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applied Set-Valued Analysis and Optimization 2024年第3期6卷 275-294页

作者： Anh, P.N. Thach, H.T.C. 1Lab of Applied Mathematics and Computing Posts and Telecommunications Institute of Technology Hanoi Vietnam 2University of Transport Technology Hanoi Vietnam

This paper presents two new algorithms for solving multivalued variational inequality problems in a real Hilbert space. By combining the nonexpansiveness of proximal operators associated with the proper lower semicontinuous convex function of the problems and inertial techniques, we demonstrate the weak convergence of the iteration sequences generated by our first algorithm under monotone and Lipschitz continuous assumptions of the cost mappings. Next, we use Mann iteration technique to obtain the second algorithm and show its strong convergence. Finally, we give some numerical results for two proposed algorithms and comparison with some other known algorithms. ©2024 applied Set-Valued Analysis and Optimization.

关键词： Variational techniques

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Thermodynamic analysis of algorithmic cooling protocols: Efficiency metrics and improved designs

引用

Physical Review A 2024年第2期110卷 022215-022215页

作者： Junan Lin Nayeli A. Rodríguez-Briones Eduardo Martín-Martínez Raymond Laflamme Toronto Ontario M5T 3J1 Canada Department of Chemistry Miller Institute for Basic Research in Science 468 Donner Lab Berkeley California 94720 USA Institute for Quantum Computing Department of Applied Mathematics Department of Physics and Astronomy

Algorithmic cooling (AC) protocols have been predominantly studied for their cooling capabilities, with limited attention paid to their thermodynamic properties. This work explores an alternative perspective by analyzing a broad family of AC protocols from a thermodynamic standpoint. First, we give an in-depth review and formal classification of standard AC protocols. Leveraging the transfer matrix formalism, we achieve a consistent calculation of performance metrics, encompassing both cooling limits and target state evolution. We obtained a unification of these diverse cooling limits into a single, coherent mathematical expression, streamlining comparative analyses. Then, to assess the efficiency of coherent cooling protocols, we introduce two generic metrics: the coefficient of performance K and Landauer's Ratio RL, and establish a direct interrelation. Applying these metrics, we thoroughly evaluate selected AC protocols, highlighting their relative strengths. Finally, we propose improved versions of AC protocols that exhibit enhanced thermodynamic performance, achieving desired target temperatures with lower work inputs. This research contributes to a deeper understanding of AC protocols and provides valuable insights for designing efficient cooling strategies in various applications.

关键词： Quantum computation Quantum information processing Quantum information theory Quantum thermodynamics

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Ethical Aspects of Computational Modelling in Science, Decision Support and Communication 15th

Ethical Aspects of Computational Modelling in Science, Decis...

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15th International Workshop on Artificial Life and Evolutionary Computation, WIVACE 2021

作者： Füchslin, Rudolf Marcel Ambühl, Jacques Faggian, Alessia Fellermann, Harold M. Flumini, Dandolo Geller, Armando Hanczyc, Martin M. Klinkert, Andreas Krütli, Pius Matuttis, Hans-Georg Ott, Thomas Scheidegger, Stephan Schmid, Gary Bruno Smieszek, Timo Schneider, Johannes J. Steiner, Albert Weyland, Mathias S. Institute of Applied Mathematics and Physics Zurich University of Applied Sciences Zurich Technikumstrasse 9 Winterthur8400 Switzerland European Centre for Living Technology Ca’ Bottacin Dorsoduro 3911 Calle Crosera Venice30123 Italy World Bank Group Geneva Switzerland University of Trento Trento38123 Italy School of Computing Newcastle University Science Square 1 Newcastle Upon TyneNE4 5TG United Kingdom GmbH Fraumünsterstrasse 11 Zurich8001 Switzerland Institute of Data Analysis and Process Design Zurich University of Applied Sciences Rosenstrasse 3 Winterthur8400 Switzerland Transdisciplinarity Lab ETH Zurich Zurich8092 Switzerland Department of Mechanical Engineering and Intelligent Systems The University of Electrocommunications Tokyo182-8585 Japan Institute of Computational Life Sciences Zurich University of Applied Sciences Schloss 1 Wädenswil8820 Switzerland Swiss NeuroCreations GmbH Hambergersteig 25 Zurich8008 Switzerland Muesmattweg 70 Allschwil4123 Switzerland

ISBN: (纸本)9783031239281

The development of data science, the increase of computational power, the availability of the internet infrastructure for data exchange and the urgency for an understanding of complex systems require a responsible and ethical use of computational models in science, communication and decision-making. Starting with a discussion of the width of different purposes of computational models, we first investigate the process of model construction as an interplay of theory and experimentation. We emphasise the different aspects of the tension between model variables and experimentally measurable observables. The resolution of this tension is a prerequisite for the responsible use of models and an instrumental part of using models in the scientific processes. We then discuss the impact of models and the responsibility that results from the fact that models support and may also guide experimentation. Further, we investigate the difference between computational modelling in an interdisciplinary science project and computational models as tools in transdisciplinary decision support. We regard the communication of model structures and modelling results as essential;however, this communication cannot happen in a technical manner, but model structures and modelling results must be translated into a "narrative." We discuss the role of concepts from disciplines such as literary theory, communication science, and cultural studies and the potential gains that a broader approach can obtain. Considering concepts from the liberal arts, we conclude that there is, besides the responsibility of the model author, also a responsibility of the user/reader of the modelling results. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Decision making

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Experimental Activation of Strong Local Passive States with Quantum Information

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Physical Review Letters 2023年第11期130卷 110801-110801页

作者： Nayeli A. Rodríguez-Briones Hemant Katiyar Eduardo Martín-Martínez Raymond Laflamme Department of Chemistry University of California Berkeley California 94720 USA Miller Institute for Basic Research in Science 468 Donner Lab Berkeley California 94720 USA Institute for Quantum Computing University of Waterloo Waterloo Ontario N2L 3G1 Canada Department of Physics and Astronomy University of Waterloo Waterloo Ontario N2L 3G1 Canada Perimeter Institute for Theoretical Physics 31 Caroline Street North Waterloo Ontario N2L 2Y5 Canada Department of Applied Mathematics University of Waterloo Waterloo Ontario N2L 3G1 Canada

Strong local passivity is a property of multipartite quantum systems from which it is impossible to extract energy locally. Surprisingly, if the strong local passive state displays entanglement, it could be possible to locally activate energy density by adding classical communication between different partitions of the system, through so-called “quantum energy teleportation” protocols. Here, we report both the first experimental observation of local activation of energy density on an entangled state and the first realization of a quantum energy teleportation protocol using nuclear magnetic resonance on a bipartite quantum system.

关键词： Quantum correlations in quantum information Quantum entanglement Quantum information processing Quantum protocols Quantum teleportation Quantum thermodynamics Quantum many-body systems Nuclear magnetic resonance

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Thermodynamic Analysis of Algorithmic Cooling Protocols: Efficiency Metrics and Improved Designs

arXiv

引用

arXiv 2024年

作者： Lin, Junan Rodríguez-Briones, Nayeli A. Martín-Martínez, Eduardo Laflamme, Raymond National Research Council Canada TorontoON Canada Department of Chemistry University of California BerkeleyCA94720 United States Miller Institute for Basic Research in Science 468 Donner Lab BerkeleyCA94720 United States Institute for Quantum Computing University of Waterloo WaterlooONN2L 3G1 Canada Department of Applied Mathematics University of Waterloo WaterlooONN2L 3G1 Canada Perimeter Institute for Theoretical Physics WaterlooONN2L 2Y5 Canada Department of Physics and Astronomy University of Waterloo WaterlooONN2L 3G1 Canada

Algorithmic cooling (AC) protocols have been predominantly studied for their cooling capabilities, with limited attention paid to their thermodynamic properties. This work explores a novel perspective by analyzing a broad family of AC protocols from a thermodynamic standpoint. First, we give an in-depth review and formal classification of standard AC protocols. Leveraging the transfer matrix formalism, we achieve a consistent calculation of performance metrics, encompassing both cooling limits and target state evolution. We obtained a unification of these diverse cooling limits into a single, coherent mathematical expression, streamlining comparative analyses. Then, to assess the efficiency of coherent cooling protocols, we introduce two generic metrics: the coefficient of performance K and the Landauer Ratio RL, and establish a direct interrelation. Applying these metrics, we thoroughly evaluate selected AC protocols, highlighting their relative strengths. Finally, we propose improved versions of AC protocols that exhibit enhanced thermodynamic performance, achieving desired target temperatures with lower work inputs. This research contributes to a deeper understanding of AC protocols and provides valuable insights for designing efficient cooling strategies in various applications. © 2024, CC BY-NC-SA.

关键词： Cooling

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Efficiently improving the performance of noisy quantum computers

arXiv

引用

arXiv 2022年

作者： Ferracin, Samuele Hashim, Akel Ville, Jean-Loup Naik, Ravi Carignan-Dugas, Arnaud Qassim, Hammam Morvan, Alexis Santiago, David I. Siddiqi, Irfan Wallman, Joel J. Keysight Technologies Canada KanataONK2K 2W5 Canada Department of Applied Mathematics University of Waterloo WaterlooONN2L 3G1 Canada Quantum Nanoelectronics Laboratory Dept. of Physics University of California at Berkeley BerkeleyCA94720 United States Applied Math and Computational Research Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Materials Sciences Division Lawrence Berkeley National Lab BerkeleyCA94720 United States IBM Quantum Canada Alice & Bob United States Google Quantum AI United States ORCA Computing Canada

Using near-term quantum computers to achieve a quantum advantage requires efficient strategies to improve the performance of the noisy quantum devices presently available. We develop and experimentally validate two efficient error mitigation protocols named "Noiseless Output Extrapolation" and "Pauli Error Cancellation" that can drastically enhance the performance of quantum circuits composed of noisy cycles of gates. By combining popular mitigation strategies such as probabilistic error cancellation and noise amplification with efficient noise reconstruction methods, our protocols can mitigate a wide range of noise processes that do not satisfy the assumptions underlying existing mitigation protocols, including non-local and gate-dependent processes. We test our protocols on a four-qubit superconducting processor at the Advanced Quantum Testbed. We observe significant improvements in the performance of both structured and random circuits, with up to 86% improvement in variation distance over the unmitigated outputs. Our experiments demonstrate the effectiveness of our protocols, as well as their practicality for current hardware platforms. © 2022, CC BY.

关键词： Quantum computers

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Leveraging randomized compiling for the quantum imaginary-time-evolution algorithm

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Physical Review Research 2022年第3期4卷 033140-033140页

作者： Jean-Loup Ville Alexis Morvan Akel Hashim Ravi K. Naik Marie Lu Bradley Mitchell John-Mark Kreikebaum Kevin P. O'Brien Joel J. Wallman Ian Hincks Joseph Emerson Ethan Smith Ed Younis Costin Iancu David I. Santiago Irfan Siddiqi Quantum Nanoelectronics Laboratory Dept. of Physics University of California at Berkeley Berkeley California 94720 USA Computational Research Division Lawrence Berkeley National Lab Berkeley California 94720 USA Materials Sciences Division Lawrence Berkeley National Lab Berkeley California 94720 USA Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Inst. for Quantum Computing and Dept. of Applied Mathematics University of Waterloo Waterloo Ontario Canada N2L 3G1 Quantum Benchmark Inc. Kitchener Ontario Canada N2H 5G5

Recent progress in noisy intermediate-scale quantum (NISQ) hardware shows that quantum devices may be able to tackle complex problems even without error correction. However, coherent errors due to the increased complexity of these devices is an outstanding issue. They can accumulate through a circuit, making their impact on algorithms hard to predict and mitigate. Iterative algorithms like quantum imaginary time evolution are susceptible to these errors. This article presents the combination of both noise tailoring using randomized compiling and error mitigation with purification. We also show that cycle benchmarking gives an estimate of the reliability of the purification. We apply this method to the quantum imaginary time evolution of a transverse field Ising model and report an energy estimation error and a ground-state infidelity both below 1%. Our methodology is general and can be used for other algorithms and platforms. We show how combining noise tailoring and error mitigation will push forward the performance of NISQ devices.

关键词： Measurement-based quantum computing Quantum algorithms Quantum benchmarking Quantum computation Quantum control Quantum information processing Quantum simulation

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Experimental Activation of Strong Local Passive States with Quantum Information

arXiv

引用

arXiv 2022年

作者： Rodríguez-Briones, Nayeli A. Katiyar, Hemant Martín-Martínez, Eduardo Laflamme, Raymond Department of Chemistry University of California BerkeleyCA94720 United States Miller Institute for Basic Research in Science 468 Donner Lab BerkeleyCA94720 United States Institute for Quantum Computing University of Waterloo WaterlooONN2L 3G1 Canada Department of Physics & Astronomy University of Waterloo WaterlooONN2L 3G1 Canada Perimeter Institute for Theoretical Physics 31 Caroline St. N. WaterlooONN2L 2Y5 Canada Department of Applied Mathematics University of Waterloo WaterlooONN2L 3G1 Canada

Strong local passivity is a property of multipartite quantum systems from which it is impossible to extract energy locally. Surprisingly, if the strong local passive state displays entanglement, it could be possible to locally activate energy density by adding classical communication between different partitions of the system, through so-called "quantum energy teleportation" protocols. Here, we report both the first experimental observation of local activation of energy density on an entangled state and the first realization of a quantum energy teleportation protocol using nuclear magnetic resonance on a bipartite quantum system. Copyright © 2022, The Authors. All rights reserved.

关键词： Activation energy

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Randomized Compiling for Scalable Quantum computing on a Noisy Superconducting Quantum Processor

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Physical Review X 2021年第4期11卷 041039-041039页

作者： Akel Hashim Ravi K. Naik Alexis Morvan Jean-Loup Ville Bradley Mitchell John Mark Kreikebaum Marc Davis Ethan Smith Costin Iancu Kevin P. O’Brien Ian Hincks Joel J. Wallman Joseph Emerson Irfan Siddiqi Quantum Nanoelectronics Laboratory Department of Physics University of California at Berkeley Berkeley California 94720 USA Graduate Group in Applied Science and Technology University of California at Berkeley Berkeley California 94720 USA Computational Research Division Lawrence Berkeley National Lab Berkeley California 94720 USA Materials Sciences Division Lawrence Berkeley National Lab Berkeley California 94720 USA Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge Massachusetts 02142 USA Quantum Benchmark Inc. Kitchener Ontario N2H 5G5 Canada Keysight Technologies Canada Kanata Ontario K2K 2W5 Canada Institute for Quantum Computing and Department of Applied Mathematics University of Waterloo Waterloo Ontario N2L 3G1 Canada

The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic miscalibrations, drift, and crosstalk in the control of qubits can lead to a coherent form of error that has no classical analog. Coherent errors severely limit the performance of quantum algorithms in an unpredictable manner, and mitigating their impact is necessary for realizing reliable quantum computations. Moreover, the average error rates measured by randomized benchmarking and related protocols are not sensitive to the full impact of coherent errors and therefore do not reliably predict the global performance of quantum algorithms, leaving us unprepared to validate the accuracy of future large-scale quantum computations. Randomized compiling is a protocol designed to overcome these performance limitations by converting coherent errors into stochastic noise, dramatically reducing unpredictable errors in quantum algorithms and enabling accurate predictions of algorithmic performance from error rates measured via cycle benchmarking. In this work, we demonstrate significant performance gains under randomized compiling for the four-qubit quantum Fourier transform algorithm and for random circuits of variable depth on a superconducting quantum processor. Additionally, we accurately predict algorithm performance using experimentally measured error rates. Our results demonstrate that randomized compiling can be utilized to leverage and predict the capabilities of modern-day noisy quantum processors, paving the way forward for scalable quantum computing.

关键词： Quantum algorithms Quantum benchmarking Quantum control Quantum information with solid state qubits

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The unbearable hardness of unknotting 35

The unbearable hardness of unknotting

引用

35th International Symposium on Computational Geometry, SoCG 2019

作者： de Mesmay, Arnaud Rieck, Yo'av Sedgwick, Eric Tancer, Martin Univ. Grenoble Alpes CNRS Grenoble INP1 GIPSA-lab Grenoble38000 France Department of Mathematical Sciences University of Arkansas FayettevilleAR72701 United States School of Computing DePaul University 243 S. Wabash Ave ChicagoIL60604 United States Department of Applied Mathematics Charles University Malostranské nám. 25 Praha 1118 00 Czech Republic

ISBN: (纸本)9783959771047

We prove that deciding if a diagram of the unknot can be untangled using at most k Reidemeister moves (where k is part of the input) is NP-hard. We also prove that several natural questions regarding links in the 3-sphere are NP-hard, including detecting whether a link contains a trivial sublink with n components, computing the unlinking number of a link, and computing a variety of link invariants related to four-dimensional topology (such as the 4-ball Euler characteristic, the slicing number, and the 4-dimensional clasp number). © Arnaud de Mesmay, Yo’av Rieck, Eric Sedgwick, and Martin Tancer.

关键词： Intermediate invariants Knot Link NP-hard Reidemeister move Unknot recognition Unlinking number

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