DOCSLIB.ORG

Time-Varying Quantum Channel Models for Superconducting Qubits ✉ Josu Etxezarreta Martinez 1 , Patricio Fuentes 1, Pedro Crespo1 and Javier Garcia-Frias2

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Time-Varying Quantum Channel Models for Superconducting Qubits ✉ Josu Etxezarreta Martinez 1 , Patricio Fuentes 1, Pedro Crespo1 and Javier Garcia-Frias2 www.nature.com/npjqi ARTICLE OPEN Time-varying quantum channel models for superconducting qubits ✉ Josu Etxezarreta Martinez 1 , Patricio Fuentes 1, Pedro Crespo1 and Javier Garcia-Frias2 The decoherence effects experienced by the qubits of a quantum processor are generally characterized using the amplitude damping time (T1) and the dephasing time (T2). Quantum channel models that exist at the time of writing assume that these parameters are fixed and invariant. However, recent experimental studies have shown that they exhibit a time-varying (TV) behaviour. These time-dependant fluctuations of T1 and T2, which become even more pronounced in the case of superconducting qubits, imply that conventional static quantum channel models do not capture the noise dynamics experienced by realistic qubits with sufficient precision. In this article, we study how the fluctuations of T1 and T2 can be included in quantum channel models. We propose the idea of time-varying quantum channel (TVQC) models, and we show how they provide a more realistic portrayal of decoherence effects than static models in some instances. We also discuss the divergence that exists between TVQCs and their static counterparts by means of a metric known as the diamond norm. In many circumstances this divergence can be significant, which indicates that the time-dependent nature of decoherence must be considered, in order to construct models that capture the real nature of quantum devices. npj Quantum Information (2021) 7:115 ; https://doi.org/10.1038/s41534-021-00448-5 1234567890():,; INTRODUCTION mathematical abstraction that describes the decoherence phe- Quantum error correction (QEC) is considered to be an essential nomenon. However, such channels cannot be efficiently simulated building block in the endeavor of the scientific community to in a classical computer for qubit counts that exceed a small limit. construct fully operational devices capable of conveying the For this reason, a quantum information theory technique known advantages that quantum technology heralds. The value of these as twirling has been used, in order to approximate N AD and N APD 16 error correction strategies, commonly known as quantum error to the classically tractable family of Pauli channels, N P . The correction codes (QECCs), lies in the fact that they protect dynamics of the N APD channel depend on the qubit relaxation quantum information from decoherence, a phenomenon to which time, T1, and the dephasing time, T2, while the N AD channel quantum information is so sensitive that quantum computation is depends solely on T1. These dependencies are also displayed by essentially unfeasible in the absence of error correction schemes. the Pauli channel families obtained by twirling the original In consequence, the quantum information community has gone channels. All these models consider T1 and T2 to be fixed to extraordinary lengths to construct QECCs that are capable of parameters (i.e., they do not fluctuate over time). This implies that efficiently reversing the deleterious effects that quantum informa- the noise dynamics experienced by the qubits in a quantum tion experiences due to the interaction between qubits and their device are identical for each quantum information processing task, surrounding environment. This has led to the design of several independently of when the task is performed. promising families of QECCs, such as quantum Reed-Muller The assumption that T1 and T2 are time invariant has been codes1, quantum low-density parity-check (QLDPC) codes2, disproven in recent experimental studies on quantum proces- – quantum low-density generator matrix codes3–5, quantum con- sors17 21. The data presented in these studies showed that these volutional codes6, quantum turbo codes (QTCs)7–11, and quantum parameters experience time variations of up to 50% of their mean topological codes12,13. It is important to point out that the value in the sample data, which strongly suggests that the aforementioned QECCs are utilized in the context of conventional dynamics of the decoherence effects change drastically as a qubit-based quantum computation, in which the physical function of time. These fluctuations suggest that qubit-based elements are realized by discrete two-level systems. Other QECCs implemented in superconducting circuits will not perform, promising routes toward universal quantum computation and in average, as predicted by considering quantum channels to be error correction exist, such as bosonic codes14,15. In this paper, we static through all the error correction rounds. A possible solution focus on error correction based on two-level physical construc- to deal with these fluctuations when designing QECCs is to tions, and all the discussions refer to this specific approach assume a worst parameters scenario. In this way, one can assure to QECC. that the QECCs will operate reliably for any realization. However, Quantum error models that describe the decoherence pro- the resource consumption of QECCs designed in this manner cesses that corrupt quantum information become a necessity, would be far from optimal, since a higher number of physical when seeking to construct any of the aforementioned error qubits (due to the lower rate or longer blocklength needed to correction methods. The amplitude damping channel, N AD, and correct the worst-case scenario) would be required. This will result the combined amplitude and phase damping channel, N APD, are a in a rather suboptimal solution. Therefore, it is relevant to include pair of widely used quantum channels that provide a the time variation of the decoherence parameters into the 1Department of Basic Sciences, Tecnun - University of Navarra, San Sebastian, Spain. 2Department of Electrical and Computer Engineering, University of Delaware, Newark, DE, ✉ USA. email: [email protected] Published in partnership with The University of New South Wales J. Etxezarreta Martinez et al. 2 quantum channel model, and to study the implications of such where the damping {γ(ω, t)} and scattering {λ(ω, t)} stochastic variations on QEC. processes are functions of the qubit relaxation time {T1(ω, t)} and In this paper, we amalgamate the findings of the aforementioned the qubit dephasing time {T2(ω, t)} stochastic processes. They are studies with the existing models for quantum noise, proposing time- given by varying quantum channels (TVQCs) for superconducting qubits, t À ω; Nðρ; ω; tÞ. The proposed model is characterized by the fact that γðω; tÞ¼1 À e T1ð tÞ and (5) the Kraus operators describing its dynamics are random processes t 2t ω; À ω; whose behavior is governed by the haphazard nature of T1 and T2. λðω; tÞ¼1 À eT1ð tÞ T2ð tÞ: (6) We use the diamond norm22,23 distance between quantum channels fl {T (ω, t)} and {T (ω, t)} are modeled as wide-sense stationary jjN 1 ÀN2jjÅ to show that neglecting the uctuating of T1 and T2 1 2 may result in an unrealistic model for quantum noise. By analyzing random processes with means μT1 and μT2, respectively, and with the statistical properties of the decoherence parameters, we assess an experimentally measured power spectral density (PSD, the when the TV noise channel model will substantially deviate from the Fourier transform of the covariance function), KjðτÞ¼ ω; Δ μ ω; μ = static channel assumption. Finally, we provide a qualitative analysis E½ðT jð t þ tÞÀ Tj ÞðT jð tÞÀ Tj Þ, j 1, 2, where E denotes regarding the implications of this decoherence model on QECCs by the expected value. simulating Kitaev toric codes and QTCs. Twirled approximations of time-varying quantum channels RESULTS The twirled approximations provide us with approximated quantum channel models that incorporate the time-dependant Time-varying quantum channels fluctuations of T1 and T2, and at the same time can be efficiently We define a TVQC, Nðρ; ω; tÞ,as implemented in classical computers16. The time-varying (TV) Pauli X 16,24 ρ; ω; ω; ρ y ω; ; twirl approximation, N PTAðρ; ω; tÞ, is the Pauli channel Nð tÞ¼ Ekð tÞ Ekð tÞ (1) k obtained by twirling a TVQC by the n-fold Pauli group Pn. ω Twirling the TVAD channel will lead to the Pauli channel where the Ek( , t) linear operators are the so-called Kraus operators (TVADPTA) described by the probabilities that each of the Pauli of the operator-sum representation of a quantum channel. Note ω matrices has of taking place. Note that in this context these that the matrices {Ek( , t)} are continuous-time random processes probabilities are realizations of the random processes16,24: 1234567890():,; that will determine the time variations of the TVQC. Consequently, ω; ω; ω; ω; ; the channel dynamics will experience temporal fluctuations pIð tÞ¼1 À pxð tÞÀpyð tÞÀpzð tÞ ω t determined by the random processes {Ek( , t)}. 1 À ω; p ω; t p ω; t 1 e T1ð tÞ and Decoherence arises from a wide range of physical processes xð Þ¼ yð Þ¼4 ð À Þ (7) t t À ω; À ω; involved in the interaction of the qubits with their environment. ω; 1 T1ð tÞ 2T1ð tÞ : pzð tÞ¼ ð1 þ e À 2e Þ Nonetheless, a fairly complete mathematical model of these 4 harmful noise effects can be obtained by combining the time- For the TVAPD channel, the TVAPDPTA approximation is varying amplitude damping channel (TVAD), and the time-varying described by the realizations of the following stochastic processes phase damping or dephasing channel (TVPD)16 into the time- for each of the Pauli matrices16,24 varying combined amplitude and phase damping channel p ðω; tÞ¼1 À p ðω; tÞÀp ðω; tÞÀp ðω; tÞ; (TVAPD), N ðρ; ω; tÞ. The Kraus operators of these TVQCs are: I x y z APD t 1 À ω; p ðω; tÞ¼p ðω; tÞ¼ ð1 À e T1ð tÞÞ and (8) ● Time-varying amplitude damping channels (TVAD), x y 4 t t ρ; ω; 1 ÀT ω;t ÀT ðω;tÞ N ADð tÞ, p ðω; tÞ¼ ð1 þ e 1ð Þ À 2e 2 Þ; z 4 10pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where, once again, T (ω, t) and T (ω, t) are stochastic processes.
Load more

Recommended publications
  • Pilot Quantum Error Correction for Global
    Pilot Quantum Error Correction for Global- Scale Quantum Communications Laszlo Gyongyosi*1,2, Member, IEEE, Sandor Imre1, Member, IEEE 1Quantum Technologies Laboratory, Department of Telecommunications Budapest University of Technology and Economics 2 Magyar tudosok krt, H-1111, Budapest, Hungary 2Information Systems Research Group, Mathematics and Natural Sciences Hungarian Academy of Sciences H-1518, Budapest, Hungary *[email protected] Real global-scale quantum communications and quantum key distribution systems cannot be implemented by the current fiber and free-space links. These links have high attenuation, low polarization-preserving capability or extreme sensitivity to the environment. A potential solution to the problem is the space-earth quantum channels. These channels have no absorption since the signal states are propagated in empty space, however a small fraction of these channels is in the atmosphere, which causes slight depolarizing effect. Furthermore, the relative motion of the ground station and the satellite causes a rotation in the polarization of the quantum states. In the current approaches to compensate for these types of polarization errors, high computational costs and extra physical apparatuses are required. Here we introduce a novel approach which breaks with the traditional views of currently developed quantum-error correction schemes. The proposed solution can be applied to fix the polarization errors which are critical in space-earth quantum communication systems. The channel coding scheme provides capacity-achieving communication over slightly depolarizing space-earth channels. I. Introduction Quantum error-correction schemes use different techniques to correct the various possible errors which occur in a quantum channel. In the first decade of the 21st century, many revolutionary properties of quantum channels were discovered [12-16], [19-22] however the efficient error- correction in quantum systems is still a challenge.
    [Show full text]
  • Models of Quantum Complexity Growth
    Models of quantum complexity growth Fernando G.S.L. Brand~ao,a;b;c;d Wissam Chemissany,b Nicholas Hunter-Jones,* e;b Richard Kueng,* b;c John Preskillb;c;d aAmazon Web Services, AWS Center for Quantum Computing, Pasadena, CA bInstitute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125 cDepartment of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA 91125 dWalter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125 ePerimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 *Corresponding authors: [email protected] and [email protected] Abstract: The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the size of the shortest quantum computation that executes the unitary or prepares the state. It is reasonable to expect that the complexity of a quantum state governed by a chaotic many- body Hamiltonian grows linearly with time for a time that is exponential in the system size; however, because it is hard to rule out a short-cut that improves the efficiency of a computation, it is notoriously difficult to derive lower bounds on quantum complexity for particular unitaries or states without making additional assumptions. To go further, one may study more generic models of complexity growth. We provide a rigorous connection between complexity growth and unitary k-designs, ensembles which capture the randomness of the unitary group. This connection allows us to leverage existing results about design growth to draw conclusions about the growth of complexity.
    [Show full text]
  • Booklet of Abstracts
    Booklet of abstracts Thomas Vidick California Institute of Technology Tsirelson's problem and MIP*=RE Boris Tsirelson in 1993 implicitly posed "Tsirelson's Problem", a question about the possible equivalence between two different ways of modeling locality, and hence entanglement, in quantum mechanics. Tsirelson's Problem gained prominence through work of Fritz, Navascues et al., and Ozawa a decade ago that establishes its equivalence to the famous "Connes' Embedding Problem" in the theory of von Neumann algebras. Recently we gave a negative answer to Tsirelson's Problem and Connes' Embedding Problem by proving a seemingly stronger result in quantum complexity theory. This result is summarized in the equation MIP* = RE between two complexity classes. In the talk I will present and motivate Tsirelson's problem, and outline its connection to Connes' Embedding Problem. I will then explain the connection to quantum complexity theory and show how ideas developed in the past two decades in the study of classical and quantum interactive proof systems led to the characterization (which I will explain) MIP* = RE and the negative resolution of Tsirelson's Problem. Based on joint work with Ji, Natarajan, Wright and Yuen available at arXiv:2001.04383. Joonho Lee, Dominic Berry, Craig Gidney, William Huggins, Jarrod McClean, Nathan Wiebe and Ryan Babbush Columbia University | Macquarie University | Google | Google Research | Google | University of Washington | Google Efficient quantum computation of chemistry through tensor hypercontraction We show how to achieve the highest efficiency yet for simulations with arbitrary basis sets by using a representation of the Coulomb operator known as tensor hypercontraction (THC). We use THC to express the Coulomb operator in a non-orthogonal basis, which we are able to block encode by separately rotating each term with angles that are obtained via QROM.
    [Show full text]
  • 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.
    [Show full text]
  • Robustbase: Basic Robust Statistics
    Package ‘robustbase’ June 2, 2021 Version 0.93-8 VersionNote Released 0.93-7 on 2021-01-04 to CRAN Date 2021-06-01 Title Basic Robust Statistics URL http://robustbase.r-forge.r-project.org/ Description ``Essential'' Robust Statistics. Tools allowing to analyze data with robust methods. This includes regression methodology including model selections and multivariate statistics where we strive to cover the book ``Robust Statistics, Theory and Methods'' by 'Maronna, Martin and Yohai'; Wiley 2006. Depends R (>= 3.5.0) Imports stats, graphics, utils, methods, DEoptimR Suggests grid, MASS, lattice, boot, cluster, Matrix, robust, fit.models, MPV, xtable, ggplot2, GGally, RColorBrewer, reshape2, sfsmisc, catdata, doParallel, foreach, skewt SuggestsNote mostly only because of vignette graphics and simulation Enhances robustX, rrcov, matrixStats, quantreg, Hmisc EnhancesNote linked to in man/*.Rd LazyData yes NeedsCompilation yes License GPL (>= 2) Author Martin Maechler [aut, cre] (<https://orcid.org/0000-0002-8685-9910>), Peter Rousseeuw [ctb] (Qn and Sn), Christophe Croux [ctb] (Qn and Sn), Valentin Todorov [aut] (most robust Cov), Andreas Ruckstuhl [aut] (nlrob, anova, glmrob), Matias Salibian-Barrera [aut] (lmrob orig.), Tobias Verbeke [ctb, fnd] (mc, adjbox), Manuel Koller [aut] (mc, lmrob, psi-func.), Eduardo L. T. Conceicao [aut] (MM-, tau-, CM-, and MTL- nlrob), Maria Anna di Palma [ctb] (initial version of Comedian) 1 2 R topics documented: Maintainer Martin Maechler <[email protected]> Repository CRAN Date/Publication 2021-06-02 10:20:02 UTC R topics documented: adjbox . .4 adjboxStats . .7 adjOutlyingness . .9 aircraft . 12 airmay . 13 alcohol . 14 ambientNOxCH . 15 Animals2 . 18 anova.glmrob . 19 anova.lmrob .
    [Show full text]
  • A Practical Guide to Support Predictive Tasks in Data Science
    A Practical Guide to Support Predictive Tasks in Data Science Jose´ Augusto Camaraˆ Filho1, Jose´ Maria Monteiro1,Cesar´ Lincoln Mattos1 and Juvencioˆ Santos Nobre2 1Department of Computing, Federal University of Ceara,´ Fortaleza, Ceara,´ Brazil 2Department of Statistics and Applied Mathematics, Federal University of Ceara,´ Fortaleza, Ceara,´ Brazil Keywords: Practical Guide, Prediction, Data Science. Abstract: Currently, professionals from the most diverse areas of knowledge need to explore their data repositories in order to extract knowledge and create new products or services. Several tools have been proposed in order to facilitate the tasks involved in the Data Science lifecycle. However, such tools require their users to have specific (and deep) knowledge in different areas of Computing and Statistics, making their use practically unfeasible for non-specialist professionals in data science. In this paper, we propose a guideline to support predictive tasks in data science. In addition to being useful for non-experts in Data Science, the proposed guideline can support data scientists, data engineers or programmers which are starting to deal with predic- tive tasks. Besides, we present a tool, called DSAdvisor, which follows the stages of the proposed guideline. DSAdvisor aims to encourage non-expert users to build machine learning models to solve predictive tasks, ex- tracting knowledge from their own data repositories. More specifically, DSAdvisor guides these professionals in predictive tasks involving regression and classification. 1 INTRODUCTION dict the future, and create new services and prod- ucts (Ozdemir, 2016). Data science makes it pos- Due to a large amount of data currently available, sible to identifying patterns hidden and obtain new arises the need for professionals of different areas to insights hidden in these datasets, from complex ma- extract knowledge from their repositories to create chine learning algorithms.
    [Show full text]
  • Quantum Computing : a Gentle Introduction / Eleanor Rieffel and Wolfgang Polak
    QUANTUM COMPUTING A Gentle Introduction Eleanor Rieffel and Wolfgang Polak The MIT Press Cambridge, Massachusetts London, England ©2011 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. For information about special quantity discounts, please email [email protected] This book was set in Syntax and Times Roman by Westchester Book Group. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Rieffel, Eleanor, 1965– Quantum computing : a gentle introduction / Eleanor Rieffel and Wolfgang Polak. p. cm.—(Scientific and engineering computation) Includes bibliographical references and index. ISBN 978-0-262-01506-6 (hardcover : alk. paper) 1. Quantum computers. 2. Quantum theory. I. Polak, Wolfgang, 1950– II. Title. QA76.889.R54 2011 004.1—dc22 2010022682 10987654321 Contents Preface xi 1 Introduction 1 I QUANTUM BUILDING BLOCKS 7 2 Single-Qubit Quantum Systems 9 2.1 The Quantum Mechanics of Photon Polarization 9 2.1.1 A Simple Experiment 10 2.1.2 A Quantum Explanation 11 2.2 Single Quantum Bits 13 2.3 Single-Qubit Measurement 16 2.4 A Quantum Key Distribution Protocol 18 2.5 The State Space of a Single-Qubit System 21 2.5.1 Relative Phases versus Global Phases 21 2.5.2 Geometric Views of the State Space of a Single Qubit 23 2.5.3 Comments on General Quantum State Spaces
    [Show full text]
  • Quantum Information Science
    Quantum Information Science Seth Lloyd Professor of Quantum-Mechanical Engineering Director, WM Keck Center for Extreme Quantum Information Theory (xQIT) Massachusetts Institute of Technology Article Outline: Glossary I. Definition of the Subject and Its Importance II. Introduction III. Quantum Mechanics IV. Quantum Computation V. Noise and Errors VI. Quantum Communication VII. Implications and Conclusions 1 Glossary Algorithm: A systematic procedure for solving a problem, frequently implemented as a computer program. Bit: The fundamental unit of information, representing the distinction between two possi- ble states, conventionally called 0 and 1. The word ‘bit’ is also used to refer to a physical system that registers a bit of information. Boolean Algebra: The mathematics of manipulating bits using simple operations such as AND, OR, NOT, and COPY. Communication Channel: A physical system that allows information to be transmitted from one place to another. Computer: A device for processing information. A digital computer uses Boolean algebra (q.v.) to processes information in the form of bits. Cryptography: The science and technique of encoding information in a secret form. The process of encoding is called encryption, and a system for encoding and decoding is called a cipher. A key is a piece of information used for encoding or decoding. Public-key cryptography operates using a public key by which information is encrypted, and a separate private key by which the encrypted message is decoded. Decoherence: A peculiarly quantum form of noise that has no classical analog. Decoherence destroys quantum superpositions and is the most important and ubiquitous form of noise in quantum computers and quantum communication channels.
    [Show full text]
  • Detecting Outliers in Weighted Univariate Survey Data
    Detecting outliers in weighted univariate survey data Anna Pauliina Sandqvist∗ October 27, 2015 Preliminary Version Abstract Outliers and influential observations are a frequent concern in all kind of statistics, data analysis and survey data. Especially, if the data is asymmetrically distributed or heavy- tailed, outlier detection turns out to be difficult as most of the already introduced methods are not optimal in this case. In this paper we examine various non-parametric outlier detec- tion approaches for (size-)weighted growth rates from quantitative surveys and propose new respectively modified methods which can account better for skewed and long-tailed data. We apply empirical influence functions to compare these methods under different data spec- ifications. JEL Classification: C14 Keywords: Outlier detection, influential observation, size-weight, periodic surveys 1 Introduction Outliers are usually considered to be extreme values which are far away from the other data points (see, e.g., Barnett and Lewis (1994)). Chambers (1986) was first to differentiate between representative and non-representative outliers. The former are observations with correct values and are not considered to be unique, whereas non-representative outliers are elements with incorrect values or are for some other reasons considered to be unique. Most of the outlier analysis focuses on the representative outliers as non-representatives values should be taken care of already in (survey) data editing. The main reason to be concerned about the possible outliers is, that whether or not they are included into the sample, the estimates might differ considerably. The data points with substantial influence on the estimates are called influential observations and they should be ∗Authors address: KOF Swiss Economic Institute, ETH Zurich, Leonhardstrasse 21 LEE, CH-8092 Zurich, Switzerland.
    [Show full text]
  • Outlier Detection
    OUTLIER DETECTION Short Course Session 1 Nedret BILLOR Auburn University Department of Mathematics & Statistics, USA Statistics Conference, Colombia, Aug 8‐12, 2016 OUTLINE Motivation and Introduction Approaches to Outlier Detection Sensitivity of Statistical Methods to Outliers Statistical Methods for Outlier Detection Outliers in Univariate data Outliers in Multivariate Classical and Robust Statistical Distance‐ based Methods PCA based Outlier Detection Outliers in Functional Data MOTIVATION & INTRODUCTION Hadlum vs. Hadlum (1949) [Barnett 1978] Ozone Hole Case I: Hadlum vs. Hadlum (1949) [Barnett 1978] The birth of a child to Mrs. Hadlum happened 349 days after Mr. Hadlum left for military service. Average human gestation period is 280 days (40 weeks). Statistically, 349 days is an outlier. Case I: Hadlum vs. Hadlum (1949) [Barnett 1978] − blue: statistical basis (13634 observations of gestation periods) − green: assumed underlying Gaussian process − Very low probability for the birth of Mrs. Hadlums child for being generated by this process − red: assumption of Mr. Hadlum (another Gaussian process responsible for the observed birth, where the gestation period responsible) − Under this assumption the gestation period has an average duration and highest‐possible probability Case II: The Antarctic Ozone Hole The History behind the Ozone Hole • The Earth's ozone layer protects all life from the sun's harmful radiation. Case II: The Antarctic Ozone Hole (cont.) . Human activities (e.g. CFS's in aerosols) have damaged this shield. Less protection from ultraviolet light will, over time, lead to higher skin cancer and cataract rates and crop damage. Case II: The Antarctic Ozone Hole (cont.) Molina and Rowland in 1974 (lab study) and many studies after this, demonstrated the ability of CFC's (Chlorofluorocarbons) to breakdown Ozone in the presence of high frequency UV light .
    [Show full text]
  • Practical Quantum Cryptography and Possible Attacks
    Practical Quantum cryptography and possible attacks Alex Ling, Ilja Gerhardt, Antia Lamas-Linares, Christian Kurtsiefer 24C3 , Berlin supported by DSTA and Ministry of Education Overview Cryptography and keys What can quantum crypto do? BB84 type prepare & send implementations Quantum channels Entanglement and quantum cryptography Timing channel attack A side channel-tolerant protocol: E91 revisited Secure Communication symmetric encryption Alice key key Bob 4Kt$jtp 5L9dEe0 I want I want a coffee a coffee insecure channel ─ One time pad / Vernam Cipher: secure for one key bit per bit ─ 3DES, AES & friends: high throughput asymmetric encryption Bob key 2 n, p, q Alice key 1 4Kt$jtp 5L9dEe0 I want I want a coffee a coffee insecure channel RSA, ellipt. curves: simple, secure if you can not get key 1 from key 2 What is wrong with RSA? Bob key 2 n, p, q Alice key 1 4Kt$jtp 5L9dEe0 I want I want a coffee a coffee insecure channel ....if you can not get key 1 from key 2 take dedicated hardware find a clever algorithm ...and you get take a quantum computer the key! take some time..... Classical Key Distribution trusted courier Alice key key Bob tamper-safe devices key key Alice Bob Quantum Key Distribution 1 “ trusted ” courier.... Alice key key Bob information is carried by physical objects: hole in paper, ink, magnetic domain, electrical charge, dye spot, radio wave, light pulse,... classical physics: copying is possible (----> insecure) Photons carry information polarization for 0 and 1: vertical horizontal use polarizing beam splitter to recover 0 or 1: Quantum mechanics...
    [Show full text]
  • Supercomputer Simulations of Transmon Quantum Computers Quantum Simulations of Transmon Supercomputer
    IAS Series IAS Supercomputer simulations of transmon quantum computers quantum simulations of transmon Supercomputer 45 Supercomputer simulations of transmon quantum computers Dennis Willsch IAS Series IAS Series Band / Volume 45 Band / Volume 45 ISBN 978-3-95806-505-5 ISBN 978-3-95806-505-5 Dennis Willsch Schriften des Forschungszentrums Jülich IAS Series Band / Volume 45 Forschungszentrum Jülich GmbH Institute for Advanced Simulation (IAS) Jülich Supercomputing Centre (JSC) Supercomputer simulations of transmon quantum computers Dennis Willsch Schriften des Forschungszentrums Jülich IAS Series Band / Volume 45 ISSN 1868-8489 ISBN 978-3-95806-505-5 Bibliografsche Information der Deutschen Nationalbibliothek. Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografe; detaillierte Bibliografsche Daten sind im Internet über http://dnb.d-nb.de abrufbar. Herausgeber Forschungszentrum Jülich GmbH und Vertrieb: Zentralbibliothek, Verlag 52425 Jülich Tel.: +49 2461 61-5368 Fax: +49 2461 61-6103 [email protected] www.fz-juelich.de/zb Umschlaggestaltung: Grafsche Medien, Forschungszentrum Jülich GmbH Titelbild: Quantum Flagship/H.Ritsch Druck: Grafsche Medien, Forschungszentrum Jülich GmbH Copyright: Forschungszentrum Jülich 2020 Schriften des Forschungszentrums Jülich IAS Series, Band / Volume 45 D 82 (Diss. RWTH Aachen University, 2020) ISSN 1868-8489 ISBN 978-3-95806-505-5 Vollständig frei verfügbar über das Publikationsportal des Forschungszentrums Jülich (JuSER) unter www.fz-juelich.de/zb/openaccess. This is an Open Access publication distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract We develop a simulator for quantum computers composed of superconducting transmon qubits.
    [Show full text]