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arXiv 2020年

作者： Tong, Yu An, Dong Wiebe, Nathan Lin, Lin Department of Mathematics University of California BerkeleyCA94720 United States Department of Computer Science University of Toronto TorontoON Canada Department of Physics M5S 1A1 University of Washington SeattleWA98195 United States High Performance Computing Division Pacific Northwest National Laboratory RichlandWA99354 United States Department of Mathematics Challenge Institute for Quantum Computation University of California Berkeley Computational Research Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States

Preconditioning is the most widely used and effective way for treating ill-conditioned linear systems in the context of classical iterative linear system solvers. We introduce a quantum primitive called fast inversion, which can be used as a preconditioner for solving quantum linear systems. The key idea of fast inversion is to directly block-encode a matrix inverse through a quantum circuit implementing the inversion of eigenvalues via classical arithmetics. We demonstrate the application of preconditioned linear system solvers for computing single-particle Green's functions of quantum many-body systems, which are widely used in quantum physics, chemistry, and materials science. We analyze the complexities in three scenarios: the Hubbard model, the quantum many-body Hamiltonian in the planewave-dual basis, and the Schwinger model. We also provide a method for performing Green's function calculation in second quantization within a fixed particle manifold and note that this approach may be valuable for simulation more broadly. Besides solving linear systems, fast inversion also allows us to develop fast algorithms for computing matrix functions, such as the efficient preparation of Gibbs states. We introduce two efficient approaches for such a task, based on the contour integral formulation and the inverse transform respectively. Copyright © 2020, The Authors. All rights reserved.

关键词： Inverse problems

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Chaos in a quantum rotor model

arXiv

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arXiv 2019年

作者： Cheng, Gong Swingle, Brian Condensed Matter Theory Center and Department of Physics University of Maryland College ParkMD20742 United States Maryland Center for Fundamental Physics Joint Center for Quantum Information and Computer Science College ParkMD20742 United States Institute for Advanced Study PrincetonNJ08540 United States

We study scrambling in a model consisting of a number N of M-component quan- tum rotors coupled by random infinite-range interactions. This model is known to have both a paramagnetic phase and a spin glass phase separated by second order phase transition. We calculate in perturbation theory the squared commutator of rotor fields at different sites in the paramagnetic phase, to leading non-trivial order at large N and large M. This quantity diagnoses the onset of quantum chaos in this system, and we show that the squared commutator grows exponentially with time, with a Lyapunov exponent proportional to 1 M. At high temperature, the Lyapunov exponent limits to a value set by the microscopic couplings, while at low temperature, the exponent exhibits a T4 dependence on temperature T. Copyright © 2019, The Authors. All rights reserved.

关键词： Differential equations

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Constant gap between conventional strategies and those based on C*-dynamics for self-embezzlement

arXiv

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arXiv 2018年

作者： Cleve, Richard Collins, Benoît Liu, Li Paulsen, Vern Institute for Quantum Computing Cheriton School of Computer Science University of Waterloo Canada Department of Mathematics Kyoto University Kyoto606-8502 Japan Institute for Quantum Computing Department of Pure Mathematics University of Waterloo Canada

We consider a bipartite transformation that we call self-embezzlement and use it to prove a constant gap between the capabilities of two models of quantum information: the conventional model, where bipartite systems are represented by tensor products of Hilbert spaces;and a natural model of quantum information processing for abstract states on C*-algebras, where joint systems are represented by tensor products of C*-algebras. We call this the C*-circuit model and show that it is a special case of the commuting-operator model (in that it can be translated into such a model). For the conventional model, we show that there exists a constant ∊0 > 0 such that self-embezzlement cannot be achieved with precision parameter less than ∊0 (i.e., the fidelity cannot be greater than 1 − ∊0);whereas, in the C*-circuit model—as well as in a commuting-operator model—the precision can be 0 (i.e., fidelity 1). Self-embezzlement is not a non-local game, hence our results do not impact the celebrated Connes Embedding conjecture. Instead, the significance of these results is to exhibit a reasonably natural quantum information processing problem for which there is a constant gap between the capabilities of the conventional Hilbert space model and the commuting-operator or C*-circuit model. © 2018, CC BY.

关键词： Hilbert spaces

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quantum engineering with hybrid magnonics systems and materials

arXiv

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arXiv 2021年

作者： Awschalom, D.D. Du, C.H.R. He, R. Heremans, F.J. Hoffmann, A. Hou, J.T. Kurebayashi, H. Li, Y. Liu, L. Novosad, V. Sklenar, J. Sullivan, S.E. Sun, D. Tang, H. Tiberkevich, V. Trevillian, C. Tsen, A.W. Weiss, L.R. Zhang, W. Zhang, X. Zhao, L. Zollitsch, C.W. Pritzker School of Molecular Engineering University of Chicago ChicagoIL United States Materials Science Division Center for Molecular Engineering Argonne National Laboratory LemontIL United States Department of Physics University of California San Diego San DiegoCA92093 United States Department of Electrical and Computer Engineering Texas Tech University LubbockTX79409 United States Materials Research Laboratory Department of Materials Science and Engineering University of Illinois at Urbana-Champaign UrbanaIL61801 United States Electrical Engineering and Computer Science Massachusetts Institute of Technology CambridgeMA United States London Centre for Nanotechnology University College London 17-19 Gordon Street LondonWCH1 0AH United Kingdom Materials Science Division Argonne National Laboratory LemontIL United States Department of Physics and Astronomy Wayne State University DetroitMI48201 United States Department of Physics North Carolina State University RaleighNC27695 United States Department of Electrical Engineering Yale University New HavenCT United States Department of Physics Oakland University MI48309 United States Institute for Quantum Computing Department of Chemistry University of Waterloo WaterlooON Canada Center for Nanoscale Materials Argonne National Laboratory LemontIL United States Department of Physics University of Michigan Ann ArborMI48109 United States

quantum technology has made tremendous strides over the past two decades with remarkable advances in materials engineering, circuit design and dynamic operation. In particular, the integration of different quantum modules has benefited from hybrid quantum systems, which provide an important pathway for harnessing the different natural advantages of complementary quantum systems and for engineering new functionalities. This review focuses on the current frontiers with respect to utilizing magnetic excitatons or magnons for novel quantum functionality. Magnons are the fundamental excitations of magnetically ordered solid-state materials and provide great tunability and flexibility for interacting with various quantum modules for integration in diverse quantum systems. The concomitant rich variety of physics and material selections enable exploration of novel quantum phenomena in materials science and engineering. In addition, the relative ease of generating strong coupling and forming hybrid dynamic systems with other excitations makes hybrid magnonics a unique platform for quantum engineering. We start our discussion with circuit-based hybrid magnonic systems, which are coupled with microwave photons and acoustic phonons. Subsequently, we are focusing on the recent progress of magnon-magnon coupling within confined magnetic systems. Next we highlight new opportunities for understanding the interactions between magnons and nitrogen-vacancy centers for quantum sensing and implementing quantum interconnects. Lastly, we focus on the spin excitations and magnon spectra of novel quantum materials investigated with advanced optical characterization. Copyright © 2021, The Authors. All rights reserved.

关键词： quantum optics

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Time-dependent Hamiltonian simulation with L1-norm scaling

arXiv

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arXiv 2019年

作者： Berry, Dominic W. Childs, Andrew M. Su, Yuan Wang, Xin Wiebe, Nathan Department of Physics and Astronomy Macquarie University SydneyNSW2109 Australia Department of Computer Science University of Maryland College ParkMD20742 United States Institute for Advanced Computer Studies Joint Center for Quantum Information and Computer Science University of Maryland College ParkMD20742 United States Institute for Quantum Computing Baidu Research Beijing100193 China Department of Physics University of Washington SeattleWA98195 United States Pacific Northwest National Laboratory RichlandWA99354 United States Google Inc. VeniceCA90291 United States

The difficulty of simulating quantum dynamics depends on the norm of the Hamiltonian. When the Hamiltonian varies with time, the simulation complexity should only depend on this quantity instantaneously. We develop quantum simulation algorithms that exploit this intuition. For sparse Hamiltonian simulation, the gate complexity scales with the (Formula presented), whereas the best previous results scale with (Formula presented). We also show analogous results for Hamiltonians that are linear combinations of unitaries. Our approaches thus provide an improvement over previous simulation algorithms that can be substantial when the Hamiltonian varies significantly. We introduce two new techniques: a classical sampler of time-dependent Hamiltonians and a rescaling principle for the Schrödinger equation. The rescaled Dyson-series algorithm is nearly optimal with respect to all parameters of interest, whereas the sampling-based approach is easier to realize for near-term simulation. These algorithms could potentially be applied to semi-classical simulations of scattering processes in quantum chemistry. Copyright © 2019, The Authors. All rights reserved.

关键词： Hamiltonians

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Eavesdropper’s ability to attack a free-space quantum-key-distribution receiver in atmospheric turbulence

arXiv

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arXiv 2019年

作者： Chaiwongkhot, Poompong Kuntz, Katanya B. Zhang, Yanbao Huang, Anqi Bourgoin, Jean-Philippe Sajeed, Shihan Lütkenhaus, Norbert Jennewein, Thomas Makarov, Vadim Institute for Quantum Computing University of Waterloo WaterlooONN2L 3G1 Canada Department of Physics and Astronomy University of Waterloo WaterlooONN2L 3G1 Canada NTT Basic Research Laboratories NTT Corporation AtsugiKanagawa Japan NTT Research Center for Theoretical Quantum Physics NTT Corporation AtsugiKanagawa Japan Institute for Quantum Information & State Key Laboratory of High Performance Computing College of Computer National University of Defense Technology Changsha410073 China Department of Electrical and Computer Engineering University of Waterloo WaterlooONN2L 3G1 Canada Aegis Quantum WaterlooON Canada Department of Electrical and Computer Engineering University of Toronto M5S 3G4 Canada Quantum Information Science Program Canadian Institute for Advanced Research TorontoONM5G 1Z8 Canada Russian Quantum Center Skolkovo Moscow143025 Russia Shanghai Branch National Laboratory for Physical Sciences at Microscale and CAS Center for Excellence in Quantum Information University of Science and Technology of China Shanghai201315 China NTI Center for Quantum Communications National University of Science and Technology MISiS Moscow119049 Russia

The ability of an eavesdropper (Eve) to perform an intercept-resend attack on a free-space quantum key distribution (QKD) receiver by precisely controlling the incidence angle of an attack laser has been previously demonstrated. However, such an attack could be ineffective in the presence of atmospheric turbulence due to beam wander and spatial mode aberrations induced by the air’s varying index of refraction. We experimentally investigate the impact turbulence has on Eve’s attack on a free-space polarization-encoding QKD receiver by emulating atmospheric turbulence with a spatial light modulator. Our results identify how well Eve would need to compensate for turbulence to perform a successful attack by either reducing her distance to the receiver, or using beam wavefront correction via adaptive optics. Furthermore, we use an entanglement-breaking scheme to find a theoretical limit on the turbulence strength that hinders Eve’s attack. Copyright © 2019, The Authors. All rights reserved.

关键词： Atmospheric turbulence

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Noisy intermediate-scale quantum (NISQ) algorithms

arXiv

引用

arXiv 2021年

作者： Bharti, Kishor Cervera-Lierta, Alba Kyaw, Thi Ha Haug, Tobias Alperin-Lea, Sumner Anand, Abhinav Degroote, Matthias Heimonen, Hermanni Kottmann, Jakob S. Menke, Tim Mok, Wai-Keong Sim, Sukin Kwek, Leong-Chuan Aspuru-Guzik, Alán Centre for Quantum Technologies National University of Singapore Singapore117543 Singapore Department of Computer Science University of Toronto Toronto ONM5S 2E4 Canada Chemical Physics Theory Group Department of Chemistry University of Toronto TorontoONM5G 1Z8 Canada Qols Blackett Laboratory Imperial College London SW7 2AZ United Kingdom Boehringer Ingelheim Amsterdam Netherlands Department of Physics Harvard University CambridgeMA02138 United States Research Laboratory of Electronics Massachusetts Institute of Technology CambridgeMA02139 United States Department of Physics Massachusetts Institute of Technology CambridgeMA02139 United States Department of Chemistry and Chemical Biology Harvard University CambridgeMA02138 United States MajuLab CNRS-UNS-NUS-NTU International Joint Research Unit Umi 3654 Singapore Singapore National Institute of Education Institute of Advanced Studies Nanyang Technological University Singapore637616 Singapore Vector Institute for Artificial Intelligence TorontoONM5S 1M1 Canada Canadian Institute for Advanced Research TorontoONM5G 1Z8 Canada

A universal fault-tolerant quantum computer that can solve efficiently problems such as integer factorization and unstructured database search requires millions of qubits with low error rates and long coherence times. While the experimental advancement towards realizing such devices will potentially take decades of research, noisy intermediate-scale quantum (NISQ) computers already exist. These computers are composed of hundreds of noisy qubits, i.e. qubits that are not error-corrected, and therefore perform imperfect operations in a limited coherence time. In the search for quantum advantage with these devices, algorithms have been proposed for applications in various disciplines spanning physics, machine learning, quantum chemistry and combinatorial optimization. The goal of such algorithms is to leverage the limited available resources to perform classically challenging tasks. In this review, we provide a thorough summary of NISQ computational paradigms and algorithms. We discuss the key structure of these algorithms, their limitations, and advantages. We additionally provide a comprehensive overview of various benchmarking and software tools useful for programming and testing NISQ devices. Copyright © 2021, The Authors. All rights reserved.

关键词： Machine learning

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Certifying optimality for convex quantum channel optimization problems

arXiv

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arXiv 2018年

作者： Coutts, Bryan Girard, Mark Watrous, John Institute for Quantum Computing University of Waterloo Canada School of Computer Science University of Waterloo Canada Canadian Institute for Advanced Research Toronto Canada

We identify necessary and sufficient conditions for a quantum channel to be optimal for any convex optimization problem in which the optimization is taken over the set of all quantum channels of a fixed size. Optimality conditions for convex optimization problems over the set of all quantum measurements of a given system having a fixed number of measurement outcomes are obtained as a special case. In the case of linear objective functions for measurement optimization problems, our conditions reduce to the well-known Holevo-Yuen-Kennedy-Lax measurement optimality conditions. We illustrate how our conditions can be applied to various state transformation problems having non-linear objective functions based on the fidelity, trace distance, and quantum relative entropy. © 2018, CC BY.

关键词： quantum entanglement

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Security analysis of practical continuous-variable quantum key distribution systems under laser seeding attack

arXiv

引用

arXiv 2019年

作者： Zheng, Yi Huang, Peng Huang, Anqi Peng, Jinye Zeng, Guihua College of Information Science and Technology Northwest University Xi’anShaanxi710127 China State Key Laboratory of Advanced Optical Communication Systems and Networks Center of Quantum Information Sensing and Processing Shanghai Jiao Tong University Shanghai200240 China Institute for Quantum Information & State Key Laboratory of High Performance Computing College of Computer National University of Defense Technology Changsha410073 China Greatwall Quantum Laboratory China Greatwall Technology Changsha410205 China

Here, we investigate the security of the practical one-way CVQKD and CV-MDI-QKD systems under laser seeding attack. In particular, Eve can inject a suitable light into the laser diodes of the light source modules in the two kinds of practical CVQKD systems, which results in the increased intensity of the generated optical signal. The parameter estimation under the attack shows that the secret key rates of these two schemes may be overestimated, which opens a security loophole for Eve to successfully perform an intercept-resend attack on these systems. To close this loophole, we propose a real-time monitoring scheme to precisely evaluate the secret key rates of these schemes. The analysis results indicate the implementation of the proposed monitoring scheme can effectively resist this potential attack. Copyright © 2019, The Authors. All rights reserved.

关键词： Light sources

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quantum singular value transformation and beyond: Exponential improvements for quantum matrix arithmetics

arXiv

引用

arXiv 2018年

作者： Gilyén, András Su, Yuan Low, Guang Hao Wiebe, Nathan QuSoft Cwi University of Amsterdam Netherlands Department of Computer Science Institute for Advanced Computer Studies Joint Center for Quantum Information and Computer Science University of Maryland United States Microsoft Research Quantum Architectures and Computing Group United States

quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation" algorithm capable of harnessing this exponential advantage, that can apply polynomial transformations to the singular values of a block of a unitary, generalizing the optimal Hamiltonian simulation results of Low and Chuang [LC17a]. The proposed quantum circuits have a very simple structure, often give rise to optimal algorithms and have appealing constant factors, while typically only use a constant number of ancilla qubits. We show that singular value transformation leads to novel algorithms. We give an efficient solution to a "non-commutative" measurement problem used for efficient ground-state-preparation of certain local Hamiltonians, and propose a new method for singular value estimation. We also show how to exponentially improve the complexity of implementing fractional queries to unitaries with a gapped spectrum. Finally, as a quantum machine learning application we show how to efficiently implement principal component regression. "Singular value transformation" is conceptually simple and efficient, and leads to a unified framework of quantum algorithms incorporating a variety of quantum speed-ups. We illustrate this by showing how it generalizes a number of prominent quantum algorithms, and quickly derive the following algorithms: Optimal Hamiltonian simulation, implementing the Moore-Penrose pseudoinverse with exponential precision, fixed-point amplitude amplification, robust oblivious amplitude amplification, fast QMA amplification, fast quantum OR lemma, certain quantum walk results and several quantum machine learning algorithms. In order to exploit the strengths of the presented method it is useful to know its limitations too, therefore we also prove a lower bound on the efficiency of singular value transformation, which of

关键词： Hamiltonians

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