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Quantification of Entanglement and Coherence with Purity Detection

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arXiv 2023年

作者： Zhang, Ting Smith, Graeme Smolin, John A. Liu, Lu Peng, Xu-Jie Zhao, Qi Girolami, Davide Ma, Xiongfeng Yuan, Xiao Lu, He School of Physics State Key Laboratory of Crystal Materials Shandong University Jinan250100 China JILA University of Colorado/NIST 440 UCB BoulderCO80309 United States Center for Theory of Quantum Matter University of Colorado BoulderCO80309 United States Department of Physics University of Colorado 390 UCB BoulderCO80309 United States IBM T.J. Watson Research Center 1101 Kitchawan Road Yorktown HeightsNY10598 United States QICI Quantum Information and Computation Initiative Department of Computer Science The University of Hong Kong Pokfulam Road Hong Kong DISAT Politecnico di Torino Corso Duca degli Abruzzi 24 Torino10129 Italy Center for Quantum Information Institute for Interdisciplinary Information Sciences Tsinghua University Beijing100084 China Center on Frontiers of Computing Studies Peking University Beijing100871 China School of Computer Science Peking University Beijing100871 China Shenzhen Research Institute of Shandong University Shenzhen518057 China

Entanglement and coherence are fundamental properties of quantum systems, promising to power the near future quantum technologies. Yet, their quantification, rather than mere detection, generally requires reconstructing the spectrum of quantum states, i.e., experimentally challenging measurement sets that increase exponentially with the system size. Here, we demonstrate quantitative bounds to operationally useful entanglement and coherence that are universally valid, analytically computable, and experimentally friendly. Specifically, our main theoretical results are lower and upper bounds to the coherent information and the relative entropy of coherence in terms of local and global purities of quantum states. To validate our proposal, we experimentally implement two purity detection methods in an optical system: shadow estimation with random measurements and collective measurements on pairs of state copies. The experiment shows that both the coherent information and the relative entropy of coherence of pure and mixed unknown quantum states can be bounded by purity functions. Our research offers an efficient means of verifying large-scale quantum information processing without spectrum reconstruction. © 2023, CC BY.

关键词： Optical systems

Experimental Simulation of Loop quantum Gravity on a Photonic Chip

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arXiv 2022年

作者： van der Meer, Reinier Huang, Zichang Anguita, Malaquias Correa Qu, Dongxue Hooijschuur, Peter Liu, Hongguang Han, Muxin Renema, Jelmer J. Cohen, Lior MESA+ Institute University of Twente P.O. box 217 Enschede7500AE Netherlands State Key Laboratory of Surface Physics Department of Physics Center for Field Theory and Particle Physics Institute for Nanoelectronic devices and Quantum Computing Fudan University Shanghai200433 China Shanghai Qi Zhi Institute Shanghai200030 China Department of Physics Florida Atlantic University 777 Glades Road Boca RatonFL33431 United States Institut für Quantengravitation Universität Erlangen-Nürnberg Staudtstr. 7/B2 Erlangen91058 Germany Department of Electrical Computer and Energy Engineering University of Colorado Boulder CO80309 United States

The unification of general relativity and quantum theory is one of the fascinating problems of modern physics. One leading solution is Loop quantum Gravity (LQG). Simulating LQG may be important for providing predictions which can then be tested experimentally. However, such complex quantum simulations cannot run efficiently on classical computers, and quantum computers or simulators are needed. Here, we experimentally demonstrate quantum simulations of spinfoam amplitudes of LQG on an integrated photonics quantum processor. We simulate a basic transition of LQG and show that the derived spinfoam vertex amplitude falls within 4% error with respect to the theoretical prediction, despite experimental imperfections. We also discuss how to generalize the simulation for more complex transitions, in realistic experimental conditions, which will eventually lead to a quantum advantage demonstration as well as expand the toolbox to investigate LQG. Copyright © 2022, The Authors. All rights reserved.

关键词： quantum computers

High-Order Randomized Compiler for Hamiltonian Simulation

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PRX quantum 2024年第2期5卷 020330-020330页

作者： Kouhei Nakaji Mohsen Bagherimehrab Alán Aspuru-Guzik Chemical Physics Theory Group Department of Chemistry University of Toronto Toronto Ontario Canada M5S 3H6 Research Center for Emerging Computing Technologies National Institute of Advanced Industrial Science and Technology (AIST) 1-1-1 Umezono Tsukuba Ibaraki 305-8568 Japan Quantum Computing Center Keio University 3-14-1 Hiyoshi Kohoku-ku Yokohama Kanagawa 223-8522 Japan Department of Computer Science University of Toronto Toronto Ontario Canada M5S 2E4 Vector Institute for Artificial Intelligence Toronto Ontario Canada M5G 1M1 Department of Chemical Engineering & Applied Chemistry University of Toronto Toronto Ontario Canada M5S 3E5 Department of Materials Science & Engineering University of Toronto Toronto Ontario Canada M5S 3E4 Canadian Institute for Advanced Research (CIFAR) Toronto Ontario Canada M5S 1M1

Hamiltonian simulation is known to be one of the fundamental building blocks of a variety of quantum algorithms such as its most immediate application, that of simulating many-body systems to extract their physical properties. In this work, we present qSWIFT, a high-order randomized algorithm for Hamiltonian simulation. In qSWIFT, the required number of gates for a given precision is independent of the number of terms in the Hamiltonian, while the systematic error is exponentially reduced with regard to the order parameter. In this respect, our qSWIFT is a higher-order counterpart of the previously proposed quantum stochastic drift protocol (qDRIFT), the number of gates in which scales linearly with the inverse of the precision required. We construct the qSWIFT channel and establish a rigorous bound for the systematic error quantified by the diamond norm. qSWIFT provides an algorithm to estimate given physical quantities by using a system with one ancilla qubit, which is as simple as other product-formula-based approaches such as regular Trotter-Suzuki decompositions and qDRIFT. Our numerical experiment reveals that the required number of gates in qSWIFT is significantly reduced compared to qDRIFT. In particular, the advantage is significant for problems where high precision is required; e.g., to achieve a systematic relative propagation error of 10−6, the required number of gates in third-order qSWIFT is 1000 times smaller than that of qDRIFT.

关键词： quantum computation quantum simulation

Efficient charge-preserving excited state preparation with variational quantum algorithms

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arXiv 2024年

作者： Chandani, Zohim Ikeda, Kazuki Kang, Zhong-Bo Kharzeev, Dmitri E. McCaskey, Alexander Palermo, Andrea Ramakrishnan, C.R. Rao, Pooja Sundaram, Ranjani G. Yu, Kwangmin NVIDIA Quantum Algorithm Engineering London United Kingdom Department of Physics University of Massachusetts Boston BostonMA02125 United States Center for Nuclear Theory Department of Physics and Astronomy Stony Brook University Stony BrookNY11794-3800 United States Co-design Center for Quantum Advantage Department of Physics and Astronomy Stony Brook University Stony BrookNY11794-3800 United States Department of Physics and Astronomy University of California Los AngelesCA90095 United States Mani L. Bhaumik Institute for Theoretical Physics University of California Los AngelesCA90095 United States Center for Quantum Science and Engineering University of California Los AngelesCA90095 United States Energy and Photon Sciences Directorate Condensed Matter and Materials Science Division Brookhaven National Laboratory UptonNY11973-5000 United States NVIDIA Quantum Computing Architecture Santa ClaraCA United States Department of Computer Science Stony Brook University Stony BrookNY11794-3800 United States NVIDIA Quantum Algorithm Engineering Santa ClaraCA United States Computational Science Initiative Brookhaven National Laboratory UptonNY11973-5000 United States

Determining the spectrum and wave functions of excited states of a system is crucial in quantum physics and chemistry. Low-depth quantum algorithms, such as the Variational quantum Eigensolver (VQE) and its variants, can be used to determine the ground-state energy. However, current approaches to computing excited states require numerous controlled unitaries, making the application of the original Variational quantum Deflation (VQD) algorithm to problems in chemistry or physics suboptimal. In this study, we introduce a charge-preserving VQD (CPVQD) algorithm, designed to incorporate symmetry and the corresponding conserved charge into the VQD framework. This results in dimension reduction, significantly enhancing the efficiency of excitedstate computations. We present benchmark results with GPU-accelerated simulations using systems up to 24 qubits, showcasing applications in high-energy physics, nuclear physics, and quantum chemistry. This work is performed on NERSC's Perlmutter system using NVIDIA's open-source platform for accelerated quantum supercomputing - CUDA-Q. © 2024, CC BY.

关键词： Wave functions

Opportunities for nuclear physics & quantum information science

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arXiv 2019年

作者： Cloët, Ian C. Dietrich, Matthew R. Cloët, Ian C. Dietrich, Matthew R. Arrington, John Bazavov, Alexei Bishof, Michael Freese, Adam Gorshkov, Alexey V. Grassellino, Anna Hafidi, Kawtar Jacob, Zubin McGuigan, Michael Meurice, Yannick Meziani, Zein-Eddine Mueller, Peter Muschik, Christine Osborn, James Otten, Matthew Petreczky, Peter Polakovic, Tomas Poon, Alan Pooser, Raphael Roggero, Alessandro Saffman, Mark VanDevender, Brent Zhang, Jiehang Zohar, Erez Physics Division Argonne National Laboratory ArgonneIL60439 United States Department of Computational Mathematics Science and Engineering Michigan State University East LansingMI48824 United States Department of Physics and Astronomy Michigan State University East LansingMI48824 United States Joint Quantum Institute NIST/University of Maryland College ParkMD20742 United States Joint Center for Quantum Information and Computer Science NIST/University of Maryland College ParkMD20742 United States Fermi National Accelerator Laboratory Batavia IL60510 United States Northwestern University EvanstonIL60208 United States Birck Nanotechnology Center and Purdue Quantum Center School of Electrical and Computer Engineering Purdue University West LafayetteIN47906 United States Computational Science Initiative Brookhaven National Laboratory UptonNY11973 United States Department of Physics and Astronomy University of Iowa Iowa CityIA52242 United States Institute for Quantum Computing and Department of Physics and Astronomy University of Waterloo West Waterloo ON Canada ALCF Argonne National Laboratory ArgonneIL60439 United States Nanoscience and Technology Division Argonne National Laboratory ArgonneIL60439 United States Physics Department Brookhaven National Laboratory UptonNY11973 United States Physics and Material Science Divisions Argonne National Laboratory ArgonneIL60439 United States Institute for Nuclear and Particle Astrophysics and Nuclear Science Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Quantum Information Science Group Computational Sciences and Engineering Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Institute for Nuclear Theory University of Washington SeattleWA98195 United States Department of Physics University of Wisconsin MadisonWI53706 United States Pacific Northwest National Laboratory RichlandWA99354 United States Max Planck Institute of Quantum Opti

This whitepaper is an outcome of the workshop Intersections between Nuclear Physics and quantum Information held at Argonne National Laboratory on 28-30 March 2018 [***/npqi2018/]. The workshop brought together 116 national and international experts in nuclear physics and quantum information science to explore opportunities for the two fields to collaborate on topics of interest to the U.S. Department of Energy (DOE) Office of Science, Office of Nuclear Physics, and more broadly to U.S. society and industry. The workshop consisted of 22 invited and 10 contributed talks, as well as three panel discussion sessions. Topics discussed included quantum computation, quantum simulation, quantum sensing, nuclear physics detectors, nuclear many-body problem, entanglement at collider energies, and lattice gauge theories. Copyright © 2019, The Authors. All rights reserved.

关键词： Lattice theory

The generative quantum eigensolver (GQE) and its application for ground state search

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arXiv 2024年

作者： Nakaji, Kouhei Kristensen, Lasse Bjørn Campos-Gonzalez-Angulo, Jorge A. Vakili, Mohammad Ghazi Huang, Haozhe Bagherimehrab, Mohsen Gorgulla, Christoph Wong, FuTe McCaskey, Alex Kim, Jin-Sung Nguyen, Thien Rao, Pooja Aspuru-Guzik, Alan Chemical Physics Theory Group Department of Chemistry University of Toronto TorontoON Canada 1-1-1 Umezono Ibaraki Tsukuba Japan Quantum Computing Center Keio University 3-14-1 Hiyoshi Kohoku-ku Kanagawa Yokohama Japan Department of Computer Science University of Toronto TorontoON Canada Vector Institute for Artificial Intelligence TorontoON Canada Department of Physics Faculty of Arts and Sciences Harvard University CambridgeMA United States Department of Structural Biology St. Jude Children’s Research Hospital MemphisTN United States Institute of Medical Science University of Toronto TorontoON Canada NVIDIA Santa ClaraCA United States Department of Chemical Engineering & Applied Chemistry University of Toronto TorontoON Canada Department of Materials Science & Engineering University of Toronto TorontoON Canada Canadian Institute for Advanced Research TorontoON Canada

We introduce the generative quantum eigensolver (GQE), a novel method for applying classical generative models for quantum simulation. The GQE algorithm optimizes a classical generative model to produce quantum circuits with desired properties. Here, we develop a transformer-based implementation, which we name the generative pre-trained transformer-based (GPT) quantum eigensolver (GPT-QE), leveraging both pre-training on existing datasets and training without any prior knowledge. We demonstrate the effectiveness of training and pre-training GPT-QE in the search for ground states of electronic structure Hamiltonians. GQE strategies can extend beyond the problem of Hamiltonian simulation into other application areas of quantum computing. Copyright © 2024, The Authors. All rights reserved.

关键词： Ground state

quantum Simulation for High-Energy Physics

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PRX quantum 2023年第2期4卷 027001-027001页

作者： Christian W. Bauer Zohreh Davoudi A. Baha Balantekin Tanmoy Bhattacharya Marcela Carena Wibe A. de Jong Patrick Draper Aida El-Khadra Nate Gemelke Masanori Hanada Dmitri Kharzeev Henry Lamm Ying-Ying Li Junyu Liu Mikhail Lukin Yannick Meurice Christopher Monroe Benjamin Nachman Guido Pagano John Preskill Enrico Rinaldi Alessandro Roggero David I. Santiago Martin J. Savage Irfan Siddiqi George Siopsis David Van Zanten Nathan Wiebe Yukari Yamauchi Kübra Yeter-Aydeniz Silvia Zorzetti Physics Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA Department of Physics Maryland Center for Fundamental Physics and the NSF Institute for Robust Quantum Simulation University of Maryland College Park Maryland 20742 USA Department of Physics University of Wisconsin Madison Wisconsin 53706 USA T-2 Los Alamos National Laboratory Los Alamos New Mexico 87545 USA Fermi National Accelerator Laboratory Batavia Illinois 60510 USA Enrico Fermi Institute University of Chicago Chicago Illinois 60637 USA Kavli Institute for Cosmological Physics University of Chicago Chicago Illinois 60637 USA Department of Physics University of Chicago Chicago Illinois 60637 USA Department of Physics and Illinois Center for the Advanced Study of the Universe and Illinois Quantum Information Science and Technology Center University of Illinois Urbana Illinois 61801 USA QuEra Computing Inc Boston Massachusetts 02135 USA Department of Mathematics University of Surrey Guildford Surrey GU2 7XH United Kingdom Center for Nuclear Theory Department of Physics and Astronomy Stony Brook University New York 11794-3800 USA Department of Physics Brookhaven National Laboratory Upton New York 11973 USA Peng Huanwu Center for Fundamental Theory Hefei Anhui 230026 China Interdisciplinary Center for Theoretical Study University of Science and Technology of China Hefei Anhui 230026 China Pritzker School of Molecular Engineering Chicago Quantum Exchange and Kadanoff Center for Theoretical Physics University of Chicago Illinois 60637 USA qBraid Co. Harper Court 5235 Chicago Illinois 60615 USA Department of Physics Harvard University Cambridge Massachusetts 02138 USA Department of Physics and Astronomy University of Iowa Iowa City Iowa 52242 USA Duke Quantum Center Duke University Durham North Carolina 27701 USA Department of Electrical and Computer Engineering Duke University Durham North Carolina 27708 USA Department of Physics Duke University

It is for the first time that quantum simulation for high-energy physics (HEP) is studied in the U.S. decadal particle-physics community planning, and in fact until recently, this was not considered a mainstream topic in the community. This fact speaks of a remarkable rate of growth of this subfield over the past few years, stimulated by the impressive advancements in quantum information sciences (QIS) and associated technologies over the past decade, and the significant investment in this area by the government and private sectors in the U.S. and other countries. High-energy physicists have quickly identified problems of importance to our understanding of nature at the most fundamental level, from tiniest distances to cosmological extents, that are intractable with classical computers but may benefit from quantum advantage. They have initiated, and continue to carry out, a vigorous program in theory, algorithm, and hardware co-design for simulations of relevance to the HEP mission. This Roadmap is an attempt to bring this exciting and yet challenging area of research to the spotlight, and to elaborate on what the promises, requirements, challenges, and potential solutions are over the next decade and beyond.

关键词： quantum simulation

Towards provably efficient quantum algorithms for large-scale machine-learning models

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arXiv 2023年

作者： Liu, Junyu Liu, Minzhao Liu, Jin-Peng Ye, Ziyu Wang, Yunfei Alexeev, Yuri Eisert, Jens Jiang, Liang Pritzker School of Molecular Engineering The University of Chicago ChicagoIL60637 United States Department of Computer Science The University of Chicago ChicagoIL60637 United States Chicago Quantum Exchange ChicagoIL60637 United States Kadanoff Center for Theoretical Physics The University of Chicago ChicagoIL60637 United States qBraid Co. ChicagoIL60615 United States SeQure ChicagoIL60615 United States Department of Physics The University of Chicago ChicagoIL60637 United States Computational Science Division Argonne National Laboratory LemontIL60439 United States Simons Institute for the Theory of Computing University of California BerkeleyCA94720 United States Department of Mathematics University of California BerkeleyCA94720 United States Center for Theoretical Physics Massachusetts Institute of Technology CambridgeMA02139 United States Martin A. Fisher School of Physics Brandeis University WalthamMA02453 United States Dahlem Center for Complex Quantum Systems Free University Berlin Berlin14195 Germany

Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that fault-tolerant quantum computing could possibly provide provably efficient resolutions for generic (stochastic) gradient descent algorithms, scaling as O(T2 × polylog(n)), where n is the size of the models and T is the number of iterations in the training, as long as the models are both sufficiently dissipative and sparse, with small learning rates. Based on earlier efficient quantum algorithms for dissipative differential equations, we find and prove that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. In practice, we benchmark instances of large machine learning models from 7 million to 103 million parameters. We find that, in the context of sparse training, a quantum enhancement is possible at the early stage of learning after model pruning, motivating a sparse parameter download and re-upload scheme. Our work shows solidly that faulttolerant quantum algorithms could potentially contribute to most state-of-the-art, large-scale machine-learning problems. Copyright © 2023, The Authors. All rights reserved.

关键词： Differential equations

Two-kind boson mixture honeycomb Hamiltonian of Bloch exciton-polaritons

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Physical Review B 2019年第4期99卷 045302-045302页

作者： Haining Pan K. Winkler Mats Powlowski Ming Xie A. Schade M. Emmerling M. Kamp S. Klembt C. Schneider Tim Byrnes S. Höfling Na Young Kim Institute for Quantum Computing University of Waterloo 200 University Ave. West Waterloo ON Canada N2L 3G1 Condensed Matter Theory Center and Joint Quantum Institute Department of Physics University of Maryland College Park Maryland 20742 USA Technische Physik Physikalisches Institut Universität Würzbug D-97074 Würzburg Germany Department of Electrical and Computer Engineering University of Waterloo 200 University Ave. West Waterloo ON Canada N2L 3G1 Department of Physics The University of Texas at Austin Austin Texas 78712 USA State Key Laboratory of Precision Spectroscopy School of Physical and Material Sciences East China Normal University Shanghai 200062 China New York University Shanghai 1555 Century Ave. Pudong Shanghai 200122 China NYU-ECNU Institute of Physics at NYU Shanghai 366 Zhongshan Road North Shanghai 200062 China Department of Physics New York University New York New York 10003 USA School of Physics and Astronomy University of St. Andrews St. Andrews KY16 9SS United Kingdom Department of Physics and Astronomy University of Waterloo 200 University Ave. West Waterloo ON Canada N2L 3G1 Department of Chemistry University of Waterloo 200 University Ave. West Waterloo ON Canada N2L 3G1

The electronic band structure of a solid is a collection of allowed bands separated by forbidden bands, revealing the geometric symmetry of the crystal structures. Comprehensive knowledge of the band structure with band parameters explains intrinsic physical, chemical, and mechanical properties of the solid. Here we report the artificial polaritonic band structures of two-dimensional honeycomb lattices for microcavity exciton-polaritons using GaAs semiconductors in the wide-range detuning values, from cavity photonlike (red-detuned) to excitonlike (blue-detuned) regimes. In order to understand the experimental band structures and their band parameters, such as gap energies, bandwidths, hopping integrals, and density of states, we originally establish a polariton band theory within an augmented plane wave method with two-kind bosons, cavity photons trapped at the lattice sites, and freely moving excitons. In particular, this two-kind band theory is absolutely essential to elucidate the exciton effect in the band structures of blue-detuned exciton-polaritons, where the flattened excitonlike dispersion appears at larger in-plane momentum values captured in our experimental access window. We reach an excellent agreement between theory and experiments in all detuning values.

关键词： Band gap Electronic structure Polaritons quantum wells