Faisal Shah Khan

Synthesis of multi-qudit hybrid and d-valued quantum logic circuits by decomposition

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 [Multi-valued logic gates for quantum computation, Phys. Rev. A 62 (2000) 052309. [10]], Daboul et al. [Quantum gates on hybrid qudits, J. Phys. A Math. Gen. 36 (2003) 2525-2536. [5]], and Bartlett et al. [Quantum encodings in spin systems and harmonic oscillators, Phys. Rev. A 65 (2002) 052316. [17]]. 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. [Generalized Euler angle parameterization for SU(N), J. Phys. A Math. Gen. 35 (2002) 10467-10501. [15]] have shown that the unitary evolution matrix (gate) can be synthesized in terms of its Euler angle parametrization. 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.

Mini-maximizing two qubit quantum computations

Two qubit quantum computations are viewed as two player, strictly competitive games and a game-theoretic measure of optimality of these computations is developed. To this end, the geometry of Hilbert space of quantum computations is used to establish the equivalence of game-theoretic solution concepts of Nash equilibrium and mini-max outcomes in games of this type, and quantum mechanisms are designed for realizing these mini-max outcomes.

OCTONIONIZATION OF THREE PLAYER, TWO STRATEGY MAXIMALLY ENTANGLED QUANTUM GAMES

We develop an octonionic representation of the payo function for a three player, two strategy, maximally entangled quantum game.

Dominant strategies in two-qubit quantum computations

Nash equilibrium is a solution concept in non-strictly competitive, noncooperative game theory that finds applications in various scientific and engineering disciplines. A non-strictly competitive, noncooperative 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.

THE ROLE OF CORRELATION IN QUANTUM AND CLASSICAL GAMES

We use the example of playing a 2-player game with entangled quantum objects to investigate the effect of quantum correlation. We find that for simple game scenarios it is classical correlation that is the central feature and that these simple quantum games are not sensitive to the quantum part of the correlation. In these games played with quantum objects it is possible to transform a game such as Prisoners Dilemma into the game of Chicken. We show that this behavior, and the associated enhanced equilibrium payoff over playing the game with quantum objects in nonentangled states, is entirely due to the classical part of the correlation. Generalizing these games to the pure strategy 2-player quantum game where the players have finite strategy sets and a projective joint measurement is made on the output state produced by the players, we show that a given quantum game of this form can always be reproduced by a classical model, such as a communication channel. Where entanglement is a feature of the these 2-player quantum games the matrix of expected outcomes for the players can be reproduced by a classical channel with correlated noise.

Advances in the Quantum Theoretical Approach to Image Processing Applications

In this article, a detailed survey of the quantum approach to image processing is presented. Recently, it has been established that existing quantum algorithms are applicable to image processing tasks allowing quantum informational models of classical image processing. However, efforts continue in identifying the diversity of its applicability in various image processing domains. Here, in addition to reviewing some of the critical image processing applications that quantum mechanics have targeted, such as denoising, edge detection, image storage, retrieval, and compression, this study will also highlight the complexities in transitioning from the classical to the quantum domain. This article shall establish theoretical fundamentals, analyze performance and evaluation, draw key statistical evidence to support claims, and provide recommendations based on published literature mostly during the period from 2010 to 2015.

A Simulink model of an active island detection technique for inverter-based distributed generation

With the increased involvement of Distributed Power Generation Systems (DPGSs) into the conventional power system, the structure has evolved and therefore has brought in various challenges albeit improving flexibility and smartness of the system. This paper addresses modeling one of these challenges where a Simulink model for inverter-based distributed generation (IBDG) active islanding detection technique is introduced. Out of the various types of active islanding detection methods, the modeling of the general electric islanding detection method which uses the positive feedback of the voltage or frequency at the point of common coupling (PCC) for the detection of an island is presented. This methodology is modeled and applied for an IBDG connected to a low voltage distribution network. The simulation results are presented for a 20kW, three-phase IBDG showing that the system is able to detect islanding and cease the current flow from the IBDG even under critical operating condition of a close matching between the power delivered by the inverter and the load demand (zero nondetection zone operation).

Quantum games: a review of the history, current state, and interpretation

We review both theoretical and experimental developments in the area of quantum games since the inception of the subject circa 1999. We will also offer a narrative on the controversy that surrounded the subject in its early days, and how this controversy has affected the development of the subject.

High-ISO image de-noising using burst filtering

Cameras allow capturing images in low light conditions by adjusting the level of their ISO setting. ISO, which stands for International Standards Organization, controls the sensitivity of a cameras sensor. A high-ISO value amplifies not only the images signal but also the noise signal, giving both of them a high gain depending on the chosen ISO level. This results in statistically unpredictable noise distribution with different intensities all over the image. In this paper, this type of high-ISO noise and its different characteristics will be investigated; particularly its effect in the luminance and chrominance channels. Based on these differences, a burst filtering algorithm that is based on bilateral filtering and median stacking is proposed.

A game theoretic approach to quantizing Markov processese

In the context of quantum information theory, “quantization” of various mathematical constructions is said to occur upon the replacement, at various points in the construction, of the classical randomization notion of probability distribution with higher order randomization notions from quantum mechanics such as quantum superposition with measurement. For this to be done “properly”, a faithful copy of the original construction is required to exist within the new “quantum” one, just as is required when a function is extended to a larger domain. Here, Markov processes that serve as mathematical models of history dependent Parrondo games are quantized properly.