Quantum Codes for Simplifying Design and Suppressing Decoherence in Superconducting Phase-Qubits

We introduce simple qubit-encodings and logic gates which eliminate the need for certain difficult single-qubit operations in superconducting phase-qubits, while preserving universality. The simplest encoding uses two physical qubits per logical qubit. Two architectures for its implementation are proposed: one employing N physical qubits out of which N/2 are ancillas fixed in the |1 state, the other employing N/2+1 physical qubits, one of which is a bus qubit connected to all others. Details of a minimal set of universal encoded logic operations are given, together with recoupling schemes, that require nanosecond pulses. A generalization to codes with higher ratio of number of logical qubits per physical qubits is presented. Compatible decoherence and noise suppression strategies are also discussed. PACS: 03.67.Lx; 85.25.Hv; 03.67.-a; 89.70.+c     

An evolutionary approach to identify logical components

ContextIdentifying suitable components during the software design phase is an important way to obtain more maintainable software. Many methods including Graph Partitioning, Clustering-based, CRUD-based, and FCA-based methods have been proposed to identify components at an early stage of software design. However, most of these methods use classical clustering techniques, which rely on expert judgment.ObjectiveIn this paper, we propose a novel method for component identification, called SBLCI (Search-Based Logical Component Identification), which is based on GA (genetic algorithm), and complies with an iterative scheme to obtain logical components.MethodSBLCI identifies logical components of a system from its analysis models using a customized GA, which considers cohesion and coupling metrics as its fitness function, and has four novel guided GA operators based on the cohesive component concept. In addition, SBLCI has an iterative scheme in which it initially identifies high-level components in the first iteration. Then, in the next iterations, it identifies low-level sub-components for each identified component in previous iterations.ResultsWe evaluated the effectiveness of SBLCI with three real-world cases. Results revealed that SBLCI is a better alternative for identifying logical components and sub-components in comparison with existing component identification methods.     

Implementing a noise protected logical qubit in methyl groups via microwave irradiation

We propose a proof-of-principle experiment to encode one logical qubit in noise protected subspace of three identical spins in a methyl group. The symmetry analysis of the wavefunction shows that this fermionic system exhibits a symmetry correlation between the spatial degree of freedom and the spin degree of freedom. We show that one can use this correlation to populate the noiseless subsystem by relying on the interaction between the electric dipole moment of the methyl group with a circularly polarized microwave field. Logical gates are implemented by controlling both the intensity and phase of the applied field.     

Collision-based computing implemented by soldier crab swarms

Collision-based computing schemes are implemented using propagating and interacting localisations. When two or more travelling localisations collide, they may reflect or merge into a new localisation. Presence/absence of a localisation in a specified site of a physical space represents True/False values of Boolean variables. Incoming trajectories symbolise inputs and outgoing trajectories are outputs. Logical gates are implemented by collisions between the localisations. We demonstrate how primitives of the collision-based computing can be implemented using swarms of soldier crabs in laboratory experiments. Soldier crabs, Mictyris guinotae, exhibit coherent collective behaviour on an intertidal flat at a daytime low-tide period. The soldier crabs' swarm often moves as a single entity with definite yet dynamically changing boundary. We utilise swarms of soldier crabs to implement a Boolean logic gate. The gate has two inputs and three outputs. Values of the inputs and outputs are represented by crab swarm size or a proportion of crabs in the input and output channels. We demonstrate that the gate performs logical conjunction and negation.     

Slime mould foraging behaviour as optically coupled logical operations

Physarum polycephalum is a macroscopic plasmodial slime mould whose apparently ‘intelligent’ behaviour patterns may be interpreted as computation. We employ plasmodial phototactic responses to construct laboratory prototypes of NOT and NAND logical gates with electrical inputs/outputs and optical coupling in which the slime mould plays dual roles of computing device and electrical conductor. Slime mould logical gates are fault tolerant and resettable. The results presented here demonstrate the malleability and resilience of biological systems and highlight how the innate behaviour patterns of living substrates may be used to implement useful computation.     

Logical and information aspects in surface science: friction,capillarity, and superhydrophobicity

Abstract

Logical and information aspects of friction and wetting (including the adhesion, capillarity, and superhydrophobicity) are discussed. Friction involves paradoxes, such as the Painlevé paradoxes of non-existence or non-uniqueness of solutions in mechanical systems of rigid bodies with dry friction. These paradoxes can be treated by introducing ternary logic with the three basic states: rest-motion-undefined. When elastic deformation is introduced, the paradoxical solutions correspond to frictional instabilities leading to rest-motion-unstable as three states of a system. The dynamic evolution of a frictional interface towards a limit cycle can be viewed as a process of erasing the information about the interface due to the instabilities. Furthermore, while friction force is universal, it is not treated as a fundamental force and can be considered as an epiphenomenon of various synergetic mechanisms. This further relates friction to other surface effects, including the capillarity, with its binary logic of wetting states and a possibility of droplet computation for lab-on-a-chip microfluidic reactors. We discuss the logical foundation of biomimetic superhydrophobic surface design and how it is different from the conventional design. Both friction and wetting can be used for novel unconventional logical and computational devices.     

Qualitative temporal analysis: Towards a full implementation of the Fault Tree Handbook

The Fault Tree Handbook has become the de facto standard for fault tree analysis (FTA), defining the notation and mathematical foundation of this widely used safety analysis technique. The Handbook recognises that classical combinatorial fault trees employing only Boolean gates cannot capture the potentially critical significance of the temporal ordering of failure events in a system. Although the Handbook proposes two dynamic gates that could remedy this, a Priority-AND and an Exclusive-OR gate, these gates were never accurately defined. This paper proposes extensions to the logical foundation of fault trees that enable use of these dynamic gates in an extended and more powerful FTA. The benefits of this approach are demonstrated on a generic triple-module standby redundant system exhibiting dynamic behaviour.     

Multi-input volistor logic XNOR gates

ABSTRACT

A novel approach utilising the emerging memristor technology is introduced for realising a 2-input primitive XNOR gate. This gate enables in-memory computing and is used as a building block of multi-input XNOR gates. The XNOR gate is realised with eight memristors of two crossbar arrays. The average power consumption of an 8-input XNOR gate is calculated and compared with its counterpart realised with CMOS technology – the XNOR gate consumes less power. ESOP realisation can be directly implemented with XNOR gates. Our simulation results and comparisons show the benefit of the proposed XNOR gate in terms of delay, area, and power.

Volistor logic XNOR gate. (a) Circuit diagram of two-input volistor logic XNOR gate. Input voltages are applied to memristors S ₁ and S ₂ through horizontal wires W _in1 and W _in2, and the output which is logical AND of states S ₁ and S ₂ is calculated by applying V _READ to vertical wire W _XNOR. (b) Block diagram of two-input volistor logic gate. (c) A multi-input volistor logic XNOR gate can be implemented by connecting two XNOR gates though CMOS switches.     

An Explicit Universal Gate-Set for Exchange-Only Quantum Computation

A single physical interaction might not be universal for quantum computation in general. It has been shown, however, that in some cases it can achieve universal quantum computation over a subspace. For example, by encoding logical qubits into arrays of multiple physical qubits, a single isotropic or anisotropic exchange interaction can generate a universal logical gate-set. Recently, encoded universality for the exchange interaction was explicitly demonstrated on three-qubit arrays, the smallest nontrivial encoding. We now present the exact specification of a discrete universal logical gate-set on four-qubit arrays. We show how to implement the single qubit operations exactly with at most 3 nearest neighbor exchange operations and how to generate the encoded controlled-NOT with 27 parallel nearest neighbor exchange interactions or 50 serial gates, obtained from extensive numerical optimization using genetic algorithms and Nelder–Mead searches. We also give gate-switching times for the three-qubit encoding to much higher accuracy than previously and provide the full speci.cation for exact CNOT for this encoding. Our gate-sequences are immediately applicable to implementations of quantum circuits with the exchange interaction. PACS: 03.67.Lx, 03.65.Ta, 03.65.Fd, 89.70.+c     

A Language for Verification and Manipulation of Web Documents: (Extended Abstract)

In this paper we develop the language theory underpinning the logical framework PLF. This language features lambda abstraction with patterns and application via pattern-matching. Reductions are allowed in patterns. The framework is particularly suited as a metalanguage for encoding rewriting logics and logical systems where proof terms have a special syntactic constraints, as in term rewriting systems, and rule-based languages. PLF is a conservative extension of the well-known Edinburgh Logical Framework LF. Because of sophisticated pattern matching facilities PLF is suitable for verification and manipulation of HXML documents.     

A GENERAL SYSTEM LOGICAL THEORY

The General System Logical Theory (GSLT) is obtained by combining Resconi's logical theory of systems with Jessel's theory of secondary sources. In the present paper we give a first account of GSLT, of its foundation, its main features, and most obvious applications. GSLT is defined by its aims and concretized by a new specific concept, that of an Elementary Logical System (ELS). ELS may be connected with Lie algebras. The systems formerly dealt with by Resconi's and Jessel's separate theories are identified as particular ELS. Subsequently are built up various networks of ELS, leading thus to natural and powerful extensions of the classical feedback theory. Finally GSLT is applied to three very different topics: wave propagations (or any physical nature), Riemann geometries and chemical controls, showing thus its versatility and usefulness.     

Function synthesis algorithm based on RTD-based three-variable universal logic gates

Compared with complementary metal–oxide semiconductor (CMOS), the resonant tunneling device (RTD) has better performances; it is the most promising candidate for next-generation integrated circuit devices. The universal logic gate is an important unit circuit because of its powerful logic function, but there are few function synthesis algorithms that can implement an n-variable logical function by RTD-based universal logic gates. In this paper, we propose a new concept, i.e., the truth value matrix. With it a novel disjunctive decomposition algorithm can be used to decompose an arbitrary n-variable logical function into three-variable subset functions. On this basis, a novel function synthesis algorithm is proposed, which can implement arbitrary n-variable logical functions by RTD-based universal threshold logic gates (UTLGs), RTD-based three-variable XOR gates (XOR3s), and RTD-based three-variable universal logic gate (ULG3s). When this proposed function synthesis algorithm is used to implement an n-variable logical function, if the function is a directly disjunctive decomposition one, the circuit structure will be very simple, and if the function is a non-directly disjunctive decomposition one, the circuit structure will be simpler than when using only UTLGs or ULG3s. The proposed function synthesis algorithm is straightforward to program, and with this algorithm it is convenient to implement an arbitrary n-variable logical function by RTD-based universal logic gates.     

On logical universality of Belousov-Zhabotinsky vesicles

Belousov-Zhabotinsky (BZ) excitable chemical medium exhibits a rich variety of spatial patterns of excitation. In a sub-excitable light-sensitive chemical medium, an asymmetric disturbing or excitation, causes formation of localized travelling excitation wave-fragments. When two or more wave-fragments collide, they annihilate or merge into new wave-fragment. The wave-fragments can be thought as elementary units of information and their interaction sites as a logical gates. Size and life span of a wave-fragment depends on a level of medium’s illumination. By encapsulating BZ reaction into a lipid vesicle, we can manipulate the BZ-derived logical gates. By interpreting wave-fragments as values of Boolean variables, we design a collision-based polymorphic logical gate in BZ vesicles. The gate implements operation xnor for low illumination, and it acts as nor gate for high illumination.     

Wittgenstein’s Tractatus Project as Philosophy of Information

It is argued that the Tractatus Project of Logical Atomism, in which the world is conceived of as the totality of independent atomic facts, can usefully be understood by conceiving of each fact as a bit in ‘logical space’. Wittgenstein himself thinks in terms of logical space. His ‘elementary propositions’, which express atomic facts, are interpreted as tuples of co-ordinates which specify the location of a bit in logical space. He says that signs for elementary propositions are arrangements of names. Here, the names are understood as numerical symbols specifying coordinates. It is argued that, using this approach, the so-called ‘colour-exclusion’ problem, which was Wittgenstein’s reason for abandoning the Tractatus, is in fact soluble. However, if logical space is a continuum then some coordinates will need to be expressed by numerical symbols that are infinite in size. How is this to be understood in Tractatus terms? It is shown that, in the Tractatus, Wittgenstein did recognise the possibility of infinite propositions and sentences expressing them. At first sight his approach to infinite sentences, and the approach of the present paper, seem to differ, but it is argued that the difference is superficial. Finally, we address the question of whether Logical Atomism is viable and this raises issues concerning its relationship to natural science.     

Files d'attente exponentielles ayant des parametres non-stationnaires dans le temps

Summary There exist a large number of Queueing Systems having a non-stationary behavior. We call non-stationarity, random time-variations of some parameters of the system (i.e. the input or service rates). A typical example is a reliability system which corresponds to the unpredictable breakdown or failure of the server. Random intensity models are natural for describing such phenomena.We introduce a model with randomly changing service rate. It does not obey a certain independence assumption often made in Queueing Theory. A complete analysis of the model is carried out, explicit results and performance curves are given. Jury's criteria are used to find Necessary and Sufficient Conditions for Stability. These criteria are easy to use and allow us to find the conditions of stability which were not obtained in many previous studies.     

PRL: A probabilistic relational language

In this paper, we describe the syntax and semantics for a probabilistic relational language (PRL). PRL is a recasting of recent work in Probabilistic Relational Models (PRMs) into a logic programming framework. We show how to represent varying degrees of complexity in the semantics including attribute uncertainty, structural uncertainty and identity uncertainty. Our approach is similar in spirit to the work in Bayesian Logic Programs (BLPs), and Logical Bayesian Networks (LBNs). However, surprisingly, there are still some important differences in the resulting formalism; for example, we introduce a general notion of aggregates based on the PRM approaches. One of our contributions is that we show how to support richer forms of structural uncertainty in a probabilistic logical language than have been previously described. Our goal in this work is to present a unifying framework that supports all of the types of relational uncertainty yet is based on logic programming formalisms. We also believe that it facilitates understanding the relationship between the frame-based approaches and alternate logic programming approaches, and allows greater transfer of ideas between them. Editors: Hendrik Blockeel, David Jensen and Stefan Kramer An erratum to this article is available at .     

On generalization/specialization for conceptual graphs

Abstract

This paper centres on the generalization/specialization relation in the framework of conceptual graphs (this relation corresponds to logical subsumption when considering logical formulas associated with conceptual graphs). Results given here apply more generally to any model where knowledge is described by labelled graphs and reasoning is based on graph subsumption, as in semantic networks or in structural machine learning. The generalization/specialization relation, as defined by Sowa, is first precisely analysed, in particular its links with a graph morphism, called projection. Besides Sowa's specialization relation (which is a preorder), another one is actually used in some practical applications (which is an order). These are comparatively studied. The second topic of this paper is the design of efficient algorithms for computing these specialization relations. Since the associated problems are NP-hard, the form of the graphs is restricted in order to arrive at polynomial algorithms. In particular, polynomial algorithms are presented for computing a projection from a conceptual ‘tree’ to any conceptual graph, and for counting the number of such projections. The algorithms are also described in a generic way, replacing the projection by a parametrized graph morphism, and conceptual graphs by directed labelled graphs.     

Logical problems of systems analysis of organization-and-engineering systems and main ways to solve them

Logical problems of systems analysis of organization-and-engineering systems in the modern industry are discussed. The logical foundations of the systems analysis are analyzed. A methodological function of objective structures in a systems analysis of organization-and-engineering systems is found, and a relationship of these structures as results of analysis and synthesis of objectives is established. The main ways to solve logical problems for systems analysis of organization-and-engineering systems that allow solving logical problems are identified. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 140–147, May–June 2006.