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arXiv 2020年

作者： Huang, Xing Ma, Chen-Te Shu, Hongfei Wu, Chih-Hung Institute of Modern Physics Northwest University Xi'An710069 China Shaanxi Key Laboratory for Theoretical Physics Frontiers Xi'An710069 China NSFC-SPTP Peng Huanwu Center for Fundamental Theory Xi'An710127 China Asia Pacific Center for Theoretical Physics Pohang University of Science and Technology Gyeongsangbuk-do Pohang37673 Korea Republic of Guangdong Provincial Key Laboratory of Nuclear Science Institute of Quantum Matter South China Normal University Guangdong Guangzhou510006 China School of Physics and Telecommunication Engineering South China Normal University Guangdong Guangzhou510006 China Guangdong-Hong Kong Joint Laboratory of Quantum Matter Southern Nuclear Science Computing Center South China Normal University Guangzhou510006 China The Laboratory for Quantum Gravity and Strings Department of Mathematics and Applied Mathematics University of Cape Town Private Bag Rondebosch7700 South Africa Beijing101408 China Tsinghua University Beijing100084 China Nordita KTH Royal Institute of Technology Stockholm University Roslagstullsbacken 23 StockholmSE-106 91 Sweden Department of Physics Tokyo Institute of Technology Tokyo152-8551 Japan Department of Physics University of California Santa BarbaraCA93106 United States

We first derive the boundary theory from the U(1) Chern-Simons theory. The boundary action on an n-sheet manifold appears from its back-reaction of the Wilson line. The reason is that the U(1) Chern-Simons theory can provide an exact effective action when introducing the Wilson line. The Wilson line in the pure AdS3 Einstein gravity is equivalent to entanglement entropy in the boundary theory up to classical gravity. The U(1) Chern-Simons theory deviates by a self-interaction term from the gauge formulation on the boundary. We also compare the Hayward term in the SL(2) Chern-Simons formulation to the Wilson line approach. Introducing two wedges can reproduce the entanglement entropy for a single interval at the classical level. We propose quantum generalization by combining the bulk and Hayward terms. The quantum correction of the partition function vanishes. In the end, we calculate the entanglement entropy for a single interval. The pure AdS3 Einstein gravity theory shows a shift of central charge by 26 at the one-loop level. The U(1) Chern-Simons theory does not show a shift from the quantum effect. The result is the same in the weak gravitational constant limit. The non-vanishing quantum correction shows that the Hayward term is incorrect. Copyright © 2020, The Authors. All rights reserved.

关键词： Entropy

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Topological Insulators in Twisted Transition Metal Dichalcogenide Homobilayers

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Physical Review Letters 2019年第8期122卷 086402-086402页

作者： Fengcheng Wu Timothy Lovorn Emanuel Tutuc Ivar Martin A. H. MacDonald Materials Science Division Argonne National Laboratory Argonne Illinois 60439 USA Condensed Matter Theory Center and Joint Quantum Institute Department of Physics University of Maryland College Park Maryland 20742 USA Department of Physics University of Texas at Austin Austin Texas 78712 USA Department of Electrical and Computer Engineering Microelectronics Research Center The University of Texas at Austin Austin Texas 78758 USA

We show that moiré bands of twisted homobilayers can be topologically nontrivial, and illustrate the tendency by studying valence band states in ±K valleys of twisted bilayer transition metal dichalcogenides, in particular, bilayer MoTe2. Because of the large spin-orbit splitting at the monolayer valence band maxima, the low energy valence states of the twisted bilayer MoTe2 at the +K (−K) valley can be described using a two-band model with a layer-pseudospin magnetic field Δ(r) that has the moiré period. We show that Δ(r) has a topologically nontrivial skyrmion lattice texture in real space, and that the topmost moiré valence bands provide a realization of the Kane-Mele quantum spin-Hall model, i.e., the two-dimensional time-reversal-invariant topological insulator. Because the bands narrow at small twist angles, a rich set of broken symmetry insulating states can occur at integer numbers of electrons per moiré cell.

关键词： Electronic structure Kane-Mele model quantum spin Hall effect Topological insulators Transition metal dichalcogenides Two-dimensional electron system

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quantum circuit approximations and entanglement renormalization for the Dirac field in 1+1 dimensions

arXiv

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arXiv 2019年

作者： Witteveen, Freek Scholz, Volkher Swingle, Brian Walter, Michael Korteweg-de Vries Institute for Mathematics and QuSoft University of Amsterdam Netherlands Department of Physics Ghent University Belgium Condensed Matter Theory Center Maryland Center for Fundamental Physics Joint Center for Quantum Information and Computer Science Department of Physics University of Maryland United States Institute for Theoretical Physics Institute for Language Logic and Computation University of Amsterdam Netherlands

The multiscale entanglement renormalization ansatz describes quantum many-body states by a hierarchical entanglement structure organized by length scale. Numerically, it has been demonstrated to capture critical lattice models and the data of the corresponding conformal field theories with high accuracy. However, a rigorous understanding of its success and precise relation to the continuum is still lacking. To address this challenge, we provide an explicit construction of entanglement-renormalization quantum circuits that rigorously approximate correlation functions of the massless Dirac conformal field theory. We directly target the continuum theory: discreteness is introduced by our choice of how to probe the system, not by any underlying short-distance lattice regulator. To achieve this, we use multiresolution analysis from wavelet theory to obtain an approximation scheme and to implement entanglement renormalization in a natural way. This could be a starting point for constructing quantum circuit approximations for more general conformal field theories. Copyright © 2019, The Authors. All rights reserved.

关键词： Continuum mechanics

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From independent sets and vertex colorings to isotropic spaces and isotropic decompositions: Another bridge between graphs and alternating matrix spaces

arXiv

引用

arXiv 2019年

作者： Bei, Xiaohui Chen, Shiteng Guan, Ji Qiao, Youming Sun, Xiaoming School of Physical and Mathematical Sciences Nanyang Technological University Singapore State Key Laboratory of Computer Science Institute of Software Chinese Academy of Sciences Beijing China Centre for Quantum Software and Information University of Technology Sydney Australia Institute of Computing Technology Chinese Academy of Sciences University of Chinese Academy of Sciences Beijing China

In the 1970's, Lovász built a bridge between graphs and alternating matrix spaces, in the context of perfect matchings (FCT 1979). A similar connection between bipartite graphs and matrix spaces plays a key role in the recent resolutions of the non-commutative rank problem (Garg-Gurvits-Oliveira-Wigderson, FOCS 2016;Ivanyos-Qiao-Subrahmanyam, ITCS 2017). In this paper, we lay the foundation for another bridge between graphs and alternating matrix spaces, in the context of independent sets and vertex colorings. The corresponding structures in alternating matrix spaces are isotropic spaces and isotropic decompositions, both useful structures in group theory and manifold theory. We first show that the maximum independent set problem and the vertex c-coloring problem reduce to the maximum isotropic space problem and the isotropic c-decomposition problem, respectively. Next, we show that several topics and results about independent sets and vertex colorings have natural correspondences for isotropic spaces and decompositions. These include algorithmic problems, such as the maximum independent set problem for bipartite graphs, and exact exponential-time algorithms for the chromatic number, as well as mathematical questions, such as the number of maximal independent sets, and the relation between the maximum degree and the chromatic number. These connections lead to new interactions between graph theory and algebra. Some results have concrete applications to group theory and manifold theory, and we initiate a variant of these structures in the context of quantum information theory. Finally, we propose several open questions for further exploration. Copyright © 2019, The Authors. All rights reserved.

关键词： Group theory

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On speeding up factoring with quantum SAT solvers

arXiv

引用

arXiv 2019年

作者： Mosca, Michele Basso, João Marcos Vensi Verschoor, Sebastian R. Institute for Quantum Computing University of Waterloo Canada Department of Physics and Astronomy Tufts University United States Department of Combinatorics & Optimization University of Waterloo Canada Perimeter Institute for Theoretical Physics Waterloo Canada evolutionQ Inc. Waterloo Canada David R. Cheriton School of Computer Science University of Waterloo Canada

There have been several efforts to apply quantum SAT solving methods to factor large integers. While these methods may provide insight into quantum SAT solving, to date they have not led to a convincing path to integer factorization that is competitive with the best known classical method, the Number Field Sieve. Many of the techniques tried involved directly encoding multiplication to SAT or an equivalent NP-hard problem and looking for satisfying assignments of the variables representing the prime factors. The main challenge in these cases is that, to compete with the Number Field Sieve, the quantum SAT solver would need to be superpolynomially faster than classical SAT solvers. In this paper the use of SAT solvers is restricted to a smaller task related to factoring: finding smooth numbers, which is an essential step of the Number Field Sieve. We present a SAT circuit that can be given to quantum SAT solvers such as annealers in order to perform this step of factoring. If quantum SAT solvers achieve any speedup over classical brute-force search, then our factoring algorithm is faster than the classical NFS. Copyright © 2019, The Authors. All rights reserved.

关键词： Model checking

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Roadmap on quantum nanotechnologies

arXiv

引用

arXiv 2021年

作者： Laucht, Arne Hohls, Frank Ubbelohde, Niels Fernando Gonzalez-Zalba, M. Reilly, David J. Stobbe, Søren Schröder, Tim Scarlino, Pasquale Koski, Jonne V. Dzurak, Andrew Yang, Chih-Hwan Yoneda, Jun Kuemmeth, Ferdinand Bluhm, Hendrik Pla, Jarryd Hill, Charles Salfi, Joe Oiwa, Akira Muhonen, Juha T. Verhagen, Ewold LaHaye, M.D. Kim, Hyun Ho Tsen, Adam W. Culcer, Dimitrie Geresdi, Attila Mol, Jan A. Mohan, Varun Jain, Prashant K. Baugh, Jonathan Centre for Quantum Computation and Communication Technology School of Electrical Engineering and Telecommunications UNSW SydneyNSW2052 Australia Physikalisch-Technische Bundesanstalt Braunschweig38116 Germany Quantum Motion Technologies Nexus Discovery Way LeedsLS2 3AA United Kingdom School of Physics University of Sydney SydneyNSW2006 Australia Microsoft Corporation Station Q Sydney University of Sydney SydneyNSW2006 Australia Department of Photonics Engineering DTU Fotonik Technical University of Denmark Building 343 Kgs. LyngbyDK-2800 Denmark Department of Physics Humboldt-Universität zu Berlin Berlin12489 Germany Department of Physics ETH Zürich ZürichCH-8093 Switzerland Niels Bohr Institute University of Copenhagen Copenhagen2100 Denmark JARA-FIT Institute for Quantum Information RWTH Aachen University and Forschungszentrum Jülich Aachen52074 Germany School of Physics University of Melbourne Melbourne Australia Department of Electrical and Computer Engineering The University of British Columbia VancouverBCV6T 1Z4 Canada The Institute of Scientific and Industrial Research Osaka University Ibaraki Osaka567-0047 Japan Center for Quantum Information and Quantum Biology Institute for open and Transdisciplinary Research Initiative Osaka University Osaka560-8531 Japan Center for Nanophotonics AMOLF Amsterdam1098 XG Netherlands School of Physics The University of New South Wales Sydney2052 Australia Australian Research Council Centre of Excellence in Future Low-Energy Electronics Technologies UNSW Node The University of New South Wales Sydney2052 Australia QuTech and Kavli Institute of Nanoscience Delft University of Technology Delft2600 GA Netherlands School of Physics and Astronomy Queen Mary University of London E1 4NS United Kingdom Department of Materials Science and Engineering University of Illinois at Urbana-Champaign UrbanaIL61801 United States Department of Chemistry University of Illinois at Urbana-Champaign Urbana

quantum phenomena are typically observable at length and time scales smaller than those of our everyday experience, often involving individual particles or excitations. The past few decades have seen a revolution in the ability to structure matter at the nanoscale, and experiments at the single particle level have become commonplace. This has opened wide new avenues for exploring and harnessing quantum mechanical effects in condensed matter. These quantum phenomena, in turn, have the potential to revolutionize the way we communicate, compute and probe the nanoscale world. Here, we review developments in key areas of quantum research in light of the nanotechnologies that enable them, with a view to what the future holds. Materials and devices with nanoscale features are used for quantum metrology and sensing, as building blocks for quantum computing, and as sources and detectors for quantum communication. They enable explorations of quantum behaviour and unconventional states in nano- and opto-mechanical systems, low-dimensional systems, molecular devices, nano-plasmonics, quantum electrodynamics, scanning tunnelling microscopy, and more. This rapidly expanding intersection of nanotechnology and quantum science/technology is mutually beneficial to both fields, laying claim to some of the most exciting scientific leaps of the last decade, with more on the horizon. © 2021, CC BY.

关键词： quantum computers

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The influence of high-energy local orbitals and electron-phonon interactions on the band gaps and optical spectra of hexagonal boron nitride

arXiv

引用

arXiv 2020年

作者： Shen, Tong Zhang, Xiao-Wei Shang, Honghui Zhang, Min-Ye Wang, Xinqiang Wang, En-Ge Jiang, Hong Li, Xin-Zheng State Key Laboratory for Artificial Microstructure and Mesoscopic Physics Frontier Science Center for Nano-optoelectronics School of Physics Peking University Beijing China International Center for Quantum Materials and School of Physics Peking University Beijing China State Key Laboratory of Computer Architecture Institute of Computing Technology Chinese Academy of Sciences Beijing China Beijing National Laboratory for Molecular Sciences College of Chemistry and Molecular Engineering Peking University Beijing China Collaborative Innovation Center of Quantum Matter Peking University Beijing100871 China Ceramic Division Songshan Lake Lab Institute of Physics Chinese Academy of Sciences Guangdong China School of Physics Liaoning University Shenyang China Beijing National Laboratory for Molecular Sciences College of Chemistry and Molecular Engineering Peking University Beijing China Collaborative Innovation Center of Quantum Matter Peking University Beijing China

We report ab initio band diagram and optical absorption spectra of hexagonal boron nitride (h-BN), focusing on unravelling how the completeness of basis set for GW calculations and how electron-phonon interactions (EPIs) impact on them. The completeness of basis set, an issue which was seldom discussed in previous optical spectra calculations of h-BN, is found crucial in providing converged quasiparticle band gaps. In the comparison among three different codes, we demonstrate that by including high-energy local orbitals in the all-electron linearized augmented plane waves based GW calculations, the quasiparticle direct and fundamental indirect band gaps are widened by ∼0.2 eV, giving values of 6.81 eV and 6.25 eV respectively at the GW0 level. EPIs, on the other hand, reduce them to 6.62 eV and 6.03 eV respectively at 0 K, and 6.60 eV and 5.98 eV respectively at 300 K. With clamped crystal structure, the first peak of the absorption spectrum is at 6.07 eV, originating from the direct exciton contributed by electron transitions around K in the Brillouin zone. After including the EPIs-renormalized quasiparticles in the Bethe-Salpeter equation, the exciton-phonon coupling shifts the first peak to 5.83 eV at 300 K, lower than the experimental value of ∼6.00 eV. This accuracy is acceptable to an ab initio description of excited states with no fitting parameter. Copyright © 2020, The Authors. All rights reserved.

关键词： III-V semiconductors

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The speed of quantum information spreading in chaotic systems

arXiv

引用

arXiv 2019年

作者： Couch, Josiah Eccles, Stefan Nguyen, Phuc Swingle, Brian Xu, Shenglong Weinberg Theory Group Department of Physics University of Texas at Austin AustinTX United States Maryland Center for Fundamental Physics University of Maryland College ParkMD20742 United States Condensed Matter Theory Center Maryland Center for Fundamental Physics Joint Institute for Quantum Information and Computer Science Department of Physics University of Maryland College Park United States Condensed Matter Theory Center Department of Physics University of Maryland College Park United States

We present a general theory of quantum information propagation in chaotic quantum many-body systems. The generic expectation in such systems is that quantum information does not propagate in localized form;instead, it tends to spread out and scramble into a form that is inaccessible to local measurements. To characterize this spreading, we define an information speed via a quench-type experiment and derive a general formula for it as a function of the entanglement density of the initial state. As the entanglement density varies from zero to one, the information speed varies from the entanglement speed to the butterfly speed. We verify that the formula holds both for a quantum chaotic spin chain and in field theories with an AdS/CFT gravity dual. For the second case, we study in detail the dynamics of entanglement in two-sided Vaidya-AdSReissner-Nordstrom black branes. We also show that, with an appropriate decoding process, quantum information can be construed as moving at the information speed, and, in the case of AdS/CFT, we show that a locally detectable signal propagates at the information speed in a spatially local variant of the traversable wormhole setup. Copyright © 2019, The Authors. All rights reserved.

关键词： Speed

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Entanglement entropy, quantum fluctuations, and thermal entropy in topological phases

arXiv

引用

arXiv 2019年

作者： Hu, Yuting Wan, Yidun State Key Laboratory of Surface Physics Fudan University Shanghai200433 China Department of Physics Center for Field Theory and Particle Physics Fudan University Shanghai200433 China Institute for Nanoelectronic Devices and Quantum Computing Fudan University Shanghai200433 China Department of Physics Institute for Quantum Science and Engineering Southern University of Science and Technology Shenzhen518055 China CAS Key Laboratory of Microscale Magnetic Resonance Department of Modern Physics University of Science and Technology of China Hefei Anhui230026 China Collaborative Innovation Center of Advanced Microstructures Nanjing210093 China

Entanglement entropy in topologically ordered matter phases has been computed extensively using various methods. In this paper, we study the entanglement entropy of topological phases in two-spaces from a new perspective-the perspective of quasiparticle fluctuations. In this picture, the entanglement spectrum of a topologically ordered system is identified with the spectrum of quasiparticle fluctuations of the system, and the entanglement entropy measures the maximal quasiparticle fluctuations on the EB. As a consequence, entanglement entropy corresponds to the thermal entropy of the quasiparticles at infinite temperature on the entanglement boundary. We corroborates our results with explicit computation in the quantum double model with/without boundaries. We then systematically construct the reduced density matrices of the quantum double model on generic 2-surfaces with boundaries. Copyright © 2019, The Authors. All rights reserved.

关键词： Entropy

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Variational quantum circuits for quantum state tomography

arXiv

引用

arXiv 2019年

作者： Liu, Yong Wang, Dongyang Xue, Shichuan Huang, Anqi Fu, Xiang Qiang, Xiaogang Xu, Ping Huang, He-Liang Deng, Mingtang Guo, Chu Yang, Xuejun Wu, Junjie Institute for Quantum Information & State Key Laboratory of High Performance Computing College of Computer National University of Defense Technology Changsha410073 China National Innovation Institute of Defense Technology AMS Beijing100071 China Henan Key Laboratory of Quantum Information and Cryptography IEU Zhengzhou450001 China Hefei National Laboratory for Physical Sciences at Microscale Department of Modern Physics University of Science and Technology of China HefeiAnhui230026 China CAS Centre for Excellence Synergetic Innovation Centre in Quantum Information and Quantum Physics University of Science and Technology of China Hefei Anhui230026 China Quantum Intelligence Lab Supremacy Future Technologies Guangzhou511340 China

We propose a hybrid quantum-classical algorithm for quantum state tomography. Given an unknown quantum state, a quantum machine learning algorithm is used to maximize the fidelity between the output of a variational quantum circuit and this state. The number of parameters of the variational quantum circuit grows linearly with the number of qubits and the circuit depth. After that, a subsequent classical algorithm is used to reconstruct the unknown quantum state. We demonstrate our method by performing numerical simulations to reconstruct the ground state of a one-dimensional quantum spin chain, using a variational quantum circuit simulator. Our method is suitable for near-term quantum computing platforms, and could be used for relatively large-scale quantum state tomography for experimentally relevant quantum states. Copyright © 2019, The Authors. All rights reserved.

关键词： Numerical methods

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