Susan Stepney

Searching for highly entangled multi-qubit states

We present a simple numerical optimization procedure to search for highly entangled states of 2, 3, 4 and 5 qubits. We develop a computationally tractable entanglement measure based on the negative partial transpose criterion, which can be applied to quantum systems of an arbitrary number of qubits. The search algorithm attempts to optimize this entanglement cost function to find the maximal entanglement in a quantum system. We present highly entangled 4-qubit and 5-qubit states discovered by this search. We show that the 4-qubit state is not quite as entangled, according to two separate measures, as the conjectured maximally entangled Higuchi–Sudbery state. Using this measure, these states are more highly entangled than the 4-qubit and 5-qubit GHZ states. We also present a conjecture about the NPT measure, inspired by some of our numerical results, that the single-qubit reduced states of maximally entangled states are all totally mixed.

The design of s-boxes by simulated annealing

Substitution boxes (S-boxes) are important components in many modern-day symmetric key ciphers. Their study has attracted a great deal of attention over many years. The emergence of a variety of cryptosystem attacks has shown that substitutions must be designed with great care. Some general criteria such as high non-linearity and low autocorrelation have been proposed (providing some protection against attacks such as linear cryptanalysis and differential cryptanalysis). The design of appropriate S-boxes is a difficult task; several criteria must be traded off and the design space is huge. There has been little application of evolutionary search to the development of S-boxes. In this paper we show how a cost function that has found excellent single-out put Boolean functions can be generalised to provide improved results for small S-boxes.

Object Orientation in Z

1 Why an Object Oriented Z?.- 2 Example Specifications in Z.- 3 Halls Style.- 4 Z Expression of Refinable Objects.- 5 MooZ Case Studies.- 6 Object-Z.- 7 OOZE.- 8 Schuman & Pitt Approach.- 9 Z++.- 10 ZEST.- 11 Specification in Fresco.- A Zand HOOD.- B Bibliography.

Engineering and theoretical underpinnings of retrenchment

Refinement is reviewed, highlighting in particular the distinction between its use as a specification constructor at a high level, and its use as an implementation mechanism at a low level. Some of its shortcomings as a specification constructor at high levels of abstraction are pointed out, and these are used to motivate the adoption of retrenchment for certain high level development steps. Basic properties of retrenchment are described, including a justification of the operation proof obligation, simple examples, its use in requirements engineering and model evolution, and simulation properties. The interaction of retrenchment with refinement notions of correctness is overviewed, as is a range of other technical issues. Two case study scenarios are presented. One is a simple digital redesign control theory problem, and the other is an overview of the application of retrenchment to the Mondex Purse development.

Evolving Boolean Functions Satisfying Multiple Criteria

Many desirable properties have been identified for Boolean functions with cryptographic applications. Obtaining optimal tradeoffs among such properties is hard. In this paper we show how simulated annealing, a search technique inspired by the cooling processes of molten metals, can be used to derive functions with profiles of cryptographically-relevant properties as yet unachieved by any other technique.

Journeys in non-classical computation I: A grand challenge for computing research

1. The challengeA gateway event [35] is a change to a system that leads to the possibility of huge increases inkinds and levels of complexity. It opens up a whole new kind of phase space to the system’sdynamics.Gatewayeventsduringevolutionoflifeonearthincludetheappearanceofeukaryotes(organisms with a cell nucleus), an oxygen atmosphere, multi-cellular organisms and grass.Gatewayeventsduringthedevelopmentofmathematicsincludeeachinventionofanewclassofnumbers (negative, irrational, imaginary, ...), and dropping Euclid’s parallel postulate.A gateway event produces a profound and fundamental change to the system: Oncethrough the gateway, life is never the same again. We are currently poised on the threshold ofa significant gateway event in computation: That of breaking free from many of our current“classical computational” assumptions. Our Grand Challenge for computer science isto journey through the gateway event obtained by breaking our current classicalcomputational assumptions, and thereby develop a mature science of Non-ClassicalComputation2. Journeys versus goals

More Powerful Z Data Refinement: Pushing the State of the Art in Industrial Refinement

We have recently completed the specification and full refinement proof of a large, industrial scale application. The application was security critical, and the modelling and proof was done to increase the client’s assurance that the implemented system had no design flaws with security implications. Here we describe the application, and then discuss an essential lesson to learn concerning large proof contracts: that one must forge a path between mathematical formality on the one hand and practical achievement of results on the other. We present a number of examples of such decision points, explaining the considerations that must be made in each case.

Towards a Conceptual Framework for Artificial Immune Systems

We propose that bio-inspired algorithms are best developed and analysed in the context of a multidisciplinary conceptual framework that provides for sophisticated biological models and well-founded analytical principles, and we outline such a framework here, in the context of AIS network models. We further propose ways to unify several domains into a common meta-framework, in the context of AIS population models. We finally hint at the possibility of a novel instantiation of such a meta-framework, thereby allowing the building of a specific computational framework that is inspired by biology, but not restricted to any one particular biological domain.

Testing as Abstraction

The PROST-Objects project has developed a method for formally specifying tests. The method is based on systematic abstraction from a ‘state-plusoperation’ style specification. It is explained here, and illustrated with a small example. Test developers can use this method, along with their own skills for choosing good tests, to produce a suite of formal test specifications. The project has also developed a prototype tool, which provides organisational support for the (potentially large) collection of test specifications as they are generated.

Journeys in non-classical computation II: initial journeys and waypoints

†University of York, Heslington, York YO1 5DD, UK‡University of the West of England, Frenchay Campus, Coldharbourlane, Bristol BS16 1QY, UK{University of Portsmouth, Buckingham Building, Lion Terrace, Portsmouth PO1 3WE, UK§University of Kent, Canterbury, Kent CT2 7NZ, UKkUniversity of Cambridge, Madingley Road, Cambridge CB3 OHE, UK#University of Exeter, North Cote House, The Queen’s Drive, Exeter E4 4QJ, UK