Teleportation Systems Toward a Quantum Internet
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Quantum Computation and Complexity Theory
Quantum computation and complexity theory Course given at the Institut fÈurInformationssysteme, Abteilung fÈurDatenbanken und Expertensysteme, University of Technology Vienna, Wintersemester 1994/95 K. Svozil Institut fÈur Theoretische Physik University of Technology Vienna Wiedner Hauptstraûe 8-10/136 A-1040 Vienna, Austria e-mail: [email protected] December 5, 1994 qct.tex Abstract The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applicationsto quantum computing. Standardinterferomeric techniques are used to construct a physical device capable of universal quantum computation. Some consequences for recursion theory and complexity theory are discussed. hep-th/9412047 06 Dec 94 1 Contents 1 The Quantum of action 3 2 Quantum mechanics for the computer scientist 7 2.1 Hilbert space quantum mechanics ..................... 7 2.2 From single to multiple quanta Ð ªsecondº ®eld quantization ...... 15 2.3 Quantum interference ............................ 17 2.4 Hilbert lattices and quantum logic ..................... 22 2.5 Partial algebras ............................... 24 3 Quantum information theory 25 3.1 Information is physical ........................... 25 3.2 Copying and cloning of qbits ........................ 25 3.3 Context dependence of qbits ........................ 26 3.4 Classical versus quantum tautologies .................... 27 4 Elements of quantum computatability and complexity theory 28 4.1 Universal quantum computers ....................... 30 4.2 Universal quantum networks ........................ 31 4.3 Quantum recursion theory ......................... 35 4.4 Factoring .................................. 36 4.5 Travelling salesman ............................. 36 4.6 Will the strong Church-Turing thesis survive? ............... 37 Appendix 39 A Hilbert space 39 B Fundamental constants of physics and their relations 42 B.1 Fundamental constants of physics ..................... 42 B.2 Conversion tables .............................. 43 B.3 Electromagnetic radiation and other wave phenomena ......... -
Analysis of Nonlinear Dynamics in a Classical Transmon Circuit
Analysis of Nonlinear Dynamics in a Classical Transmon Circuit Sasu Tuohino B. Sc. Thesis Department of Physical Sciences Theoretical Physics University of Oulu 2017 Contents 1 Introduction2 2 Classical network theory4 2.1 From electromagnetic fields to circuit elements.........4 2.2 Generalized flux and charge....................6 2.3 Node variables as degrees of freedom...............7 3 Hamiltonians for electric circuits8 3.1 LC Circuit and DC voltage source................8 3.2 Cooper-Pair Box.......................... 10 3.2.1 Josephson junction.................... 10 3.2.2 Dynamics of the Cooper-pair box............. 11 3.3 Transmon qubit.......................... 12 3.3.1 Cavity resonator...................... 12 3.3.2 Shunt capacitance CB .................. 12 3.3.3 Transmon Lagrangian................... 13 3.3.4 Matrix notation in the Legendre transformation..... 14 3.3.5 Hamiltonian of transmon................. 15 4 Classical dynamics of transmon qubit 16 4.1 Equations of motion for transmon................ 16 4.1.1 Relations with voltages.................. 17 4.1.2 Shunt resistances..................... 17 4.1.3 Linearized Josephson inductance............. 18 4.1.4 Relation with currents................... 18 4.2 Control and read-out signals................... 18 4.2.1 Transmission line model.................. 18 4.2.2 Equations of motion for coupled transmission line.... 20 4.3 Quantum notation......................... 22 5 Numerical solutions for equations of motion 23 5.1 Design parameters of the transmon................ 23 5.2 Resonance shift at nonlinear regime............... 24 6 Conclusions 27 1 Abstract The focus of this thesis is on classical dynamics of a transmon qubit. First we introduce the basic concepts of the classical circuit analysis and use this knowledge to derive the Lagrangians and Hamiltonians of an LC circuit, a Cooper-pair box, and ultimately we derive Hamiltonian for a transmon qubit. -
Unconditional Quantum Teleportation
R ESEARCH A RTICLES our experiment achieves Fexp 5 0.58 6 0.02 for the field emerging from Bob’s station, thus Unconditional Quantum demonstrating the nonclassical character of this experimental implementation. Teleportation To describe the infinite-dimensional states of optical fields, it is convenient to introduce a A. Furusawa, J. L. Sørensen, S. L. Braunstein, C. A. Fuchs, pair (x, p) of continuous variables of the electric H. J. Kimble,* E. S. Polzik field, called the quadrature-phase amplitudes (QAs), that are analogous to the canonically Quantum teleportation of optical coherent states was demonstrated experi- conjugate variables of position and momentum mentally using squeezed-state entanglement. The quantum nature of the of a massive particle (15). In terms of this achieved teleportation was verified by the experimentally determined fidelity analogy, the entangled beams shared by Alice Fexp 5 0.58 6 0.02, which describes the match between input and output states. and Bob have nonlocal correlations similar to A fidelity greater than 0.5 is not possible for coherent states without the use those first described by Einstein et al.(16). The of entanglement. This is the first realization of unconditional quantum tele- requisite EPR state is efficiently generated via portation where every state entering the device is actually teleported. the nonlinear optical process of parametric down-conversion previously demonstrated in Quantum teleportation is the disembodied subsystems of infinite-dimensional systems (17). The resulting state corresponds to a transport of an unknown quantum state from where the above advantages can be put to use. squeezed two-mode optical field. -
Quantum Error Modelling and Correction in Long Distance Teleportation Using Singlet States by Joe Aung
Quantum Error Modelling and Correction in Long Distance Teleportation using Singlet States by Joe Aung Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering and Computer Science at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 2002 @ Massachusetts Institute of Technology 2002. All rights reserved. Author ................... " Department of Electrical Engineering and Computer Science May 21, 2002 72-1 14 Certified by.................. .V. ..... ..'P . .. ........ Jeffrey H. Shapiro Ju us . tn Professor of Electrical Engineering Director, Research Laboratory for Electronics Thesis Supervisor Accepted by................I................... ................... Arthur C. Smith Chairman, Department Committee on Graduate Students BARKER MASSACHUSE1TS INSTITUTE OF TECHNOLOGY JUL 3 1 2002 LIBRARIES 2 Quantum Error Modelling and Correction in Long Distance Teleportation using Singlet States by Joe Aung Submitted to the Department of Electrical Engineering and Computer Science on May 21, 2002, in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering and Computer Science Abstract Under a multidisciplinary university research initiative (MURI) program, researchers at the Massachusetts Institute of Technology (MIT) and Northwestern University (NU) are devel- oping a long-distance, high-fidelity quantum teleportation system. This system uses a novel ultrabright source of entangled photon pairs and trapped-atom quantum memories. This thesis will investigate the potential teleportation errors involved in the MIT/NU system. A single-photon, Bell-diagonal error model is developed that allows us to restrict possible errors to just four distinct events. The effects of these errors on teleportation, as well as their probabilities of occurrence, are determined. -
Bidirectional Quantum Controlled Teleportation by Using Five-Qubit Entangled State As a Quantum Channel
Bidirectional Quantum Controlled Teleportation by Using Five-qubit Entangled State as a Quantum Channel Moein Sarvaghad-Moghaddam1,*, Ahmed Farouk2, Hussein Abulkasim3 to each other simultaneously. Unfortunately, the proposed Abstract— In this paper, a novel protocol is proposed for protocol required additional quantum and classical resources so implementing BQCT by using five-qubit entangled states as a that the users required two-qubit measurements and applying quantum channel which in the same time, the communicated users global unitary operations. There are many approaches and can teleport each one-qubit state to each other under permission prototypes for the exploitation of quantum principles to secure of controller. The proposed protocol depends on the Controlled- the communication between two parties and multi-parties [18, NOT operation, proper single-qubit unitary operations and single- 19, 20, 21, 22]. While these approaches used different qubit measurement in the Z-basis and X-basis. The results showed that the protocol is more efficient from the perspective such as techniques for achieving a private communication among lower shared qubits and, single qubit measurements compared to authorized users, but most of them depend on the generation of the previous work. Furthermore, the probability of obtaining secret random keys [23, 2]. In this paper, a novel protocol is Charlie’s qubit by eavesdropper is reduced, and supervisor can proposed for implementing BQCT by using five-qubit control one of the users or every two users. Also, we present a new entanglement state as a quantum channel. In this protocol, users method for transmitting n and m-qubits entangled states between may transmit an unknown one-qubit quantum state to each other Alice and Bob using proposed protocol. -
Al Transmon Qubits on Silicon-On-Insulator for Quantum Device Integration Andrew J
Al transmon qubits on silicon-on-insulator for quantum device integration Andrew J. Keller, Paul B. Dieterle, Michael Fang, Brett Berger, Johannes M. Fink, and Oskar Painter Citation: Appl. Phys. Lett. 111, 042603 (2017); doi: 10.1063/1.4994661 View online: http://dx.doi.org/10.1063/1.4994661 View Table of Contents: http://aip.scitation.org/toc/apl/111/4 Published by the American Institute of Physics Articles you may be interested in Superconducting noise bolometer with microwave bias and readout for array applications Applied Physics Letters 111, 042601 (2017); 10.1063/1.4995981 A silicon nanowire heater and thermometer Applied Physics Letters 111, 043504 (2017); 10.1063/1.4985632 Graphitization of self-assembled monolayers using patterned nickel-copper layers Applied Physics Letters 111, 043102 (2017); 10.1063/1.4995412 Perfectly aligned shallow ensemble nitrogen-vacancy centers in (111) diamond Applied Physics Letters 111, 043103 (2017); 10.1063/1.4993160 Broadband conversion of microwaves into propagating spin waves in patterned magnetic structures Applied Physics Letters 111, 042404 (2017); 10.1063/1.4995991 Ferromagnetism in graphene due to charge transfer from atomic Co to graphene Applied Physics Letters 111, 042402 (2017); 10.1063/1.4994814 APPLIED PHYSICS LETTERS 111, 042603 (2017) Al transmon qubits on silicon-on-insulator for quantum device integration Andrew J. Keller,1,2 Paul B. Dieterle,1,2 Michael Fang,1,2 Brett Berger,1,2 Johannes M. Fink,1,2,3 and Oskar Painter1,2,a) 1Kavli Nanoscience Institute and Thomas J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA 2Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA 3Institute for Science and Technology Austria, 3400 Klosterneuburg, Austria (Received 3 April 2017; accepted 5 July 2017; published online 25 July 2017) We present the fabrication and characterization of an aluminum transmon qubit on a silicon-on-insulator substrate. -
The Quantum Bases for Human Expertise, Knowledge, and Problem-Solving (Extended Version with Applications)
A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Bickley, Steve J.; Chan, Ho Fai; Schmidt, Sascha Leonard; Torgler, Benno Working Paper Quantum-sapiens: The quantum bases for human expertise, knowledge, and problem-solving (Extended version with applications) CREMA Working Paper, No. 2021-14 Provided in Cooperation with: CREMA - Center for Research in Economics, Management and the Arts, Zürich Suggested Citation: Bickley, Steve J.; Chan, Ho Fai; Schmidt, Sascha Leonard; Torgler, Benno (2021) : Quantum-sapiens: The quantum bases for human expertise, knowledge, and problem- solving (Extended version with applications), CREMA Working Paper, No. 2021-14, Center for Research in Economics, Management and the Arts (CREMA), Zürich This Version is available at: http://hdl.handle.net/10419/234629 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative Commons Licences), you genannten Lizenz gewährten Nutzungsrechte. -
Arxiv:2009.07590V2 [Quant-Ph] 9 Dec 2020
Emulating quantum teleportation of a Majorana zero mode qubit He-Liang Huang,1, 2, 3 Marek Naro˙zniak,4, 5 Futian Liang,1, 2, 3 Youwei Zhao,1, 2, 3 Anthony D. Castellano,1, 2, 3 Ming Gong,1, 2, 3 Yulin Wu,1, 2, 3 Shiyu Wang,1, 2, 3 Jin Lin,1, 2, 3 Yu Xu,1, 2, 3 Hui Deng,1, 2, 3 Hao Rong,1, 2, 3 6, 7, 8 1, 2, 3 4, 8, 9, 5 1, 2, 3, 1, 2, 3 Jonathan P. Dowling ∗, Cheng-Zhi Peng, Tim Byrnes, Xiaobo Zhu, † and Jian-Wei Pan 1Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China 2Shanghai Branch, CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China 3Shanghai Research Center for Quantum Sciences, Shanghai 201315, China 4New York University Shanghai, 1555 Century Ave, Pudong, Shanghai 200122, China 5Department of Physics, New York University, New York, NY 10003, USA 6Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA 7Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China 8NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China 9State Key Laboratory of Precision Spectroscopy, School of Physical and Material Sciences, East China Normal University, Shanghai 200062, China (Dated: December 10, 2020) Topological quantum computation based on anyons is a promising approach to achieve fault- tolerant quantum computing. -
Analysis of a Quantum Memory with Optical Interface in Diamond
Faraday Discussions Towards quantum networks of single spins: analysis of a quantum memory with optical interface in diamond Journal: Faraday Discussions Manuscript ID: FD-ART-06-2015-000113 Article Type: Paper Date Submitted by the Author: 23-Jun-2015 Complete List of Authors: Blok, Machiel; QuTech, Delft University of Technology Kalb, Norbert; QuTech, Delft University of Technology Reiserer, Andreas; QuTech, Delft University of Technology Taminiau, Tim Hugo; QuTech, Delft University of Technology Hanson, Ronald; QuTech, Delft University of Technology Page 1 of 18 Faraday Discussions Towards quantum networks of single spins: analysis of a quantum memory with optical interface in diamond M.S. Blok 1,† , N. Kalb 1, † , A. Reiserer 1, T.H. Taminiau 1 and R. Hanson 1,* 1QuTech and Kavli Institute of Nanoscience, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands †These authors contributed equally to this work * corresponding author: [email protected] Abstract Single defect centers in diamond have emerged as a powerful platform for quantum optics experiments and quantum information processing tasks 1. Connecting spatially separated nodes via optical photons 2 into a quantum network will enable distributed quantum computing and long-range quantum communication. Initial experiments on trapped atoms and ions as well as defects in diamond have demonstrated entanglement between two nodes over several meters 3-6. To realize multi-node networks, additional quantum bit systems that store quantum states while new entanglement links are established are highly desirable. Such memories allow for entanglement distillation, purification and quantum repeater protocols that extend the size, speed and distance of the network 7-10 . -
Quantum Technology: Advances and Trends
American Journal of Engineering and Applied Sciences Review Quantum Technology: Advances and Trends 1Lidong Wang and 2Cheryl Ann Alexander 1Institute for Systems Engineering Research, Mississippi State University, Vicksburg, Mississippi, USA 2Institute for IT innovation and Smart Health, Vicksburg, Mississippi, USA Article history Abstract: Quantum science and quantum technology have become Received: 30-03-2020 significant areas that have the potential to bring up revolutions in various Revised: 23-04-2020 branches or applications including aeronautics and astronautics, military Accepted: 13-05-2020 and defense, meteorology, brain science, healthcare, advanced manufacturing, cybersecurity, artificial intelligence, etc. In this study, we Corresponding Author: Cheryl Ann Alexander present the advances and trends of quantum technology. Specifically, the Institute for IT innovation and advances and trends cover quantum computers and Quantum Processing Smart Health, Vicksburg, Units (QPUs), quantum computation and quantum machine learning, Mississippi, USA quantum network, Quantum Key Distribution (QKD), quantum Email: [email protected] teleportation and quantum satellites, quantum measurement and quantum sensing, and post-quantum blockchain and quantum blockchain. Some challenges are also introduced. Keywords: Quantum Computer, Quantum Machine Learning, Quantum Network, Quantum Key Distribution, Quantum Teleportation, Quantum Satellite, Quantum Blockchain Introduction information and the computation that is executed throughout a transaction (Humble, 2018). The Tokyo QKD metropolitan area network was There have been advances in developing quantum established in Japan in 2015 through intercontinental equipment, which has been indicated by the number of cooperation. A 650 km QKD network was established successful QKD demonstrations. However, many problems between Washington and Ohio in the USA in 2016; a still need to be fixed though achievements of QKD have plan of a 10000 km QKD backbone network was been showcased. -
Deterministic Quantum Teleportation Received 18 February; Accepted 26 April 2004; Doi:10.1038/Nature02600
letters to nature Mars concretion systems. Although the analogue is not a perfect 24. Hoffman, N. White Mars: A new model for Mars’ surface and atmosphere based on CO2. Icarus 146, match in every geologic parameter, the mere presence of these 326–342 (2000). 25. Ferna´ndez-Remolar, D. et al. The Tinto River, an extreme acidic environment under control of iron, as spherical haematite concretions implies significant pore volumes of an analog of the Terra Meridiani hematite site of Mars. Planet. Space Sci. 53, 239–248 (2004). moving subsurface fluids through porous rock. Haematite is one of the few minerals found on Mars that can be Acknowledgements We thank the donors of the American Chemical Society Petroleum Research linked directly to water-related processes. Utah haematite concre- Fund, and the Bureau of Land Management-Grand Staircase Escalante National Monument for partial support of this research (to M.A.C. and W.T.P.). The work by J.O. was supported by the tions are similar to the Mars concretions with spherical mor- Spanish Ministry for Science and Technology and the Ramon y Cajal Program. The work by G.K. phology, haematite composition, and loose, weathered was supported by funding from the Italian Space Agency. accumulations. The abundance of quartz in the Utah example could pose challenges for finding spectral matches to the concre- Competing interests statement The authors declare that they have no competing financial tions. However, the similarities and differences of the Utah and interests. Mars haematite concretions should stimulate further investigations. Correspondence and requests for materials should be addressed to M.A.C. -
Arxiv:2009.06242V1 [Quant-Ph] 14 Sep 2020 Special Type of Highly Entangled State
Quantum teleportation of physical qubits into logical code-spaces Yi-Han Luo,1, 2, ∗ Ming-Cheng Chen,1, 2, ∗ Manuel Erhard,3, 4 Han-Sen Zhong,1, 2 Dian Wu,1, 2 Hao-Yang Tang,1, 2 Qi Zhao,1, 2 Xi-Lin Wang,1, 2 Keisuke Fujii,5 Li Li,1, 2 Nai-Le Liu,1, 2 Kae Nemoto,6, 7 William J. Munro,6, 7 Chao-Yang Lu,1, 2 Anton Zeilinger,3, 4 and Jian-Wei Pan1, 2 1Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, 230026, China 2CAS Centre for Excellence in Quantum Information and Quantum Physics, Hefei, 230026, China 3Austrian Academy of Sciences, Institute for Quantum Optics and Quantum Information (IQOQI), Boltzmanngasse 3, A-1090 Vienna, Austria 4Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, A-1090 Vienna, Austria 5Graduate School of Engineering Science Division of Advanced Electronics and Optical Science Quantum Computing Group, 1-3 Machikaneyama, Toyonaka, Osaka, 560-8531 6NTT Basic Research Laboratories & NTT Research Center for Theoretical Quantum Physics, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi-shi, Kanagawa, 243-0198, Japan 7National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan Quantum error correction is an essential tool for reliably performing tasks for processing quantum informa- tion on a large scale. However, integration into quantum circuits to achieve these tasks is problematic when one realizes that non-transverse operations, which are essential for universal quantum computation, lead to the spread of errors.