Grover's search with faults on some marked elements

Grover's algorithm is a quantum query algorithm solving the unstructured search problem of size $N$ using $O(\sqrt{N})$ queries. It provides a significant speed-up over any classical algorithm \cite{Gro96}. The running time of the algorithm, however, is very sensitive to errors in queries. It is known that if query may fail (report all marked elements as unmarked) the algorithm needs $\Omega(N)$ queries to find a marked element \cite{RS08}. \cite{AB+13} have proved the same result for the model where each marked element has its own probability to be reported as unmarked. We study the behavior of Grover's algorithm in the model where the search space contains both faulty and non-faulty marked elements. We show that in this setting it is indeed possible to find one of non-faulty marked items in $O(\sqrt{N})$ queries. We also analyze the limiting behavior of the algorithm for a large number of steps and show the existence and the structure of limiting state $\rho_{lim}$.Comment: 17 pages, 6 figure

Kvantu automātu un meklēšanas algoritmu iespējas un ierobežojumi

Kvantu skaitļošana ir nozare, kas pēta uz kvantu mehānikas likumiem balstīto skaitļošanas modeļu īpašības. Disertācija ir veltīta kvantu skaitļošanas algoritmiskiem aspektiem. Piedāvāti rezultāti trijos virzienos: Kvantu galīgi automāti Analizēta stāvokļu efektivitāte kvantu vienvirziena galīgam automātam. Uzlabota labāka zināmā eksponenciālā atšķirība [AF98] starp kvantu un klasiskajiem galīgajiem automātiem. Grovera algoritma analīze Pētīta Grovera algoritma noturība pret kļūdām. Vispārināts [RS08] loģisko kļūdu modelis un piedāvāti vairāki jauni rezultāti. Kvantu klejošana Pētīta meklēšana 2D režģī izmantojot kvantu klejošanu. Paātrināts [AKR05] kvantu klejošanas meklēšanas algoritms. Atslēgas vārdi: Kvantu galīgi automāti, eksponenciālā atšķirība, Grovera algoritms, noturība pret kļūdām, kvantu klejošana LITERATŪRA [AF98] A. Ambainis, R. Freivalds. 1-way quantum finite automata: strengths, weaknesses and generalizations. Proceedings of the 39th IEEE Conference on Foundations of Computer Science, 332-341, 1998. arXiv:quant-ph/9802062v3 [AKR05] A. Ambainis, J. Kempe, A. Rivosh. Coins make quantum walks faster. Proceedings of SODA’05, 1099-1108, 2005. [RS08] O. Regev, L. Schiff. Impossibility of a Quantum Speed-up with a Faulty Oracle. Proceedings of ICALP’2008, Lecture Notes in Computer Science, 5125:773-781, 2008.Quantum computation is the eld that investigates properties of models of computation based on the laws of the quantum mechanics. The thesis is ded- icated to algorithmic aspects of quantum computation and provides results in three directions: Quantum nite automata We study space-eciency of one-way quantum nite automata. We improve best known exponential separation [AF98] between quantum and classical one-way nite automata. Analysis of Grover's algorithm We study fault-tolerance of Grover's algorithm. We generalize the model of logical faults by [RS08] and present several new results. Quantum walks We study search by quantum walks on two-dimensional grid. We im- prove (speed-up) quantum walk search algorithm by [AKR05]. Keywords: Quantum nite automata, exponential separation, Grover's al- gorithm, fault-tolerance, quantum walks BIBLIOGRAPHY [AF98] A. Ambainis, R. Freivalds. 1-way quantum nite automata: strengths, weaknesses and gen- eralizations. Proceedings of the 39th IEEE Conference on Foundations of Computer Science, 332-341, 1998. arXiv:quant-ph/9802062v3 [AKR05] A. Ambainis, J. Kempe, A. Rivosh. Coins make quantum walks faster. Proceedings of SODA'05, 1099-1108, 2005. [RS08] O. Regev, L. Schi. Impossibility of a Quantum Speed-up with a Faulty Oracle. Proceedings of ICALP'2008, Lecture Notes in Computer Science, 5125:773-781, 2008

Design and implementation of a fault-tolerant multimedia network and a local map based (LMB) self-healing scheme for arbitrary topology networks.

by Arion Ko Kin Wa.Thesis (M.Phil.)--Chinese University of Hong Kong, 1997.Includes bibliographical references (leaves 101-[106]).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Overview --- p.1Chapter 1.2 --- Service Survivability Planning --- p.2Chapter 1.3 --- Categories of Outages --- p.3Chapter 1.4 --- Goals of Restoration --- p.4Chapter 1.5 --- Technology Impacts on Network Survivability --- p.5Chapter 1.6 --- Performance Models and Measures in Quantifying Network Sur- vivability --- p.6Chapter 1.7 --- Organization of Thesis --- p.6Chapter 2 --- Design and Implementation of A Survivable High-Speed Mul- timedia Network --- p.8Chapter 2.1 --- An Overview of CUM LAUDE NET --- p.8Chapter 2.2 --- The Network Architecture --- p.9Chapter 2.2.1 --- Architectural Overview --- p.9Chapter 2.2.2 --- Router-Node Design --- p.11Chapter 2.2.3 --- Buffer Allocation --- p.12Chapter 2.2.4 --- Buffer Transmission Priority --- p.14Chapter 2.2.5 --- Congestion Control --- p.15Chapter 2.3 --- Protocols --- p.16Chapter 2.3.1 --- Design Overview --- p.16Chapter 2.3.2 --- ACTA - The MAC Protocol --- p.17Chapter 2.3.3 --- Protocol Layering --- p.18Chapter 2.3.4 --- "Segment, Datagram and Packet Format" --- p.20Chapter 2.3.5 --- Fast Packet Routing --- p.22Chapter 2.3.6 --- Local Host NIU --- p.24Chapter 2.4 --- The Network Restoration Strategy --- p.25Chapter 2.4.1 --- The Dual-Ring Model and Assumptions --- p.26Chapter 2.4.2 --- Scenarios of Network Failure and Remedies --- p.26Chapter 2.4.3 --- Distributed Fault-Tolerant Algorithm --- p.26Chapter 2.4.4 --- Distributed Auto-Healing Algorithm --- p.28Chapter 2.4.5 --- The Network Management Signals --- p.31Chapter 2.5 --- Performance Evaluation --- p.32Chapter 2.5.1 --- Restoration Time --- p.32Chapter 2.5.2 --- Reliability Measures --- p.34Chapter 2.5.3 --- Network Availability During Restoration --- p.41Chapter 2.6 --- The Prototype --- p.42Chapter 2.7 --- Technical Problems Encountered --- p.45Chapter 2.8 --- Chapter Summary and Future Development --- p.46Chapter 3 --- A Simple Experimental Network Management Software - NET- MAN --- p.48Chapter 3.1 --- Introduction to NETMAN --- p.48Chapter 3.2 --- Network Management Basics --- p.49Chapter 3.2.1 --- The Level of Management Protocols --- p.49Chapter 3.2.2 --- Architecture Model --- p.51Chapter 3.2.3 --- TCP/IP Network Management Protocol Architecture --- p.53Chapter 3.2.4 --- A Standard Network Management Protocol On Internet - SNMP --- p.54Chapter 3.2.5 --- A Standard For Managed Information --- p.55Chapter 3.3 --- The CUM LAUDE Network Management Protocol Suite (CNMPS) --- p.56Chapter 3.3.1 --- The Architecture --- p.53Chapter 3.3.2 --- Goals of the CNMPS --- p.59Chapter 3.4 --- Highlights of NETMAN --- p.61Chapter 3.5 --- Functional Descriptions of NETMAN --- p.63Chapter 3.5.1 --- Topology Menu --- p.64Chapter 3.5.2 --- Fault Manager Menu --- p.65Chapter 3.5.3 --- Performance Meter Menu --- p.65Chapter 3.5.4 --- Gateway Utility Menu --- p.67Chapter 3.5.5 --- Tools Menu --- p.67Chapter 3.5.6 --- Help Menu --- p.68Chapter 3.6 --- Chapter Summary --- p.68Chapter 4 --- A Local Map Based (LMB) Self-Healing Scheme for Arbitrary Topology Networks --- p.70Chapter 4.1 --- Introduction --- p.79Chapter 4.2 --- An Overview of Existing DCS-Based Restoration Algorithms --- p.72Chapter 4.3 --- The Network Model and Assumptions --- p.74Chapter 4.4 --- Basics of the LMB Scheme --- p.75Chapter 4.4.1 --- Restoration Concepts --- p.75Chapter 4.4.2 --- Terminology --- p.76Chapter 4.4.3 --- Algorithm Parameters --- p.77Chapter 4.5 --- Performance Assessments --- p.78Chapter 4.6 --- The LMB Network Restoration Scheme --- p.80Chapter 4.6.1 --- Initialization - Local Map Building --- p.80Chapter 4.6.2 --- The LMB Restoration Messages Set --- p.81Chapter 4.6.3 --- Phase I - Local Map Update Phase --- p.81Chapter 4.6.4 --- Phase II - Update Acknowledgment Phase --- p.82Chapter 4.6.5 --- Phase III - Restoration and Confirmation Phase --- p.83Chapter 4.6.6 --- Phase IV - Cancellation Phase --- p.83Chapter 4.6.7 --- Re-Initialization --- p.84Chapter 4.6.8 --- Path Route Monitoring --- p.84Chapter 4.7 --- Performance Evaluation --- p.84Chapter 4.7.1 --- The Testbeds --- p.84Chapter 4.7.2 --- Simulation Results --- p.86Chapter 4.7.3 --- Storage Requirements --- p.89Chapter 4.8 --- The LMB Scheme on ATM and SONET environment --- p.92Chapter 4.9 --- Future Work --- p.94Chapter 4.10 --- Chapter Summary --- p.94Chapter 5 --- Conclusion and Future Work --- p.96Chapter 5.1 --- Conclusion --- p.95Chapter 5.2 --- Future Work --- p.99Bibliography --- p.101Chapter A --- Derivation of Communicative Probability --- p.107Chapter B --- List of Publications --- p.11

The N.K.C. Annual, 1916

Volume 1https://digitalcommons.nl.edu/yearbooks/1000/thumbnail.jp

Fault-tolerant quantum computer architectures using hierarchies of quantum error-correcting codes

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 221-238).Quantum computers have been shown to efficiently solve a class of problems for which no efficient solution is otherwise known. Physical systems can implement quantum computation, but devising realistic schemes is an extremely challenging problem largely due to the effect of noise. A quantum computer that is capable of correctly solving problems more rapidly than modern digital computers requires some use of so-called fault-tolerant components. Code-based fault-tolerance using quantum error-correcting codes is one of the most promising and versatile of the known routes for fault-tolerant quantum computation. This dissertation presents three main, new results about code-based fault-tolerant quantum computer architectures. The first result is a large new family of quantum codes that go beyond stabilizer codes, the most well-studied family of quantum codes. Our new family of codeword stabilized codes contains all known codes with optimal parameters. Furthermore, we show how to systematically find, construct, and understand such codes as a pair of codes: an additive quantum code and a classical (nonlinear) code. Second, we resolve an open question about universality of so-called transversal gates acting on stabilizer codes. Such gates are universal for classical fault-tolerant computation, but they were conjectured to be insufficient for universal fault-tolerant quantum computation. We show that transversal gates have a restricted form and prove that some important families of them cannot be quantum universal. This is strong evidence that so-called quantum software is necessary to achieve universality, and, therefore, fault-tolerant quantum computer architecture is fundamentally different from classical computer architecture. Finally, we partition the fault-tolerant design problem into levels of a hierarchy of concatenated codes and present methods, compatible with rigorous threshold theorems, for numerically evaluating these codes.(cont.) The methods are applied to measure inner error-correcting code performance, as a first step toward elucidation of an effective fault-tolerant quantum computer architecture that uses no more than a physical, inner, and outer level of coding. Of the inner codes, the Golay code gives the highest pseudothreshold of 2 x 10-3. A comparison of logical error rate and overhead shows that the Bacon-Shor codes are competitive with Knill's C₄/C₆ scheme at a base error rate of 10⁻⁴.by Andrew W. Cross.Ph.D

The William Sloane Kennedy Memorial Collection of Whitmaniana

This catalog describes the inventory of archival materials in the William Sloane Kennedy Papers and The Walt Whitman collection in the Rollins College archives and special collections department. In biographies of Walt Whitman, William Sloane Kennedy usually gets little more than a brief mention as one of Whitman\u27s most fervid supporters late in the poet\u27s life. He deserves far more attention, however, and the appearance of this catalogue of the William Sloane Kennedy Memorial Collection of Whitmaniana at Rollins College will facilitate the kind of careful study that his life and work clearly merit. From the Preface by Ed Folsom.https://scholarship.rollins.edu/archv_books/1006/thumbnail.jp

The Power...to Alter and Amend : Textual Production and Editorial Actions in Samuel Richardson\u27s Clarissa .

This dissertation is a study of texts, focusing on how texts are constructed (through both words as well as physical attributes) and how they are edited after their initial composition. The scope of this dissertation is limited to Samuel Richardson (1689-1761) and his rare 1750 third edition of Clarissa and to the characters in Clarissa and their familiar letters. I argue that the altering of a text is a negotiation of power between the editor and the author, and that editors advance their personal agendas by undermining the intentions of the author. In Chapter 1, I explain the relevancy of textual studies to literary criticism. In Chapter 2, I examine how Richardson, master printer as well as author, constructs Clarissa as a material text, meaning that he builds plot, characterization, and his didactic message through the text\u27s linguistic as well as physical features. In Chapter 3, I address the familiar letters constructed by characters within Clarissa. Although the material details of these fictional letters--including handwriting and seals--cannot be seen by readers of the novel, they can still be conceptualized in the mind and interpreted for their visual meaning. In Chapter 4, as a transition to the editing of texts, I summarize the eighteenth- and twentieth-century editorial theories most relevant to Clarissa. In Chapter 5, I evaluate Richardson\u27s role as editor of Clarissa, focusing on the textual apparatus he constructs around his novel. Richardson exploits the editorial role in a manner not seen in other eighteenth-century novels, using the apparatus to control readers\u27 interpretations. In Chapter 6, I discuss the characters in Clarissa as editors, showing how they frequently alter and even forge/rewrite letters after their initial composition. These editorial actions, which I refer to as fictional editing, expand the narrative beyond the initial act of writing and complicate the issues of characterization, gender, and subjectivity inherent in the familiar letter. In Chapter 7, I conclude by suggesting additional concerns for textual/literary critics, including the implications of lost physical details in electronic texts