models that characterize a wide range of transducers, we find that the choice of readout scheme—voltage or current—for each mechanical detector configuration implies access to either the position or velocity of the mechanical subsystem. This in turn suggests a path forward for key fundamental physics experiments such as the direct detection of dark matter particles.

关键词： Circuit quantum electrodynamics Measurement back action quantum metrology quantum nondemolition measurement quantum sensing

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Proxy convexity: a unified framework for the analysis of neural networks trained by gradient descent 21

Proxy convexity: a unified framework for the analysis of neu...

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Proceedings of the 35th International Conference on Neural Information Processing Systems

作者： Spencer Frei Quanquan Gu Simons Institute for the Theory of Computing University of California Berkeley Department of Computer Science University of California Los Angeles

ISBN: (纸本)9781713845393

Although the optimization objectives for learning neural networks are highly non-convex, gradient-based methods have been wildly successful at learning neural networks in practice. This juxtaposition has led to a number of recent studies on provable guarantees for neural networks trained by gradient descent. Unfortunately, the techniques in these works are often highly specific to the particular setup in each problem, making it difficult to generalize across different settings. To address this drawback in the literature, we propose a unified non-convex optimization framework for the analysis of neural network training. We introduce the notions of proxy convexity and proxy Polyak-Lojasiewicz (PL) inequalities, which are satisfied if the original objective function induces a proxy objective function that is implicitly minimized when using gradient methods. We show that stochastic gradient descent (SGD) on objectives satisfying proxy convexity or the proxy PL inequality leads to efficient guarantees for proxy objective functions. We further show that many existing guarantees for neural networks trained by gradient descent can be unified through proxy convexity and proxy PL inequalities.

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Optimizing Low-Energy Carbon IIoT Systems with quantum Algorithms: Performance Evaluation and Noise Robustness

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IEEE Internet of Things Journal 2025年

作者： Dave, Kshitij Innan, Nouhaila Behera, Bikash K. Mumtaz, Shahid Al-Kuwari, Saif Farouk, Ahmed The Institute of Advanced Research Gandhinagar India Quantum Physics and Magnetism Team LPMC Faculty of Sciences Ben M’sick Hassan II University of Casablanca Morocco United Arab Emirates NYUAD Research Institute NYUAD Abu Dhabi United Arab Emirates Pvt. Ltd. WB Mohanpur741246 India Nottingham Trent University Engineering Department United Kingdom The Qatar Center for Quantum Computing College of Science and Engineering Hamad Bin Khalifa University Qatar Foundation Doha Qatar The Department of Computer Science Faculty of Computers and Artificial Intelligence Hurghada University Hurghada Egypt

Low-energy carbon Internet of Things (IoT) systems are essential for sustainable development, as they reduce carbon emissions while ensuring efficient device performance. Although classical algorithms manage energy efficiency and data processing within these systems, they often face scalability and real-time processing limitations. quantum algorithms offer a solution to these challenges by delivering faster computations and improved optimization, thereby enhancing both the performance and sustainability of low-energy carbon IoT systems. Therefore, we introduced three quantum algorithms: quantum neural networks utilizing Pennylane (QNN-P), Qiskit (QNN-Q), and hybrid quantum neural networks (QNN-H). These algorithms are applied to two low-energy carbon IoT datasets—room occupancy detection (RODD) and GPS tracker (GPSD). For the RODD dataset, QNN-P achieved the highest accuracy at 0.95, followed by QNN-H at 0.91 and QNN-Q at 0.80. Similarly, for the GPSD dataset, QNN-P attained an accuracy of 0.94, QNN-H 0.87, and QNN-Q 0.74. Furthermore, the robustness of these models is verified against six noise models. The proposed quantum algorithms demonstrate superior computational efficiency and scalability in noisy environments, making them highly suitable for future low-energy carbon IoT systems. These advancements pave the way for more sustainable and efficient IoT infrastructures, significantly minimizing energy consumption while maintaining optimal device performance. © 2014 IEEE.

关键词： Zero-carbon

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Measuring Bipartite Spin Correlations of Lattice-Trapped Dipolar Atoms

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Physical Review Letters 2024年第20期133卷 203401-203401页

作者： Youssef Aziz Alaoui Sean R. Muleady Edwin Chaparro Youssef Trifa Ana Maria Rey Tommaso Roscilde Bruno Laburthe-Tolra Laurent Vernac Université Sorbonne Paris Nord Laboratoire de Physique des Lasers F-93430 Villetaneuse France CNRS UMR 7538 LPL F-93430 Villetaneuse France JILA NIST and Department of Physics University of Colorado Boulder USA Center for Theory of Quantum Matter University of Colorado Boulder Colorado 80309 USA Joint Center for Quantum Information and Computer Science NIST and University of Maryland College Park Maryland 20742 USA Joint Quantum Institute NIST and University of Maryland College Park Maryland 20742 USA Univ Lyon Ens de Lyon CNRS Laboratoire de Physique F-69342 Lyon France

We demonstrate a bipartition technique using a superlattice architecture to access correlations between alternating planes of a mesoscopic array of spin-3 chromium atoms trapped in a 3D optical lattice. Using this method, we observe that out-of-equilibrium dynamics driven by long-range dipolar interactions lead to spin anticorrelations between the two spatially separated subsystems. Our bipartite measurements reveal a subtle interplay between the anisotropy of the 3D dipolar interactions and that of the lattice structure, without requiring single-site addressing. We compare our results to theoretical predictions based on a truncated cumulant expansion and a new cluster semiclassical method that we use to investigate correlations at the microscopic scale. Comparison with a high-temperature analytical model reveals quantum thermalization at a high negative spin temperature.

关键词： Cold gases in optical lattices Dipolar atoms Dipolar gases quantum fluctuations & noise

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General limit to thermodynamic annealing performance

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Physical Review E 2023年第5期108卷 L052105-L052105页

作者： Yutong Luo Yi-Zheng Zhen Xiangjing Liu Daniel Ebler Oscar Dahlsten Blackett Laboratory Imperial College London London SW7 2AZ United Kingdom Department of Physics Southern University of Science and Technology Shenzhen 518055 China Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences University of Science and Technology of China Hefei 230026 China Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics University of Science and Technology of China Shanghai 201315 China Theory Laboratory Central Research Institute 2012 Labs Huawei Technology Company Limited Hong Kong Science Park Hong Kong SAR China Department of Computer Science The University of Hong Kong Pokfulam Road Hong Kong SAR China Department of Physics City University of Hong Kong Tat Chee Avenue Kowloon Hong Kong SAR China Shenzhen Institute for Quantum Science and Engineering and Department of Physics Southern University of Science and Technology Shenzhen 518055 China Institute of Nanoscience and Applications Southern University of Science and Technology Shenzhen 518055 China

Annealing has proven highly successful in finding minima in a cost landscape. Yet, depending on the landscape, systems often converge towards local minima rather than global ones. In this Letter, we analyze the conditions for which annealing is approximately successful in finite time. We connect annealing to stochastic thermodynamics to derive a general bound on the distance between the system state at the end of the annealing and the ground state of the landscape. This distance depends on the amount of state updates of the system and the accumulation of nonequilibrium energy, two protocol and energy landscape-dependent quantities which we show are in a trade-off relation. We describe how to bound the two quantities both analytically and physically. This offers a general approach to assess the performance of annealing from accessible parameters, both for simulated and physical implementations.

关键词： Nonequilibrium statistical mechanics quantum thermodynamics

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Bound on annealing performance from stochastic thermodynamics, with application to simulated annealing

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Physical Review E 2023年第5期108卷 054119-054119页

作者： Yutong Luo Yi-Zheng Zhen Xiangjing Liu Daniel Ebler Oscar Dahlsten Blackett Laboratory Imperial College London London SW7 2AZ United Kingdom Department of Physics Southern University of Science and Technology Shenzhen 518055 China Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences University of Science and Technology of China Hefei 230026 China Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics University of Science and Technology of China Shanghai 201315 China Theory Lab Central Research Institute 2012 Labs Huawei Technology Co. Ltd. Hong Kong Science Park Hong Kong SAR China Department of Computer Science The University of Hong Kong Pokfulam Road Hong Kong SAR China Department of Physics City University of Hong Kong Tat Chee Avenue Kowloon Hong Kong SAR China Shenzhen Institute for Quantum Science and Engineering and Department of Physics Southern University of Science and Technology Shenzhen 518055 China Institute of Nanoscience and Applications Southern University of Science and Technology Shenzhen 518055 China

Annealing is the process of gradually lowering the temperature of a system to guide it towards its lowest energy states. In an accompanying paper [Y. Luo et al., Phys. Rev. E 108, L052105 (2023)], we derived a general bound on annealing performance by connecting annealing with stochastic thermodynamics tools, including a speed limit on state transformation from entropy production. We here describe the derivation of the general bound in detail. In addition, we analyze the case of simulated annealing with Glauber dynamics in depth. We show how to bound the two case-specific quantities appearing in the bound, namely the activity, a measure of the number of microstate jumps, and the change in relative entropy between the state and the instantaneous thermal state, which is due to temperature variation. We exemplify the arguments by numerical simulations on the Sherrington-Kirkpatrick (SK) model of spin glasses.

关键词： Nonequilibrium statistical mechanics quantum statistical mechanics

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