Abstract:
A game is said to be “quantized" when the expected payoff to the player(s) is computed via the higher order randomization notion of quantum superposition followed by measurement versus the randomization notion of probability distribution. A major motivation for quantizing a game is the potential manifestation of Nash equilibria that are superior to those already available in the game. Quantum superpositions are elements of a (projective) Hilbert space which, among other things, is an inner product space. The inner product of the Hilbert space of quantum superpositions is used here to give a geometric characterization of Nash equilibrium in quantized versions of Hawk-Dove games, a class of games to which the well known game Prisoners

Abstract:
A quantum logic gate of particular interest to both electrical engineers and game theorists is the quantum multiplexer. This shared interest is due to the facts that an arbitrary quantum logic gate may be expressed, up to arbitrary accuracy, via a circuit consisting entirely of variations of the quantum multiplexer, and that certain one player games, the history dependent Parrondo games, can be quantized as games via a particular variation of the quantum multiplexer. However, to date all such quantizations have lacked a certain fundamental game theoretic property. The main result in this dissertation is the development of quantizations of history dependent quantum Parrondo games that satisfy this fundamental game theoretic property. Our approach also yields fresh insight as to what should be considered as the proper quantum analogue of a classical Markov process and gives the first game theoretic measures of multiplexer behavior.

Abstract:
Earlier work on the quantization of the history dependent (HD) Parrondo game by Flitney, Ng, and Abbott led to the FNA protocol. We propose an alternative quantization protocol for this game which differs from the FNA protocol in various aspects.

Abstract:
This letter reports a novel application of game theory to quantum informational processes which can be used to optimally classify data generated by these processes. To this end, the notion of simultaneously distinguishing a pure quantum state, generated by a quantum informational process, from its constituent observable states optimally - given the constraint of these observables being orthogonal to each other, is first introduced. This problem is solved via a non-cooperative game model and the affiliated solution concept of Nash equilibrium. The notion of Nash equilibrium quantum states is introduced and used to classify quantum data optimally.

Abstract:
Nash equilibrium is a solution concept in non-strictly competitive, non-cooperative game theory that finds applications in various scientific and engineering disciplines. A non-strictly competitive, non-cooperative game model is presented here for two qubit quantum computations that allows for the characterization of Nash equilibrium in these computations via the inner product of their state space. Nash equilibrium outcomes are optimal under given constraints and therefore offer a game-theoretic measure of constrained optimization of two qubit quantum computations.

Abstract:
Recent research in multi-valued logic for quantum computing has shown practical advantages for scaling up a quantum computer. Multivalued quantum systems have also been used in the framework of quantum cryptography, and the concept of a qudit cluster state has been proposed by generalizing the qubit cluster state. An evolutionary algorithm based synthesizer for ternary quantum circuits has recently been presented, as well as a synthesis method based on matrix factorization.In this paper, a recursive synthesis method for ternary quantum circuits based on the Cosine-Sine unitary matrix decomposition is presented.

Abstract:
Recent research in generalizing quantum computation from 2-valued qudits to d-valued qudits has shown practical advantages for scaling up a quantum computer. A further generalization leads to quantum computing with hybrid qudits where two or more qudits have different finite dimensions. Advantages of hybrid and d-valued gates (circuits) and their physical realizations have been studied in detail by Muthukrishnan and Stroud (Physical Review A, 052309, 2000), Daboul et al. (J. Phys. A: Math. Gen. 36 2525-2536, 2003), and Bartlett et al (Physical Review A, Vol.65, 052316, 2002). In both cases, a quantum computation is performed when a unitary evolution operator, acting as a quantum logic gate, transforms the state of qudits in a quantum system. Unitary operators can be represented by square unitary matrices. If the system consists of a single qudit, then Tilma et al (J.Phys. A: Math. Gen. 35 (2002) 10467-10501) have shown that the unitary evolution matrix (gate) can be synthesized in terms of its Euler angle parameterization. However, if the quantum system consists of multiple qudits, then a gate may be synthesized by matrix decomposition techniques such as QR factorization and the Cosine-sine Decomposition (CSD). In this article, we present a CSD based synthesis method for n qudit hybrid quantum gates, and as a consequence, derive a CSD based synthesis method for n qudit gates where all the qudits have the same dimension.

An experiment was conducted at Malakabad (Gadera) Dargai Malak and KPK to
study the effect of different levels of nitrogen and phosphorus on the yield
of maize varieties in randomize complete block design with split plot
arrangement. Different fertilization treatments (0:0, 100:0, 100:50, 100:100,
150:0, 150:50, 150:100, 150:150 N:P kg·ha^{-}^{1}) were assigned to main plot while, maize varieties
(Azam, Jalal and local) were kept in sub-plots. Data regarding emergence m^{-}^{2}, days to emergence, days to tasseling, days to
silking, number of cobs plant^{-}^{1}, plant height, grains cob^{-}^{1}, 1000-grain weight and grain yield were recorded.
Emergence m^{-}^{2}, days to emergence, days to tasseling, days to
silking, plant ha^{-}^{1} at harvest were not significantly affected by
different levels of nitrogen and phosphorus while number of cob plant^{-}^{1}, thousand

Abstract:
The aim of this study was to improve the performance of Least Mean Square (LMS) adaptive algorithm used for fading channel estimation. One step Least Square prediction, based on the estimate of the sampled impulse response and the estimate of their speed of variation, is used along with LMS. The efficiency of the algorithm is confirmed by simulation results for slow, moderate and fast varying mobile channel. The results show about 3 to 11 dB improvement in the Mean Square Deviation between the estimated taps and the actual ones depending on the speed of channel time variations. Pedestrian, slow and fast Vehicular channels with doppler frequencies 6, 100 and 222 Hz, respectively, are used in these tests.