Removing Leakage-Induced Correlated Errors in Superconducting Quantum Error Correction
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Conversion of a General Quantum Stabilizer Code to an Entanglement
Conversion of a general quantum stabilizer code to an entanglement distillation protocol∗ Ryutaroh Matsumoto Dept. of Communications and Integrated Systems Tokyo Institute of Technology, 152-8552 Japan Email: [email protected] April 4, 2003 Abstract We show how to convert a quantum stabilizer code to a one-way or two- way entanglement distillation protocol. The proposed conversion method is a generalization of those of Shor-Preskill and Nielsen-Chuang. The recurrence protocol and the quantum privacy amplification protocol are equivalent to the protocols converted from [[2, 1]] stabilizer codes. We also give an example of a two-way protocol converted from a stabilizer bet- ter than the recurrence protocol and the quantum privacy amplification protocol. The distillable entanglement by the class of one-way protocols converted from stabilizer codes for a certain class of states is equal to or greater than the achievable rate of stabilizer codes over the channel cor- responding to the distilled state, and they can distill asymptotically more entanglement from a very noisy Werner state than the hashing protocol. 1 Introduction arXiv:quant-ph/0209091v4 4 Apr 2003 In many applications of quantum mechanics to communication, the sender and the receiver have to share a maximally entangled quantum state of two particles. When there is a noiseless quantum communication channel, the sender can send one of two particles in a maximally entangled state to the receiver and sharing of it is easily accomplished. However, the quantum communication channel is usually noisy, that is, the quantum state of the received particle changes probabilistically from the original state of a particle. -
Simulating Quantum Field Theory with a Quantum Computer
Simulating quantum field theory with a quantum computer John Preskill Lattice 2018 28 July 2018 This talk has two parts (1) Near-term prospects for quantum computing. (2) Opportunities in quantum simulation of quantum field theory. Exascale digital computers will advance our knowledge of QCD, but some challenges will remain, especially concerning real-time evolution and properties of nuclear matter and quark-gluon plasma at nonzero temperature and chemical potential. Digital computers may never be able to address these (and other) problems; quantum computers will solve them eventually, though I’m not sure when. The physics payoff may still be far away, but today’s research can hasten the arrival of a new era in which quantum simulation fuels progress in fundamental physics. Frontiers of Physics short distance long distance complexity Higgs boson Large scale structure “More is different” Neutrino masses Cosmic microwave Many-body entanglement background Supersymmetry Phases of quantum Dark matter matter Quantum gravity Dark energy Quantum computing String theory Gravitational waves Quantum spacetime particle collision molecular chemistry entangled electrons A quantum computer can simulate efficiently any physical process that occurs in Nature. (Maybe. We don’t actually know for sure.) superconductor black hole early universe Two fundamental ideas (1) Quantum complexity Why we think quantum computing is powerful. (2) Quantum error correction Why we think quantum computing is scalable. A complete description of a typical quantum state of just 300 qubits requires more bits than the number of atoms in the visible universe. Why we think quantum computing is powerful We know examples of problems that can be solved efficiently by a quantum computer, where we believe the problems are hard for classical computers. -
Quantum Error-Correcting Codes by Concatenation QEC11
Quantum Error-Correcting Codes by Concatenation QEC11 Second International Conference on Quantum Error Correction University of Southern California, Los Angeles, USA December 5–9, 2011 Quantum Error-Correcting Codes by Concatenation Markus Grassl joint work with Bei Zeng Centre for Quantum Technologies National University of Singapore Singapore Markus Grassl – 1– 07.12.2011 Quantum Error-Correcting Codes by Concatenation QEC11 Why Bei isn’t here Jonathan, November 24, 2011 Markus Grassl – 2– 07.12.2011 Quantum Error-Correcting Codes by Concatenation QEC11 Overview Shor’s nine-qubit code revisited • The code [[25, 1, 9]] • Concatenated graph codes • Generalized concatenated quantum codes • Codes for the Amplitude Damping (AD) channel • Conclusions • Markus Grassl – 3– 07.12.2011 Quantum Error-Correcting Codes by Concatenation QEC11 Shor’s Nine-Qubit Code Revisited Bit-flip code: 0 000 , 1 111 . | → | | → | Phase-flip code: 0 + ++ , 1 . | → | | → | − −− Effect of single-qubit errors on the bit-flip code: X-errors change the basis states, but can be corrected • Z-errors at any of the three positions: • Z 000 = 000 | | “encoded” Z-operator Z 111 = 111 | −| = Bit-flip code & error correction convert the channel into a phase-error ⇒ channel = Concatenation of bit-flip code and phase-flip code yields [[9, 1, 3]] ⇒ Markus Grassl – 4– 07.12.2011 Quantum Error-Correcting Codes by Concatenation QEC11 The Code [[25, 1, 9]] The best single-error correcting code is = [[5, 1, 3]] • C0 Re-encoding each of the 5 qubits with yields = [[52, 1, 32]] -
Lecture 6: Quantum Error Correction and Quantum Capacity
Lecture 6: Quantum error correction and quantum capacity Mark M. Wilde∗ The quantum capacity theorem is one of the most important theorems in quantum Shannon theory. It is a fundamentally \quantum" theorem in that it demonstrates that a fundamentally quantum information quantity, the coherent information, is an achievable rate for quantum com- munication over a quantum channel. The fact that the coherent information does not have a strong analog in classical Shannon theory truly separates the quantum and classical theories of information. The no-cloning theorem provides the intuition behind quantum error correction. The goal of any quantum communication protocol is for Alice to establish quantum correlations with the receiver Bob. We know well now that every quantum channel has an isometric extension, so that we can think of another receiver, the environment Eve, who is at a second output port of a larger unitary evolution. Were Eve able to learn anything about the quantum information that Alice is attempting to transmit to Bob, then Bob could not be retrieving this information|otherwise, they would violate the no-cloning theorem. Thus, Alice should figure out some subspace of the channel input where she can place her quantum information such that only Bob has access to it, while Eve does not. That the dimensionality of this subspace is exponential in the coherent information is perhaps then unsurprising in light of the above no-cloning reasoning. The coherent information is an entropy difference H(B) − H(E)|a measure of the amount of quantum correlations that Alice can establish with Bob less the amount that Eve can gain. -
Universal Control and Error Correction in Multi-Qubit Spin Registers in Diamond T
LETTERS PUBLISHED ONLINE: 2 FEBRUARY 2014 | DOI: 10.1038/NNANO.2014.2 Universal control and error correction in multi-qubit spin registers in diamond T. H. Taminiau 1,J.Cramer1,T.vanderSar1†,V.V.Dobrovitski2 and R. Hanson1* Quantum registers of nuclear spins coupled to electron spins of including one with an additional strongly coupled 13C spin (see individual solid-state defects are a promising platform for Supplementary Information). To demonstrate the generality of quantum information processing1–13. Pioneering experiments our approach to create multi-qubit registers, we realized the initia- selected defects with favourably located nuclear spins with par- lization, control and readout of three weakly coupled 13C spins for ticularly strong hyperfine couplings4–10. To progress towards each NV centre studied (see Supplementary Information). In the large-scale applications, larger and deterministically available following, we consider one of these NV centres in detail and use nuclear registers are highly desirable. Here, we realize univer- two of its weakly coupled 13C spins to form a three-qubit register sal control over multi-qubit spin registers by harnessing abun- for quantum error correction (Fig. 1a). dant weakly coupled nuclear spins. We use the electron spin of Our control method exploits the dependence of the nuclear spin a nitrogen–vacancy centre in diamond to selectively initialize, quantization axis on the electron spin state as a result of the aniso- control and read out carbon-13 spins in the surrounding spin tropic hyperfine interaction (see Methods for hyperfine par- bath and construct high-fidelity single- and two-qubit gates. ameters), so no radiofrequency driving of the nuclear spins is We exploit these new capabilities to implement a three-qubit required7,23–28. -
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. -
Phd Proposal 2020: Quantum Error Correction with Superconducting Circuits
PhD Proposal 2020: Quantum error correction with superconducting circuits Keywords: quantum computing, quantum error correction, Josephson junctions, circuit quantum electrodynamics, high-impedance circuits • Laboratory name: Laboratoire de Physique de l'Ecole Normale Supérieure de Paris • PhD advisors : Philippe Campagne-Ibarcq ([email protected]) and Zaki Leghtas ([email protected]). • Web pages: http://cas.ensmp.fr/~leghtas/ https://philippecampagneib.wixsite.com/research • PhD location: ENS Paris, 24 rue Lhomond Paris 75005. • Funding: ERC starting grant. Quantum systems can occupy peculiar states, such as superpositions or entangled states. These states are intrinsically fragile and eventually get wiped out by inevitable interactions with the environment. Protecting quantum states against decoherence is a formidable and fundamental problem in physics, and it is pivotal for the future of quantum computing. Quantum error correction provides a potential solution, but its current envisioned implementations require daunting resources: a single bit of information is protected by encoding it across tens of thousands of physical qubits. Our team in Paris proposes to protect quantum information in an entirely new type of qubit with two key specicities. First, it will be encoded in a single superconducting circuit resonator whose innite dimensional Hilbert space can replace large registers of physical qubits. Second, this qubit will be rf-powered, continuously exchanging photons with a reservoir. This approach challenges the intuition that a qubit must be isolated from its environment. Instead, the reservoir acts as a feedback loop which continuously and autonomously corrects against errors. This correction takes place at the level of the quantum hardware, and reduces the need for error syndrome measurements which are resource intensive. -
Performance of Various Low-Level Decoder for Surface Codes in the Presence of Measurement Error
Air Force Institute of Technology AFIT Scholar Theses and Dissertations Student Graduate Works 3-2021 Performance of Various Low-level Decoder for Surface Codes in the Presence of Measurement Error Claire E. Badger Follow this and additional works at: https://scholar.afit.edu/etd Part of the Computer Sciences Commons Recommended Citation Badger, Claire E., "Performance of Various Low-level Decoder for Surface Codes in the Presence of Measurement Error" (2021). Theses and Dissertations. 4885. https://scholar.afit.edu/etd/4885 This Thesis is brought to you for free and open access by the Student Graduate Works at AFIT Scholar. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of AFIT Scholar. For more information, please contact [email protected]. Performance of Various Low-Level Decoders for Surface Codes in the Presence of Measurement Error THESIS Claire E Badger, B.S.C.S., 2d Lieutenant, USAF AFIT-ENG-MS-21-M-008 DEPARTMENT OF THE AIR FORCE AIR UNIVERSITY AIR FORCE INSTITUTE OF TECHNOLOGY Wright-Patterson Air Force Base, Ohio DISTRIBUTION STATEMENT A APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED. The views expressed in this document are those of the author and do not reflect the official policy or position of the United States Air Force, the United States Department of Defense or the United States Government. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. AFIT-ENG-MS-21-M-008 Performance of Various Low-Level Decoders for Surface Codes in the Presence of Measurement Error THESIS Presented to the Faculty Department of Electrical and Computer Engineering Graduate School of Engineering and Management Air Force Institute of Technology Air University Air Education and Training Command in Partial Fulfillment of the Requirements for the Degree of Master of Science in Computer Science Claire E Badger, B.S.C.S., B.S.E.E. -
Arxiv:0905.2794V4 [Quant-Ph] 21 Jun 2013 Error Correction 7 B
Quantum Error Correction for Beginners Simon J. Devitt,1, ∗ William J. Munro,2 and Kae Nemoto1 1National Institute of Informatics 2-1-2 Hitotsubashi Chiyoda-ku Tokyo 101-8340. Japan 2NTT Basic Research Laboratories NTT Corporation 3-1 Morinosato-Wakamiya, Atsugi Kanagawa 243-0198. Japan (Dated: June 24, 2013) Quantum error correction (QEC) and fault-tolerant quantum computation represent one of the most vital theoretical aspect of quantum information processing. It was well known from the early developments of this exciting field that the fragility of coherent quantum systems would be a catastrophic obstacle to the development of large scale quantum computers. The introduction of quantum error correction in 1995 showed that active techniques could be employed to mitigate this fatal problem. However, quantum error correction and fault-tolerant computation is now a much larger field and many new codes, techniques, and methodologies have been developed to implement error correction for large scale quantum algorithms. In response, we have attempted to summarize the basic aspects of quantum error correction and fault-tolerance, not as a detailed guide, but rather as a basic introduction. This development in this area has been so pronounced that many in the field of quantum information, specifically researchers who are new to quantum information or people focused on the many other important issues in quantum computation, have found it difficult to keep up with the general formalisms and methodologies employed in this area. Rather than introducing these concepts from a rigorous mathematical and computer science framework, we instead examine error correction and fault-tolerance largely through detailed examples, which are more relevant to experimentalists today and in the near future. -
Machine Learning Quantum Error Correction Codes: Learning the Toric Code
,, % % hhXPP ¨, hXH(HPXh % ,¨ Instituto de F´ısicaTe´orica (((¨lQ e@QQ IFT Universidade Estadual Paulista el e@@l DISSERTAC¸ AO~ DE MESTRADO IFT{D.009/18 Machine Learning Quantum Error Correction Codes: Learning the Toric Code Carlos Gustavo Rodriguez Fernandez Orientador Leandro Aolita Dezembro de 2018 Rodriguez Fernandez, Carlos Gustavo R696m Machine learning quantum error correction codes: learning the toric code / Carlos Gustavo Rodriguez Fernandez. – São Paulo, 2018 43 f. : il. Dissertação (mestrado) - Universidade Estadual Paulista (Unesp), Instituto de Física Teórica (IFT), São Paulo Orientador: Leandro Aolita 1. Aprendizado do computador. 2. Códigos de controle de erros(Teoria da informação) 3. Informação quântica. I. Título. Sistema de geração automática de fichas catalográficas da Unesp. Biblioteca do Instituto de Física Teórica (IFT), São Paulo. Dados fornecidos pelo autor(a). Acknowledgements I'd like to thank Giacomo Torlai for painstakingly explaining to me David Poulin's meth- ods of simulating the toric code. I'd also like to thank Giacomo, Juan Carrasquilla and Lauren Haywards for sharing some very useful code I used for the simulation and learning of the toric code. I'd like to thank Gwyneth Allwright for her useful comments on a draft of this essay. I'd also like to thank Leandro Aolita for his patience in reading some of the final drafts of this work. Of course, I'd like to thank the admin staff in Perimeter Institute { in partiuclar, without Debbie not of this would have been possible. I'm also deeply indebted to Roger Melko, who supervised this work in Perimeter Institute (where a version of this work was presented as my PSI Essay). -
UC Riverside UC Riverside Electronic Theses and Dissertations
UC Riverside UC Riverside Electronic Theses and Dissertations Title Codeword Stabilized Quantum Codes and Their Error Correction Permalink https://escholarship.org/uc/item/67h4j8p8 Author Li, Yunfan Publication Date 2010 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA RIVERSIDE Codeword Stabilized Quantum Codes and Their Error Correction A Dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Electrical Engineering by Yunfan Li August 2010 Dissertation Committee: Dr. Ilya Dumer, Chairperson Dr. Leonid Pryadko Dr. Alexander N. Korotkov Copyright by Yunfan Li 2010 The Dissertation of Yunfan Li is approved: Committee Chairperson University of California, Riverside Acknowledgments I would like to thank all people who have helped and inspired me during my doctoral study. I especially want to thank my advisor, Professor Ilya Dumer, for his important and valuable guidance during my research and study at UC Riverside. His perpetual energy and enthusiasm in research had motivated me. In addition, he was always willing to help his students with their research. As a result, research life became smooth and rewarding for me. I was delighted to interact with Professor Leonid Pryadko by attending his classes and having him as my co-advisor. I want to thank him for his guidance and joint effort in my research. I would like to thank Professor Alexander N. Korotkov. I got deep understanding about quantum computation and quantum error correcting codes from his lectures. I also want to express my thanks to Bei Zeng for the detailed explanation of the CWS code construction, to Markus Grassl for the important joint effort.