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Characterizing entanglement using quantum discord over state extensions

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arXiv 2020年

作者： Xiong, Chunhe Kim, Sunho Qiu, Daowen Kumar, Asutosh Wu, Junde Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-sen University Guangzhou510006 China Interdisciplinary Center for Quantum Information Department of Physics Zhejiang University Hangzhou310027 China School of Computer and Computing Science Zhejiang University City College Hangzhou310015 China School of Mathematical Sciences Harbin Engineering University Harbin150001 China Instituto de Telecomunicaçoes Departamento de Matemática Instituto Superior Técnico Av. Rovisco Pais Lisbon1049-001 Portugal P.G. Department of Physics Gaya College Magadh University Rampur Gaya823001 India Harish-Chandra Research Institute HBNI Chhatnag Road Jhunsi Allahabad211019 India Vaidic and Modern Physics Research Centre Bhagal Bhim Bhinmal Jalore 343029 India School of Mathematical Sciences Zhejiang University Hangzhou310027 China

We propose a framework to characterize entanglement with quantum discord, both asymmetric and symmetric, over state extensions. In particular, we show that the minimal Bures distance of discord over state extensions is equivalent to Bures distance of entanglement. This equivalence places quantum discord at a more primitive position than entanglement conceptually in the sense that entanglement can be interpreted as an irreducible part of discord over all state extensions. Based on this equivalence, we also offer an operational meaning of Bures distance of entanglement by connecting it to quantum state discriminations. Moreover, for the relative entropy part, we prove that the entanglement measure introduced by Devi and and Rajagopal [A. R. U. Devi and A. K. Rajagopal, Phys. Rev. Lett. 100, 140502 (2008)] is actually equivalent to the relative entropy of entanglement. We also provide several quantifications of entanglement based on discord measures. © 2020, CC BY-NC-ND.

关键词： quantum entanglement

Distributed quantum algorithm for Simon's problem

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arXiv 2022年

作者： Tan, Jiawei Xiao, Ligang Qiu, Daowen Luo, Le Mateus, Paulo Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-Sen University Guangzhou510006 China The Guangdong Key Laboratory of Information Security Technology Sun Yat-Sen University 510006 China QUDOOR Technologies Inc. Guangzhou China School of Physics and Astronomy Sun Yat-Sen University Zhuhai519082 China Instituto de Telecomunicações Departamento de Matemática Instituto Superior Técnico Av. Rovisco Pais Lisbon1049-001 Portugal

Limited by today's physical devices, quantum circuits are usually noisy and difficult to be designed deeply. The novel computing architecture of distributed quantum computing is expected to reduce the noise and depth of quantum circuits. In this paper, we study the Simon's problem in distributed scenarios and design a distributed quantum algorithm to solve the problem. The algorithm proposed by us has the advantage of exponential acceleration compared with the classical distributed computing, and has the advantage of square acceleration compared with the best distributed quantum algorithm proposed before. In particular, the previous distributed quantum algorithm for Simon's problem can not be extended to the case of more than two computing nodes (i.e. two subproblems), but our distributed quantum algorithm can be extended to the case of multiple computing nodes (i.e. multiple subproblems) as well. Copyright © 2022, The Authors. All rights reserved.

关键词： computer architecture

Exact distributed quantum algorithm for generalized Simon’s problem

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arXiv 2023年

作者： Li, Hao Qiu, Daowen Luo, Le Mateus, Paulo Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-sen University Guangzhou510006 China The Guangdong Key Laboratory of Information Security Technology Sun Yat-sen University 510006 China QUDOOR Technologies Inc. Zhuhai China School of Physics and Astronomy Sun Yat-sen University Zhuhai519082 China Instituto de Telecomunicações Departamento de Matemática Instituto Superior Técnico Av. Rovisco Pais Lisbon1049-001 Portugal

Simon’s problem is one of the most important problems demonstrating the power of quantum algorithms, as it greatly inspired the proposal of Shor’s algorithm. The generalized Simon’s problem is a natural extension of Simon’s problem, and also a special hidden subgroup problem: Given a function f : {0, 1}n → {0, 1}m, with the property that for any x, y ∈ {0, 1}n, there is some unknown hidden subgroup S ≤ 2n such that f(x) = f(y) iff x ⊕ y ∈ S, where |S| = 2k for some 0 ≤ k ≤ n (m ≥ n − k). The goal of generalized Simon’s problem is to find the hidden subgroup S. In this paper, we present two key contributions. Firstly, we characterize the structure of the generalized Simon’s problem in distributed scenario and introduce a corresponding distributed quantum algorithm. Secondly, we refine the algorithm to ensure exactness due to the application of quantum amplitude amplification technique. Our algorithm offers exponential acceleration compared to the distributed classical algorithm. When contrasted with the centralized quantum algorithm for the generalized Simon’s problem, our algorithm’s oracle requires fewer qubits, thus making it easier to be physically implemented. Particularly, the exact distributed quantum algorithm we develop for the generalized Simon’s problem outperforms the best previously proposed distributed quantum algorithm for Simon’s problem in terms of generalizability and exactness. Copyright © 2023, The Authors. All rights reserved.

关键词： Qubits

Preparing a commercial quantum key distribution system for certification against implementation loopholes

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arXiv 2023年

作者： Makarov, Vadim Abrikosov, Alexey Chaiwongkhot, Poompong Fedorov, Aleksey K. Huang, Anqi Kiktenko, Evgeny Petrov, Mikhail Ponosova, Anastasiya Ruzhitskaya, Daria Tayduganov, Andrey Trefilov, Daniil Zaitsev, Konstantin Russian Quantum Center Skolkovo Moscow121205 Russia Vigo Quantum Communication Center University of Vigo VigoE-36310 Spain NTI Center for Quantum Communications National University of Science and Technology MISiS Moscow119049 Russia Department of Physics Faculty of Science Mahidol University Bangkok10400 Thailand Institute for Quantum Computing University of Waterloo WaterlooONN2L 3G1 Canada Department of Physics and Astronomy University of Waterloo WaterlooONN2L 3G1 Canada Bangkok10110 Thailand QRate Skolkovo Moscow143026 Russia Institute for Quantum Information State Key Laboratory of High Performance Computing College of Computer Science and Technology National University of Defense Technology Changsha410073 China Steklov Mathematical Institute Russian Academy of Sciences Moscow119991 Russia atlanTTic Research Center University of Vigo VigoE-36310 Spain School of Telecommunication Engineering Department of Signal Theory and Communications University of Vigo VigoE-36310 Spain National Research University Higher School of Economics Moscow101000 Russia

A commercial quantum key distribution (QKD) system needs to be formally certified to enable its wide deployment. The certification should include the system’s robustness against known implementation loopholes and attacks that exploit them. Here we ready a fiber-optic QKD system for this procedure. The system has a prepare-and-measure scheme with decoy-state BB84 protocol, polarisation encoding, qubit source rate of 312.5 MHz, and is manufactured by QRate. We detail its hardware and post-processing. We analyse the hardware for known implementation loopholes, search for possible new loopholes, and discuss countermeasures. We then amend the system design to address the highest-risk loopholes identified. We also work out technical requirements on the certification lab and outline its possible structure. Copyright © 2023, The Authors. All rights reserved.

关键词： quantum cryptography

Insecurity of Detector-Device-Independent quantum Key Distribution

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Physical Review Letters 2016年第25期117卷 250505-250505页

作者： Shihan Sajeed Anqi Huang Shihai Sun Feihu Xu Vadim Makarov Marcos Curty Institute for Quantum Computing University of Waterloo Waterloo Ontario N2L 3G1 Canada Department of Electrical and Computer Engineering University of Waterloo Waterloo Ontario N2L 3G1 Canada College of Science National University of Defense Technology Changsha 410073 China Research Laboratory of Electronics Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge Massachusetts 02139 USA Department of Physics and Astronomy University of Waterloo Waterloo Ontario N2L 3G1 Canada Escuela de Ingeniería de Telecomunicación Department of Signal Theory and Communications University of Vigo Vigo E-36310 Spain

Detector-device-independent quantum key distribution (DDI-QKD) held the promise of being robust to detector side channels, a major security loophole in quantum key distribution (QKD) implementations. In contrast to what has been claimed, however, we demonstrate that the security of DDI-QKD is not based on postselected entanglement, and we introduce various eavesdropping strategies that show that DDI-QKD is in fact insecure against detector side-channel attacks as well as against other attacks that exploit devices’ imperfections of the receiver. Our attacks are valid even when the QKD apparatuses are built by the legitimate users of the system themselves, and thus, free of malicious modifications, which is a key assumption in DDI-QKD.

关键词： quantum communication quantum cryptography quantum information processing quantum optics

Generating Approximate Ground States of Molecules Using quantum Machine Learning

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arXiv 2022年

作者： Ceroni, Jack Stetina, Torin F. Kieferová, Mária Marrero, Carlos Ortiz Arrazola, Juan Miguel Wiebe, Nathan Xanadu TorontoONM5G 2C8 Canada Department of Mathematics University of Toronto TorontoONM5S 3E1 Canada Simons Institute for the Theory of Computing BerkeleyCA94704 United States Berkeley Quantum Information and Computation Center University of California BerkeleyCA94720 United States Centre for Quantum Computation and Communication Technology Centre for Quantum Software and Information University of Technology SydneyNSW2007 Australia AI & Data Analytics Division Pacific Northwest National Laboratory RichlandWA99354 United States Department of Electrical & Computer Engineering North Carolina State University RaleighNC27607 United States Department of Computer Science University of Toronto ONM5S 1A1 Canada High Performance Computing Group Pacific Northwest National Laboratory RichlandWA99354 United States

The potential energy surface (PES) of molecules with respect to their nuclear positions is a primary tool in understanding chemical reactions from first principles. However, obtaining this information is complicated by the fact that sampling a large number of ground states over a high-dimensional PES can require a vast number of state preparations. In this work, we propose using a generative quantum machine learning model to prepare quantum states at arbitrary points on the PES. The model is trained using quantum data consisting of ground-state wavefunctions associated with different classical nuclear coordinates. Our approach uses a classical neural network to convert the nuclear coordinates of a molecule into quantum parameters of a variational quantum circuit. The model is trained using a fidelity loss function to optimize the neural network parameters. We show that gradient evaluation is efficient and numerically demonstrate our method’s ability to prepare wavefunctions on the PES of hydrogen chains, water, and beryllium hydride. In all cases, we find that a small number of training points are needed to achieve very high overlap with the groundstates in practice. From a theoretical perspective, we further prove limitations on these protocols by showing that if we were able to learn across an avoided crossing using a small number of samples, then we would be able to violate Grover’s lower bound. Additionally, we prove lower bounds on the amount of quantum data needed to learn a locally optimal neural network function using arguments from quantum Fisher information. This work further identifies that quantum chemistry can be an important use case for quantum machine learning. © 2022, CC BY.

关键词： Molecules

qSWIFT: High-order randomized compiler for Hamiltonian simulation

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arXiv 2023年

作者： Nakaji, Kouhei Bagherimehrab, Mohsen Aspuru-Guzik, Alán Chemical Physics Theory Group Department of Chemistry University of Toronto TorontoON Canada 1-1-1 Umezono Ibaraki Tsukuba305-8568 Japan Quantum Computing Center Keio University 3-14-1 Hiyoshi Kohoku-ku Kanagawa Yokohama223-8522 Japan Department of Computer Science University of Toronto TorontoON Canada Vector Institute for Artificial Intelligence TorontoON Canada 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

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 Hamiltonian, while the systematic error is exponentially reduced with regards to the order parameter. In this respect, our qSWIFT is a higher-order counterpart of the previously proposed quantum stochastic drift protocol (qDRIFT), in which the number of gates 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 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. Particularly, the advantage is significant for problems where high precision is required;for example, 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. © 2023, CC BY.

关键词： Hamiltonians

quantum algorithm for Petz recovery channels and pretty good measurements

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arXiv 2020年

作者： Gilyén, András Lloyd, Seth Marvian, Iman Quek, Yihui Wilde, Mark M. Institute for Quantum Information and Matter California Institute of Technology PasadenaCA91125 United States Simons Institute for the Theory of Computing BerkeleyCA94720 United States Department of Mechanical Engineering Research Laboratory of Electronics Massachusetts Institute of Technology CambridgeMA02139 United States Department of Physics Department of Electrical and Computer Engineering Duke University DurhamNC27708 United States Information Systems Laboratory Stanford University StanfordCA94305 United States Hearne Institute for Theoretical Physics Department of Physics and Astronomy Center for Computation and Technology Louisiana State University Baton RougeLA70803 United States Stanford Institute for Theoretical Physics Stanford University StanfordCA94305 United States

The Petz recovery channel plays an important role in quantum information science as an operation that approximately reverses the effect of a quantum channel. The pretty good measurement is a special case of the Petz recovery channel, and it allows for near-optimal state discrimination. A hurdle to the experimental realization of these vaunted theoretical tools is the lack of a systematic and efficient method to implement them. This paper sets out to rectify this lack: using the recently developed tools of quantum singular value transformation and oblivious amplitude amplification, we provide a quantum algorithm to implement the Petz recovery channel when given the ability to perform the channel that one wishes to reverse. Moreover, we prove that, in some sense, our quantum algorithm’s usage of the channel implementation cannot be improved by more than a quadratic factor. Our quantum algorithm also provides a procedure to perform pretty good measurements when given multiple copies of the states that one is trying to distinguish. Copyright © 2020, The Authors. All rights reserved.

关键词： Recovery

Fast quantum algorithm for differential equations

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arXiv 2023年

作者： Bagherimehrab, Mohsen Nakaji, Kouhei Wiebe, Nathan Aspuru-Guzik, Alán Chemical Physics Theory Group Department of Chemistry University of Toronto TorontoON Canada Department of Computer Science University of Toronto TorontoON Canada 1-1-1 Umezono Ibaraki Tsukuba305-8568 Japan Quantum Computing Center Keio University 3-14-1 Hiyoshi Kohoku-ku Kanagawa Yokohama223-8522 Japan Pacific Northwest National Laboratory RichlandWA United States Canadian Institute for Advanced Research TorontoON Canada Vector Institute for Artificial Intelligence TorontoON Canada Department of Chemical Engineering & Applied Chemistry University of Toronto TorontoON Canada Department of Materials Science & Engineering University of Toronto TorontoON Canada

Partial differential equations (PDEs) are ubiquitous in science and engineering. Prior quantum algorithms for solving the system of linear algebraic equations obtained from discretizing a PDE have a computational complexity that scales at least linearly with the condition number κ of the matrices involved in the computation. For many practical applications, κ scales polynomially with the size N of the matrices, rendering a polynomial-in-N complexity for these algorithms. Here we present a quantum algorithm with a complexity that is polylogarithmic in N but is independent of κ for a large class of PDEs. Our algorithm generates a quantum state that enables extracting features of the solution. Central to our methodology is using a wavelet basis as an auxiliary system of coordinates in which the condition number of associated matrices is independent of N by a simple diagonal preconditioner. We present numerical simulations showing the effect of the wavelet preconditioner for several differential equations. Our work could provide a practical way to boost the performance of quantum-simulation algorithms where standard methods are used for discretization. © 2023, CC BY.

关键词： Matrix algebra