Single-qubit gate teleportation provides a quantum advantage

Gate-teleportation circuits are arguably among the most basic examples of computations believed to provide a quantum computational advantage: In seminal work [Quantum Inf. Comput., 4(2):134--145], Terhal and DiVincenzo have shown that these circuits elude simulation by efficient classical algorithms under plausible complexity-theoretic assumptions. Here we consider possibilistic simulation [Phys. Rev. A 106, 062430 (2022)], a particularly weak form of this task where the goal is to output any string appearing with non-zero probability in the output distribution of the circuit. We show that even for single-qubit Clifford-gate-teleportation circuits this simulation problem cannot be solved by constant-depth classical circuits with bounded fan-in gates. Our results are unconditional and are obtained by a reduction to the problem of computing the parity, a well-studied problem in classical circuit complexity.Comment: 31 pages 10 figures. Typos fixed. New Section 3.3.3 Other word problems for Clifford modulo Pauli group

Proceedings of the Third International Workshop on Neural Networks and Fuzzy Logic, volume 2

Papers presented at the Neural Networks and Fuzzy Logic Workshop sponsored by the National Aeronautics and Space Administration and cosponsored by the University of Houston, Clear Lake, held 1-3 Jun. 1992 at the Lyndon B. Johnson Space Center in Houston, Texas are included. During the three days approximately 50 papers were presented. Technical topics addressed included adaptive systems; learning algorithms; network architectures; vision; robotics; neurobiological connections; speech recognition and synthesis; fuzzy set theory and application, control and dynamics processing; space applications; fuzzy logic and neural network computers; approximate reasoning; and multiobject decision making

Treatment of imprecision in data repositories with the aid of KNOLAP

Traditional data repositories introduced for the needs of business processing, typically focus on the storage and querying of crisp domains of data. As a result, current commercial data repositories have no facilities for either storing or querying imprecise/ approximate data. No significant attempt has been made for a generic and applicationindependent representation of value imprecision mainly as a property of axes of analysis and also as part of dynamic environment, where potential users may wish to define their “own” axes of analysis for querying either precise or imprecise facts. In such cases, measured values and facts are characterised by descriptive values drawn from a number of dimensions, whereas values of a dimension are organised as hierarchical levels. A solution named H-IFS is presented that allows the representation of flexible hierarchies as part of the dimension structures. An extended multidimensional model named IF-Cube is put forward, which allows the representation of imprecision in facts and dimensions and answering of queries based on imprecise hierarchical preferences. Based on the H-IFS and IF-Cube concepts, a post relational OLAP environment is delivered, the implementation of which is DBMS independent and its performance solely dependent on the underlying DBMS engine

Foundations of Fuzzy Logic and Semantic Web Languages

This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic

Automated reasoning with uncertainties

In this work we assume that uncertainty is a multifaceted concept which admits several different measures, and present a system for automated reasoning with multiple representations of uncertainty. Our focus is on problems which present more than one of these facets and therefore in which a multivalued representation of uncertainty and the study of its possibility of computational realisation are important for designing and implementing knowledge-based systems. We present a case study on developing a computational language for reasoning with uncertainty, starting with a semantically sound and computationally tractable language and gradually extending it with specialised syntactic constructs to represent measures of uncertainty, preserving its unambiguous semantic characterisation and computability properties. Our initial language is the language of normal clauses with SLDNF as the inference rule, and we select three facets of uncertainty, which are not exhaustive but cover many situations found in practical problems: vagueness, statistics and degrees of belief. To each of these facets we associate a specific measure: fuzzy measures to vagueness, probabilities on the domain to statistics and probabilities on possible worlds to degrees of belief. The resulting language is semantically sound and computationally tractable, and admits relatively efficient implementations employing ff \Gamma fi pruning and caching

Foundations of Fuzzy Logic and Semantic Web Languages

This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic

Construction of a support tool for the design of the activity structures based computer system architectures

This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University.This thesis is a reapproachment of diverse design concepts, brought to bear upon the computer system engineering problem of identification and control of highly constrained multiprocessing (HCM) computer machines. It contributes to the area of meta/general systems methodology, and brings a new insight into the design formalisms, and results afforded by bringing together various design concepts that can be used for the construction of highly constrained computer system architectures. A unique point of view is taken by assuming the process of identification and control of HCM computer systems to be the process generated by the Activity Structures Methodology (ASM). The research in ASM has emerged from the Neuroscience research, aiming at providing the techniques for combining the diverse knowledge sources that capture the 'deep knowledge' of this application field in an effective formal and computer representable form. To apply the ASM design guidelines in the realm of the distributed computer system design, we provide new design definitions for the identification and control of such machines in terms of realisations. These realisation definitions characterise the various classes of the identification and control problem. The classes covered consist of: 1. the identification of the designer activities, 2. the identification and control of the machine's distributed structures of behaviour, 3. the identification and control of the conversational environment activities (i.e. the randomised/ adaptive activities and interactions of both the user and the machine environments), 4. the identification and control of the substrata needed for the realisation of the machine, and 5. the identification of the admissible design data, both user-oriented and machineoriented, that can force the conversational environment to act in a self-regulating manner. All extent results are considered in this context, allowing the development of both necessary conditions for machine identification in terms of their distributed behaviours as well as the substrata structures of the unknown machine and sufficient conditions in terms of experiments on the unknown machine to achieve the self-regulation behaviour. We provide a detailed description of the design and implementation of the support software tool which can be used for aiding the process of constructing effective, HCM computer systems, based on various classes of identification and control. The design data of a highly constrained system, the NUKE, are used to verify the tool logic as well as the various identification and control procedures. Possible extensions as well as future work implied by the results are considered.Government of Ira