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Photonics: A Dream of Modern Technology
Published in Tarun Kumar Gangopadhyay, Pathik Kumbhakar, Mrinal Kanti Mandal, Photonics and Fiber Optics, 2019
Sourangshu Mukhopadhyay, Shuvra Dey, Subhendu Saha
Quantum logic is the logic system in which the principle of quantum mechanics is used to develop the logic. Here the information is encoded by the quantum states of a particle. After the saturation of semiconductor-based computing, quantum logic-based computation technique is a promising area.
Introduction to Quantum Theory
Published in Andrei Khrennikov, Social Laser, 2020
This chapter contains a brief introduction to mathematical formalism and QM axiomatics. It is oriented to non-physicists. Since QM is a statistical theory it is natural to start with the classical probability model (Kolmogorov [191], 1933). Then we present the basics of the theory of Hilbert spaces and Hermitian operators and the representation of pure and mixed states by normalized vectors and density operators. This introduction is sufficient to formulate the axiomatics of QM in the form of five postulates. The projection postulate (the most questionable postulate of QM) is presented in a separate section. We sharply distinguish between the cases of quantum observables represented by Hermitian operators with nondegenerate and degenerate spectra, von Neumann’s and Ltiders’s forms of the projection postulate. The axiomatics is completed by a short section on the main interpretations of QM. The projection postulate (LUders’s form) plays a crucial role in the definition of quantum conditional (transition) probability. By operating with the latter we consider interference of probabilities for two incompatible observables as a modification of the formula of total probability by adding the interference term. This viewpoint to interference of probabilities was elaborated in a series of works by Khrennikov. Since classical probability theory is based on the Boolean algebra of events, a violation of the law of total probability can be treated as the probabilistic sign of a violation of the laws of the Boolean logics. From this viewpoint, quantum theory can be considered as representing a new kind of logic, so-called quantum logic. The latter is also briefly presented in a separate section. We continue this review with a new portion of quantum mathematics, namely the notion of the tensor product of Hilbert spaces and the tensor product of operators. After the section on Dirac’s notation with ket and bra vector, we discuss briefly the notion of qubit and entanglement of a few qubits. This chapter concludes with a presentation of the detailed analysis of the probabilistic structure of the two-slit experiment in a bunch of different experimental contexts. This contextual structure leads to a violation of the law of total probability and non-Kolmogorovean probabilistic structure of this experiment.
How to Untangle Complex Systems?
Published in Pier Luigi Gentili, Untangling Complex Systems, 2018
A strategy to make electronic computers increasingly faster and energetically efficient is to miniaturize the basic switching elements—the transistors. This strategy is called the top-down approach and the pace of its accomplishment is epitomized by Moore’s law as we learned in paragraph 13.2. The American physicist Richard Feynman (1918–1988) paved the way for an alternative strategy, called the bottom-up approach in his seminal lecture titled “There is Plenty of Room at the Bottom,” taken at the annual meeting of the American Physical Society at the end of 1959 (Feynman 1960). The bottom-up approach is based on the idea of manufacturing computers by assembling atoms and molecules. Matter at the atomic level does not behave classically but quantum-mechanically. Indeed, the subatomic particles, atoms, and molecules can be used to process a new kind of logic that is quantum logic. Quantum states of matter have different properties with respect to the classical states of matter. Therefore, quantum information is different from classical information. The elementary unit of quantum information is the qubit or quantum bit (Schumacher 1995). A qubit is a quantum system that has two accessible states, labelled as |0〉 and |1〉 (note that the “bracket” notation |〉 means that whatever is contained in the bracket is a quantum-mechanical variable), and it can exist as a superposition of them. In other words, a qubit, |Ψ〉, is a linear combination of |0〉 and |1〉: [] |Ψ〉=a|0〉+b|b〉
Hybrid small-signal model parameter extraction for GaN HEMT based on QGA
Published in International Journal of Electronics, 2023
Shaowei Wang, Jincan Zhang, Shi Yang, Min Liu, Jinchan Wang, Juwei Zhang
Hussein & Jarndal (2018). employed Particle Swarm Optimisation (PSO) algorithm to optimise the extrinsic small-signal model parameters, relying only on the measured S-parameters under cold bias conditions. Jarndal & Hussein (2018) adopted a hybrid method of direct extraction technology and PSO-based technique to extract GaN HEMT model parasitic parameters. Majumder et al. (2017) applied a unique search space exploration strategy into the PSO algorithm to obtain optimised intrinsic model parameters. However, the PSO algorithm is suitable for dealing with high-dimensional optimisation problems, which is not suitable for GaN HEMT device models that require high modelling accuracy (Dubey & Gupta, 2017; Kefi et al., 2016). Therefore, there is a necessity to propose a suitable algorithm to optimise the model parameters. The Genetic Algorithm (GA) has been found to be able to handle multiple individuals in the population, reducing the risk of falling into a local optimum solution (Potuzak, 2016; Pravesjit & Kantawong, 2017). Jarndal & Ghannouchi (2016) adopted the GA to automatically obtain large-signal model parameters of GaN HEMT device. However, it has been found that GA may produce locally optimal solutions when incorrectly chosen crossover and variational operation (Ma, 2016; Yiqiu et al., 2019). In this paper, quantum state vector expression is introduced into genetic coding to achieve chromosome evolution using quantum logic gates. The adoption of the QGA simultaneously solves the shortcomings of GA and PSO algorithm. Additionally, since the distributed parasitic effects become more significant at the higher frequency conditions, reducing its reliability accordingly, a direct extraction method of GaN HEMT small signal model parameters in the lower frequency range is designed (A. Jarndal, 2013). Meanwhile, the model parameter values are extracted and optimised step by step using the QGA combing with direct extraction technique.