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Relating entropies of quantum channels

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arXiv 2021年

作者： Kurzyk, Dariusz Pawela, Lukasz Puchala, Zbigniew Institute of Theoretical and Applied Informatics Polish Academy of Sciences ul. Baltycka 5 Gliwice44-100 Poland Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University ul. Lojasiewicza 11 Kraków30-348 Poland

In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi-Jamiolkowski state. The second one is based on the relative entropy of the output of the extended channel relative to the output of the extended completely depolarizing channel. This entropy then needs to be optimized over all possible input states. Our results first show that the former entropy provides an upper bound on the latter. Next, we show that for unital qubit channels, this bound is saturated. Finally, we conjecture and provide numerical intuitions that the bound can also be saturated for random channels as their dimension tends to infinity. © 2021, CC BY.

关键词： Entropy

EXCLUDING FALSE NEGATIVE ERROR IN CERTIFICATION OF QUANTUM CHANNELS

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arXiv 2021年

作者： Krawiec, Aleksandra Pawela, Lukasz Puchala, Zbigniew Institute of Theoretical and Applied Informatics Polish Academy of Sciences ul. Baltycka 5 Gliwice44-100 Poland Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University ul. Lojasiewicza 11 Kraków30-348 Poland

Certification of quantum channels is based on quantum hypothesis testing and involves also preparation of an input state and choosing the final measurement. This work primarily focuses on the scenario when the false negative error cannot occur, even if it leads to the growth of the probability of false positive error. We establish a condition when it is possible to exclude false negative error after a finite number of queries to the quantum channel in parallel, and we provide an upper bound on the number of queries. On top of that, we found a class of channels which allow for excluding false negative error after a finite number of queries in parallel, but cannot be distinguished unambiguously. Moreover, it will be proved that parallel certification scheme is always sufficient, however the number of steps may be decreased by the use of adaptive scheme. Finally, we consider examples of certification of various classes of quantum channels and measurements. Copyright © 2021, The Authors. All rights reserved.

关键词： Quantum entanglement

Maximization of a Convex Quadratic Form on a Polytope: Factorization and the Chebyshev Norm Bounds 6th

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Maximization of a Convex Quadratic Form on a Polytope: Facto...

6th World Congress on Global Optimization, WCGO 2019

作者： Hladík, Milan Hartman, David Faculty of Mathematics and Physics Department of Applied Mathematics Charles University Malostranské nám.Â 25 Prague11800 Czech Republic Computer Science Institute Charles University Malostranské nám.Â 25 Prague11800 Czech Republic Institute of Computer Science of the Czech Academy of Sciences Prague Czech Republic

ISBN: (纸本)9783030218027

Maximization of a convex quadratic form on a convex polyhedral set is an NP-hard problem. We focus on computing an upper bound based on a factorization of the quadratic form matrix and employment of the maximum vector norm. Effectivity of this approach depends on the factorization used. We discuss several choices as well as iterative methods to improve performance of a particular factorization. We carried out numerical experiments to compare various alternatives and to compare our approach with other standard approaches, including McCormick envelopes. © 2020, Springer Nature Switzerland AG.

关键词： Factorization

Multi-State MRAM Cells For Hardware Neuromorphic Computing

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Research Square

Research Square 2021年

作者： Rzeszut, Piotr Chęciński, Jakub Brzozowski, Ireneusz Ziętek, Slawomir Skowroński, Witold Stobiecki, Tomasz AGH University of Science and Technology Institute of Electronics Al. Mickiewicza 30 Kraków30-059 Poland AGH University of Science and Technology Faculty of Physics and Applied Computer Science Al. Mickiewicza 30 Kraków30-059 Poland

Magnetic tunnel junctions (MTJ) have been successfully applied in various sensing application and digital information storage technologies. Currently, a number of new potential applications of MTJs are being actively studied, including high-frequency electronics, energy harvesting or random number generators. Recently, MTJs have been also proposed in designs of new platforms for unconventional or bio-inspired computing. In the present work, it is shown that serially connected MTJs forming a multi-state memory cell can be used in a hardware implementation of a neural computing device. The main purpose of the multi-cell is the formation of quantized weights in the network, which can be programmed using the proposed electronic circuit. Multi-cells are connected to a CMOS-based summing amplifier and a sigmoid function generator, forming an artificial neuron. The operation of the designed network is tested using a recognition of hand-written digits in 20 × 20 pixels matrix and shows detection ratio comparable to the software algorithm, using weights stored in a multi-cell consisting of four MTJs or more. © 2021, CC BY.

关键词： Cells

Support Vector Machine reconfigurable hardware implementation on FPGA

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Franklin Open

Franklin Open 2024年 7卷

作者： Yacoub, Mohammed H. Ismail, Samar M. Said, Lobna A. Madian, Ahmed H. Radwan, Ahmed G. Nanoelectronics Integrated Systems Center (NISC) Nile University Giza 12588 Egypt School of Engineering and Computer Science University of Hertfordshire Egypt Engineering Mathematics and Physics Department Faculty of Engineering Cairo University Giza 12613 Egypt Radiation Engineering Department National Centre for Radiation Research and Technology Egyptian Atomic Energy Authority Cairo 11787 Egypt School of Engineering and Applied Sciences Nile University Giza 12588 Egypt

Support Vector Machine (SVM) is a robust Machine Learning (ML) algorithm used extensively in classification tasks. This work proposes a reconfigurable hardware implementation of the SVM classification algorithm for the linear and three kernel cases on FPGA. Efficient implementations of two generalization techniques, One-versus-All (OvA) and One-versus-One (OvO), to deal with multi-class problems are also realized on FPGA to overcome the binary nature of the SVM algorithm. The presented model is fully reconfigurable and can easily be adapted to any dataset with any number of classes or features. The results show that the proposed model excels in power efficiency, requires low area utilization, and reaches high performance up to 250.7 MHz. The two realized generalization methods, OvO and OvA, offer a trade-off between accuracy and hardware cost. OvA provides lower accuracy than OvO and is more affected by the data imbalance problem, which becomes more dominant as the number of classes increases;however, it is more resource-efficient than OvO. The proposed hardware design is realized and experimentally tested on FPGA for three different datasets, employing different linear and kernel SVM cases. The classification accuracy achieved by the reconfigurable hardware design matches the software simulation results. © 2024 The Authors

关键词： Artificial intelligence Classification Floating point FPGA Support Vector Machine

Characterization of two electronic subsystems in cuprates through optical conductivity

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arXiv 2022年

作者： Kumar, C.M.N. Akrap, A. Homes, C.C. Martino, E. Klebel-Knobloch, B. Tabis, W. Barišić, O.S. Sunko, D.K. Barišić, N. Institute of Solid State Physics TU Wien Vienna1040 Austria Institute of Physics Bijenička cesta 46 ZagrebHR-10000 Croatia The Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences 152 Radzikowskiego Str. Krakow31-342 Poland Department of Physics University of Fribourg Chemin du Musée 3 FribourgCH-1700 Switzerland Condensed Matter Physics and Materials Science Department Brookhaven National Laboratory UptonNY11973 United States National Synchrotron Light Source II Brookhaven National Laboratory UptonNY11973 United States LausanneCH-1015 Switzerland AGH University of Science and Technology Faculty of Physics and Applied Computer Science Krakow30-059 Poland Department of Physics Faculty of Science University of Zagreb Bijenička cesta 32 ZagrebHR-10000 Croatia

Understanding the physical properties of unconventional superconductors as well as of other correlated materials presents a formidable challenge. Their unusual evolution with doping, frequency, and temperature has frequently led to non-Fermi-liquid (non-FL) interpretations. Optical conductivity is a major challenge in this context. Here, the optical spectra of two archetypal cuprates, underdoped HgBa2CuO4+δ and optimally-doped Bi2Sr2CaCu2O8+δ, are interpreted based on the standard Fermi liquid (FL) paradigm. At both dopings, perfect frequency-temperature FL scaling is found to be modified by the presence of a second, gapped electronic subsystem. This non-FL component emerges as a well-defined mid-infrared spectral feature after the FL contribution—determined independently by transport—is subtracted. Temperature, frequency, and doping evolution of the MIR feature identify a gapped rather than dissipative response. In contrast, the dissipative response is found to be relevant for pnictides and ruthenates. Such an unbiased FL/non-FL separation is extended across the cuprate phase diagram, capturing all the key features of the normal state and providing a natural explanation why the superfluid density is attenuated on the overdoped side. Thus, we obtain a unified interpretation of optical responses and transport measurements in all analyzed physical regimes and all analyzed compounds. © 2022, CC BY.

关键词： Fermi liquids

Unraveling the Role of Boron Dimers in the Electrical Anisotropy and Superconductivity in Boron-Doped Diamond

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SSRN

SSRN 2024年

作者： Sobaszek, Michal Kwon, Soonho Winiarski, Michal Rutkowski, Bogdan Ryl, Jacek Klimczuk, Tomasz Wang, Dongying Li, Xinwei Bockrath, Marc Bogdanowicz, Robert Goddard, William A. Gdańsk University of Technology Faculty of Electronics Telecommunications and Informatics Department of Metrology and Optoelectronics 11/12 Narutowicza Str. 80-233 Poland Materials and Process Simulation Center California Institute of Technology 1200 East California Blvd. CA91125 United States Gdańsk University of Technology Faculty of Applied Physics and Mathematics and Advanced Materials Centre Department of Solid State Physics 11/12 Narutowicza Str. Gdańsk80-233 Poland Faculty of Metals Engineering and Industrial Computer Science AGH University of Krakow Al. A. Mickiewicza 30 Kraków30-059 Poland Advanced Materials Center Gdańsk University of Technology Narutowicza 11/12 Gdańsk80-233 Poland Department of Physics The Ohio State University ColumbusOH43210 United States

We use quantum mechanics (QM) to determine the states formed by B dopants in diamond. We find that isolated B sites prefer to form BB dimers and that the dimers pair up to form tetramers (BBCBB) that prefer to aggregate parallel to the (111) surface in the direction, one double layer below the H-terminated surface double layer. These tetramers lead to metallic character (Mott metal Insulator Transition) with holes in the valence band near the Γ point and electrons in the BBCBB tetramer promoted band along the X direction. Our experiments find very significant anisotropy in the superconductivity for boron-doped diamond thin films prepared with Microwave Plasma Assisted Chemical Vapor Deposition using deuterium-rich plasma. This leads to much higher conductivity in the X direction than the Y direction, as predicted by the QM. This phase transition to the anomalous phase is linked with the emergence of boson quantum entanglement states behaving as a bosonic insulating state. These anisotropic superconducting properties of the diamond film might enable applications such as single-photon detectors. We expect that this formation of a dirty superconductivity state is related to the BBCBB tetramers found in our QM calculations. © 2024, The Authors. All rights reserved.

关键词： Dimers

Multi-state MRAM cells for hardware neuromorphic computing

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arXiv 2021年

Magnetic tunnel junctions (MTJ) have been successfully applied in various sensing application and digital information storage technologies. Currently, a number of new potential applications of MTJs are being actively studied, including high-frequency electronics, energy harvesting or random number generators. Recently, MTJs have been also proposed in designs of a new platforms for unconventional or bio-inspired computing. In the present work, it is shown that serially connected MTJs forming a multi-state memory cell can be used in a hardware implementation of a neural computing device. A behavioral model of the multi-cell is proposed based on the experimentally determined MTJ parameters. The main purpose of the mutli-cell is the formation of the quantized weights of the network, which can be programmed using the proposed electronic circuit. Mutli-cells are connected to CMOS-based summing amplifier and sigmoid function generator, forming an artificial neuron. The operation of the designed network is tested using a recognition of the hand-written digits in 20 × 20 pixel matrix and shows detection ratio comparable to the software algorithm, using the weight stored in a multi-cell consisting of four MTJs or more. © 2021, CC BY-NC-ND.

关键词： MRAM devices

Hölder regularity of the pressure for weak solutions of the 3D Euler equations in bounded domains

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arXiv 2023年

作者： Bardos, Claude Boutros, Daniel W. Titi, Edriss S. Laboratoire J.-L. Lions BP187 Paris75252 Cedex 05 France Wolfgang Pauli Institute - Inst CNRS Pauli IRL 2842 Faculty of Mathematics University of Vienna Oskar-Morgenstern-Platz 1 WienA-1090 Austria Department of Applied Mathematics and Theoretical Physics University of Cambridge CambridgeCB3 0WA United Kingdom Department of Mathematics Texas A&M University College StationTX77843-3368 United States Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot76100 Israel

We consider the three-dimensional incompressible Euler equations on a bounded domain Ω with C4 boundary. We prove that if the velocity field u ∈ C0,α(Ω) with α > 0 (where we are omitting the time dependence), it follows that the corresponding pressure p of a weak solution to the Euler equations belongs to the Hölder space C0,α(Ω). We also prove that away from the boundary p has C0,2α regularity. In order to prove these results we use a local parametrisation of the boundary and a very weak formulation of the boundary condition for the pressure of the weak solution, as was introduced in [C. Bardos and E.S. Titi, Philos. Trans. Royal Soc. A, 380 (2022), 20210073], which is different than the commonly used boundary condition for classical solutions of the Euler equations. Moreover, we provide an explicit example illustrating the necessity of this new very weak formulation of the boundary condition for the pressure. Furthermore, we also provide a rigorous derivation of this new formulation of the boundary condition for weak solutions of the Euler equations. This result is of importance for the proof of the first half of the Onsager Conjecture, the sufficient conditions for energy conservation of weak solutions to the three-dimensional incompressible Euler equations in bounded domains. In particular, the results in this paper remove the need for separate regularity assumptions on the pressure in the proof of the Onsager *** Codes 35Q31 (primary), 35Q35, 76B03, 35J05, 35J08, 35J25, 35D30 (secondary) © 2023, CC BY.

关键词： Euler equations