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Derek Abbott

Publications and source records attributed to Derek Abbott.

At least 73 records · Page 4Linked to original sources
arXiv2011

An Analytical Approach for Memristive Nanoarchitectures

As conventional memory technologies are challenged by their technological physical limits, emerging technologies driven by novel materials are becoming an attractive option for future memory architectures. Among these technologies, Resistive Memories (ReRAM) created new possibilities because of their nano-features and unique $I$-$V$ characteristics. One particular problem that limits the maximum array size is interference from neighboring cells due to sneak-path currents. A possible device level solution to address this issue is to implement a memory array using complementary resistive switches (CRS). Although the storage mechanism for a CRS is fundamentally different from what has been reported for memristors (low and high resistances), a CRS is simply formed by two series bipolar memristors with opposing polarities. In this paper our intention is to introduce modeling principles that have been previously verified through measurements and extend the simulation principles based on memristors to CRS devices and hence provide an analytical approach to the design of a CRS array. The presented approach creates the necessary design methodology platform that will assist designers in implementation of CRS devices in future systems.

cond-mat.mtrl-sci↗
arXiv2011

Quantum Strategies Win in a Defector-Dominated Population

Quantum strategies are introduced into evolutionary games. The agents using quantum strategies are regarded as invaders whose fraction generally is 1% of a population in contrast to the 50% defectors. In this paper, the evolution of strategies on networks is investigated in a defector-dominated population, when three networks (Regular Lattice, Newman-Watts small world network, scale-free network) are constructed and three games (Prisoners' Dilemma, Snowdrift, Stag-Hunt) are employed. As far as these three games are concerned, the results show that quantum strategies can always invade the population successfully. Comparing the three networks, we find that the regular lattice is most easily invaded by agents that adopt quantum strategies. However, for a scale-free network it can be invaded by agents adopting quantum strategies only if a hub is occupied by an agent with a quantum strategy or if the fraction of agents with quantum strategies in the population is significant.

cs.GT↗
arXiv2011

Fisher information as a performance metric for locally optimum processing

For a known weak signal in additive white noise, the asymptotic performance of a locally optimum processor (LOP) is shown to be given by the Fisher information (FI) of a standardized even probability density function (PDF) of noise in three cases: (i) the maximum signal-to-noise ratio (SNR) gain for a periodic signal; (ii) the optimal asymptotic relative efficiency (ARE) for signal detection; (iii) the best cross-correlation gain (CG) for signal transmission. The minimal FI is unity, corresponding to a Gaussian PDF, whereas the FI is certainly larger than unity for any non-Gaussian PDFs. In the sense of a realizable LOP, it is found that the dichotomous noise PDF possesses an infinite FI for known weak signals perfectly processed by the corresponding LOP. The significance of FI lies in that it provides a upper bound for the performance of locally optimum processing.

physics.data-an↗
arXiv2011

Effects of mutual coupling in dual-resonance metamaterials

This Letter presents an investigation on the effects of mutual coupling in a metamaterial comprising two sets of electric-LC (ELC) resonators with different resonance frequencies. Through simulation and experiment, it is found that the two resonances experience significant shifting and weakening as they become spectrally close. An equivalent circuit model suggests that inductive coupling among the two resonator sets is a primary cause of the change in the resonance properties. This study is fundamental to designing metamaterials with an extended bandwidth or spatially variable response.

physics.optics↗
arXiv2011

Memristor-based Synaptic Networks and Logical Operations Using In-Situ Computing

We present new computational building blocks based on memristive devices. These blocks, can be used to implement either supervised or unsupervised learning modules. This is achieved using a crosspoint architecture which is an efficient array implementation for nanoscale two-terminal memristive devices. Based on these blocks and an experimentally verified SPICE macromodel for the memristor, we demonstrate that firstly, the Spike-Timing-Dependent Plasticity (STDP) can be implemented by a single memristor device and secondly, a memristor-based competitive Hebbian learning through STDP using a $1\times 1000$ synaptic network. This is achieved by adjusting the memristor's conductance values (weights) as a function of the timing difference between presynaptic and postsynaptic spikes. These implementations have a number of shortcomings due to the memristor's characteristics such as memory decay, highly nonlinear switching behaviour as a function of applied voltage/current, and functional uniformity. These shortcomings can be addressed by utilising a mixed gates that can be used in conjunction with the analogue behaviour for biomimetic computation. The digital implementations in this paper use in-situ computational capability of the memristor.

cond-mat.mtrl-sci↗
arXiv2011

Analyzing three-player quantum games in an EPR type setup

We use the formalism of Clifford Geometric Algebra (GA) to develop an analysis of quantum versions of three-player non-cooperative games. The quantum games we explore are played in an Einstein-Podolsky-Rosen (EPR) type setting. In this setting, the players' strategy sets remain identical to the ones in the mixed-strategy version of the classical game that is obtained as a proper subset of the corresponding quantum game. Using GA we investigate the outcome of a realization of the game by players sharing GHZ state, W state, and a mixture of GHZ and W states. As a specific example, we study the game of three-player Prisoners' Dilemma.

quant-ph↗
arXiv2011

Analysis of two-player quantum games in an EPR setting using geometric algebra

The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR) type setting is investigated using the mathematical formalism of Clifford geometric algebra (GA). In this setting, the players' strategy sets remain identical to the ones in the classical mixed-strategy version of the game, which is then obtained as proper subset of the corresponding quantum game. As examples, using GA we analyze the games of Prisoners' Dilemma and Stag Hunt when played in the EPR type setting.

quant-ph↗
arXiv2011

Metamaterial-inspired multichannel thin-film sensor

A multichannel thin-film sensor is implemented from a set of microstrip-coupled split-ring resonators (SRR's) with different dimensions. Each SRR exhibits a unique high-Q resonance that is sensitive to the presence of a sample in a particular area. Hence, this SRR-based sensor can function (i) to detect different samples simultaneously to increase the throughput or (ii) to characterise nominally identical samples at multiple frequencies to increase the sensor selectivity. The design principle is validated with simulation and measurement. Owing to the optimized design, sensing a low-permittivity film with a thickness as small as one thousandth of the operating wavelength is achievable.

physics.ins-det↗
arXiv2011

A Precise Error Bound for Quantum Phase Estimation

Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring symmetry in the error definitions, an exact formula can be found. This new approach may also have value in solving other related problems in quantum computing, where an expected error is calculated. Expressions for two special cases of the formula are also developed, in the limit as the number of qubits in the quantum computer approaches infinity and in the limit as the extra added qubits to improve reliability goes to infinity. It is found that this formula is useful in validating computer simulations of the phase estimation procedure and in avoiding the overestimation of the number of qubits required in order to achieve a given reliability. This formula thus brings improved precision in the design of quantum computers.

quant-ph↗
arXiv2010

A simplified approach to electromagnetism using geometric algebra

A new simplified approach for teaching electromagnetism is presented using the formalism of geometric algebra (GA) which does not require vector calculus or tensor index notation, thus producing a much more accessible presentation for students. The four-dimensional spacetime proposed is completely symmetrical between the space and time dimensions, thus fulfilling Minkowski's original vision. In order to improve student reception we also focus on forces and the conservation of energy and momentum, which take a very simple form in GA, so that students can easily build on established intuitions in using these laws developed from studying Newtonian mechanics. The potential formulation is also integrated into the presentation that allows an alternate solution path, as well as an introduction to the Lagrangian approach. Several problems are solved throughout the text to make the implementation clear. We extend previous treatment of this area, through including the potential formulation, the conservation of energy and momentum, the generalization for magnetic monopoles, as well as simplifying previously reported results through eliminating the need for the spacetime metric.

physics.ed-ph↗
arXiv2010

Compact electric-LC resonators for metamaterials

Alternative designs to an electric-LC (ELC) resonator, which is a type of metamaterial inclusion, are presented in this article. Fitting the resonator with an interdigital capacitor (IDC) helps to increase the total capacitance of the structure. In effect, its resonance frequency is shifted downwards. This implies a decreased overall resonator size with respect to its operating wavelength. As a result, the metamaterial, composed of an array of IDC-loaded ELC resonators with their collective electromagnetic response, possesses improved homogeneity and hence is less influenced by diffraction effects of individual cells. The impact of incorporating an IDC into ELC resonators in terms of the electrical size at resonance and other relevant properties are investigated through both simulation and experiment.

physics.optics↗
arXiv2010

Constructing quantum games from symmetric non-factorizable joint probabilities

We construct quantum games from a table of non-factorizable joint probabilities, coupled with a symmetry constraint, requiring symmetrical payoffs between the players. We give the general result for a Nash equilibrium and payoff relations for a game based on non-factorizable joint probabilities, which embeds the classical game. We study a quantum version of Prisoners' Dilemma, Stag Hunt, and the Chicken game constructed from a given table of non-factorizable joint probabilities to find new outcomes in these games. We show that this approach provides a general framework for both classical and quantum games without recourse to the formalism of quantum mechanics.

quant-ph↗
arXiv2010

Constructing quantum games from a system of Bell's inequalities

We report constructing quantum games directly from a system of Bell's inequalities using Arthur Fine's analysis published in early 1980s. This analysis showed that such a system of inequalities forms a set of both necessary and sufficient conditions required to find a joint distribution function compatible with a given set of joint probabilities, in terms of which the system of Bell's inequalities is usually expressed. Using the setting of a quantum correlation experiment for playing a quantum game, and considering the examples of Prisoners' Dilemma and Matching Pennies, we argue that this approach towards constructing quantum games addresses some of their well known criticisms.

quant-ph↗
arXiv2010

Memristor MOS Content Addressable Memory (MCAM): Hybrid Architecture for Future High Performance Search Engines

Large-capacity Content Addressable Memory (CAM) is a key element in a wide variety of applications. The inevitable complexities of scaling MOS transistors introduce a major challenge in the realization of such systems. Convergence of disparate technologies, which are compatible with CMOS processing, may allow extension of Moore's Law for a few more years. This paper provides a new approach towards the design and modeling of Memristor (Memory resistor) based Content Addressable Memory (MCAM) using a combination of memristor MOS devices to form the core of a memory/compare logic cell that forms the building block of the CAM architecture. The non-volatile characteristic and the nanoscale geometry together with compatibility of the memristor with CMOS processing technology increases the packing density, provides for new approaches towards power management through disabling CAM blocks without loss of stored data, reduces power dissipation, and has scope for speed improvement as the technology matures.

cond-mat.mes-hall↗
arXiv2009

Non-factorizable Joint Probabilities and Evolutionarily Stable Strategies in the Quantum Prisoner's Dilemma Game

The well known refinement of the Nash Equilibrium (NE) called an Evolutionarily Stable Strategy (ESS) is investigated in the quantum Prisoner's Dilemma (PD) game that is played using an Einstein-Podolsky-Rosen type setting. Earlier results report that in this scheme the classical NE remains intact as the unique solution of the quantum PD game. In contrast, we show here that interestingly in this scheme a non-classical solution for the ESS emerges for the quantum PD.

quant-ph↗
arXiv2008

Quantum Matching Pennies Game

A quantum version of the Matching Pennies (MP) game is proposed that is played using an Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) setting. We construct the quantum game without using the state vectors, while considering only the quantum mechanical joint probabilities relevant to the EPR-Bohm setting. We embed the classical game within the quantum game such that the classical MP game results when the quantum mechanical joint probabilities become factorizable. We report new Nash equilibria in the quantum MP game that emerge when the quantum mechanical joint probabilities maximally violate the Clauser-Horne-Shimony-Holt form of Bell's inequality.

quant-ph↗
arXiv2008

Probabilistic analysis of three-player symmetric quantum games played using the Einstein-Podolsky-Rosen-Bohm setting

This paper extends our probabilistic framework for two-player quantum games to the mutliplayer case, while giving a unified perspective for both classical and quantum games. Considering joint probabilities in the standard Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) setting for three observers, we use this setting in order to play general three-player non-cooperative symmetric games. We analyze how the peculiar non-factorizable joint probabilities provided by the EPR-Bohm setting can change the outcome of a game, while requiring that the quantum game attains a classical interpretation for factorizable joint probabilities. In this framework, our analysis of the three-player generalized Prisoner's Dilemma (PD) shows that the players can indeed escape from the classical outcome of the game, because of non-factorizable joint probabilities that the EPR setting can provide. This surprising result for three-player PD contrasts strikingly with our earlier result for two-player PD, played in the same framework, in which even non-factorizable joint probabilities do not result in escaping from the classical consequence of the game.

quant-ph↗