Resource optimization for fault-tolerant quantum computing

In this thesis we examine a variety of techniques for reducing the resources required for fault-tolerant quantum computation. First, we show how to simplify universal encoded computation by using only transversal gates and standard error correction procedures, circumventing existing no-go theorems. We then show how to simplify ancilla preparation, reducing the cost of error correction by more than a factor of four. Using this optimized ancilla preparation, we develop improved techniques for proving rigorous lower bounds on the noise threshold. Additional overhead can be incurred because quantum algorithms must be translated into sequences of gates that are actually available in the quantum computer. In particular, arbitrary single-qubit rotations must be decomposed into a discrete set of fault-tolerant gates. We find that by using a special class of non-deterministic circuits, the cost of decomposition can be reduced by as much as a factor of four over state-of-the-art techniques, which typically use deterministic circuits. Finally, we examine global optimization of fault-tolerant quantum circuits under physical connectivity constraints. We adapt techniques from VLSI in order to minimize time and space usage for computations in the surface code, and we develop a software prototype to demonstrate the potential savings.Comment: 231 pages, Ph.D. thesis, University of Waterlo

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

2D-barcode for mobile devices

2D-barcodes were designed to carry significantly more data than its 1D counterpart. These codes are often used in industrial information tagging applications where high data capacity, mobility, and data robustness are required. Wireless mobile devices such as camera phones and Portable Digital Assistants (PDAs) have evolved from just a mobile voice communication device to what is now a mobile multimedia computing platform. Recent integration of these two mobile technologies has sparked some interesting applications where 2D-barcodes work as visual tags and/or information source and camera phones performs image processing tasks on the device itself. One of such applications is hyperlink establishment. The 2D symbol captured by a camera phone is decoded by the software installed in the phone. Then the web site indicated by the data encoded in a symbol is automatically accessed and shown in the display of the camera phone. Nonetheless, this new mobile applications area is still at its infancy. Each proposed mobile 2D-barcode application has its own choice of code, but no standard exists nor is there any study done on what are the criteria for setting a standard 2D-barcode for mobile phones. This study intends to address this void. The first phase of the study is qualitative examination. In order to select a best standard 2D-barcode, firstly, features desirable for a standard 2D-barcode that is optimized for the mobile phone platform are identified. The second step is to establish the criteria based on the features identified. These features are based on the operating limitations and attributes of camera phones in general use today. All published and accessible 2D-barcodes are thoroughly examined in terms of criteria set for the selection of a best 2D-barcode for camera phone applications. In the second phase, the 2D-barcodes that have higher potential to be chosen as a standard code are experimentally examined against the three criteria: light condition, distance, whether or not a 2D-barcode supports VGA resolution. Each sample 2D-barcode is captured by a camera phone with VGA resolution and the outcome is tested using an image analysis tool written in the scientific language called MATLAB. The outcome of this study is the selection of the most suitable 2D-barcode for applications where mobile devices such as camera phones are utilized

Electronic systems-1. Lecture notes

The discipline «Electronic Systems» belongs to the cycle of professional and practical training of bachelors in the educational program «Electronic Components and Systems» is read over one semester (7) and is one of the final subjects of the bachelor's degree. In the process of studying the course, students get acquainted with the informational assessments of the ES; a description of the signals used in different purposes of the ES; methods of their processing, storage and transformation; principles of construction and operation of the ES - the selection, transformation, transmission, reception, registration and display of information. The basics of device design based on programmable logic integrated circuits (FPGA) are considered. Lecture notes contain theoretical information for up to 18 lectures and a list of recommended reading

Elucidating the neural correlates of cost-benefit decisions in a rat cortico-basal ganglia network

Adaptive value-guided decision-making often requires weighing-up of costs and benefits of pursuing an available opportunity. Several brain areas, particularly in frontal- striatal circuits, have been reported to be important for this behaviour. However, little is currently known regarding how the decision variables are represented and evolve on the single cell and population levels across these circuits within the confines of a single behavioural paradigm. We developed a novel rodent cost-benefit “accept-reject” task, in which food-restricted rats choose whether or not to run to the end of a corridor to collect sucrose pellets based on the prospective reward (4 different levels, varied trial- by-trial, signalled by auditory cues) and effort cost (3 different levels, varied over blocks of trials, implemented with barriers placed in the corridor that needed to be scaled to reach the reward magazine). Behavioural data (n=12 rats, average 1119 trials per animal) demonstrate a positive effect of reward and a negative influence of effort on the likelihood of accepting an offer, without an interaction between the two. Outcome devaluation strongly reduces acceptance of any offer. A subset of rats (n=5) were also implanted with a bespoke driveable micro-electrode array targeting, anterior cingulate cortex (ACC), medial orbitofrontal cortex (mOFC), dorsomedial striatum (DMS), ventral pallidum (VP), and subthalamic area (STA) and electrophysiological recordings were collected as they performed the task. Analysis of spiking data (n=4 rats; average 119 cells per region per animal) suggests that individual neurons in the 3 targeted basal ganglia areas (DMS, VP and STA) encode reward and/or, to a lesser extent, effort with high fidelity during cue presentation, while neurons in the two cortical areas (ACC and mOFC) display weaker tuning to reward/effort across multiple task points. By contrast, decision is progressively signalled by mOFC, DMS and VP units after action initiation. Decoding analyses using all the units from individual areas in a given session (ensembles) revealed that reward is signalled with similar spatial and temporal characteristics to single units. By contrast, effort is represented by DMS ensembles in a time-distributed manner and is dependent on diverse underlying neuronal activity profiles. These results are consistent with a parallel and distributed system for processing cost-benefit decision variables in the frontal cortical-basal ganglia network

Error correcting functional source coding with decoder side information using row-Latin rectangles

The functional source coding problem in which the receiver side information (Has-set) and demands (Want-set) include functions of source messages is studied using row-Latin rectangle. The source transmits encoded messages, called the functional source code, in order to satisfy the receiver's demands. We obtain a minimum length using the row-Latin rectangle. Next, we consider the case of transmission errors and provide a necessary and sufficient condition that a functional source code must satisfy so that the receiver can correctly decode the values of the functions in its Want-set

Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS'09)

The Symposium on Theoretical Aspects of Computer Science (STACS) is held alternately in France and in Germany. The conference of February 26-28, 2009, held in Freiburg, is the 26th in this series. Previous meetings took place in Paris (1984), Saarbr¨ucken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), W¨urzburg (1993), Caen (1994), M¨unchen (1995), Grenoble (1996), L¨ubeck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), Montpellier (2004), Stuttgart (2005), Marseille (2006), Aachen (2007), and Bordeaux (2008). ..

Proceedings of the Fifth International Mobile Satellite Conference 1997

Satellite-based mobile communications systems provide voice and data communications to users over a vast geographic area. The users may communicate via mobile or hand-held terminals, which may also provide access to terrestrial communications services. While previous International Mobile Satellite Conferences have concentrated on technical advances and the increasing worldwide commercial activities, this conference focuses on the next generation of mobile satellite services. The approximately 80 papers included here cover sessions in the following areas: networking and protocols; code division multiple access technologies; demand, economics and technology issues; current and planned systems; propagation; terminal technology; modulation and coding advances; spacecraft technology; advanced systems; and applications and experiments

Communication and cooperation in evolutionary biology

How can the concepts and results of communication theory aid evolutionary biology? This thesis argues for an explanatory framework, evolutionary communication theory, that interprets and illuminates scientific research into the phenomenon of biological signalling. By expanding the theory beyond the models and goals familiar to Claude Shannon and other engineers, real insight is gained into how strategic interplay between senders and receivers shapes signal form. Furthermore, interpreting artificial and natural signals in terms of sender-receiver teleosemantics demonstrates the explanatory role of relations borne between signals and world affairs. One of the major results of the thesis is a rejection of the orthodox distinction between Shannon and semantic information. While there are at least two useful distinctions to be drawn -- between cues and signals, and between statistical and functional content -- the terminological confusion that gave rise to the phrase `Shannon information' should be put aside for good. Chapter 1 outlines a way to capture the relationships between signals and other signal-like interactions using a multi-dimensional conceptual space called a hypercube. I argue that sender-receiver teleosemantics is uniquely well suited to capturing those aspects of communication theory that render it a viable mathematical framework for evolutionary biology. Chapter 2 discusses an early attempt to apply communication theory in evolutionary biology. Haldane & Spurway's informational interpretation of the honeybee waggle dance has recently been criticised on mathematical grounds. These criticisms lend support to scepticism about the relevance of information for evolutionary biology. I argue that the criticisms are themselves mathematically erroneous, so one route to scepticism about information is undercut. Chapter 3 explores a related line of scepticism. It is common in the philosophy of biology to treat the concepts and tools of communication theory as insufficient or irrelevant for analysing semantic content. I argue that the grounds of this supposition are based on misinterpretations of some features of communication theory. In chapter 4 I reconstruct Millikan's teleosemantics in a causal-modelling setting, highlighting the explanatory role of semantic content. In chapter 5 I respond to objections to the teleosemantic account, including the claim that the theory renders explanations of success that appeal to semantic content circular. I also argue for an interpretation of important features of communication-theoretic models in terms of teleosemantics. Chapter 6 explores another challenge to applying teleosemantics to biological signals. The theory places emphasis on cooperation between senders and receivers, but biological signals are often fraught with evolutionary conflict. I discuss recent formal work, and argue that prospects for teleosemantics are good. Finally, in chapter 7 I argue that an explanatory framework that draws on communication-theoretic concepts would be beneficial to evolutionary biology. I present case studies of communicative behaviour for which biologists offer explanations that are well interpreted through the principles of communications engineering