We present a study of the joint influence of temperature and fabrication defects on the operation of quantum-dot cellular automata (QCA) devices. Canonical ensemble, a Hubbard-type Hamiltonian and the inter-cellular Hartree approximation were used, and a statistical model has been introduced to simulate defects in the QCA devices. Parameters such as success rate and breakdown displacement factor (BDF) were defined and calculated numerically. Results show the thermal dependence of BDF values of the QCA devices. The BDF values decrease with temperature. The joint influence of randomly missing dots and temperature was also studied.
We present fault tolerant properties of various quantum-dot cellular automata (QCA) devices. Effects of temperatures and dot displacements on the operation of the fundamental devices such as a binary wire, logical gates, a crossover, and an exclusive OR (XOR) have been investigated. A Hubbard-type Hamiltonian and intercellular Hartree approximation have been used for modeling, and a uniform random distribution has been implemented for the defect simulations. The breakdown characteristics of all the devices are almost the same except the crossover. Results show that the success of any device is significantly dependent on both the fabrication defects and temperatures. We have observed unique characteristic features of the crossover. It is highly sensitive to defects of any magnitude. Results show that the presence of a crossover in a XOR design is a major factor for its failure. The effects of temperature and defects in the crossover device are pronounced and have significant impact on larger and complicated QCA devices.
Using an explicit Euler substitution, a system of differential equations was obtained, which can be used to find the solution of the time-dependent 1-dimensional Schrődinger equation for a general form of the time-dependent potential.In the framework of fundamentals of Quantum mechanics, the unitary evolution given by the Schrődinger equation is conceivable only for quasi-isolated quantum systems, i.e. systems interacting via "classical" fields, which may be obtained using quantification procedures. Actually, these fields are time-independent, or have a harmonic time-dependence. The evolution of a quantum system interacting with a non-stationary environment is given by master-type equations rather than timedependent Schrődinger equations. However, the latter are often used in many practical applications from molecular physics, quantum chemistry, quantum optics, solid state physics, etc. [1].In the recent paper [1], I. Guedes obtained the exact Schrődinger wave function for a particle in a timedependent 1-dimensional linear potential energy. For a Hamiltonian:if Schrődinger equation is tested with the trial function:one obtains two differential equations for the functions η(t) and µ(t), so one can find the solution Ψ(x, t) after solving these equations. To this end, one has to find the initial conditions, say from Ψ(x, 0). However, Ψ(x, 0) is not, generally, of the type (2), so one has to decompose Ψ(x, 0) using Fourier series:next find the initial conditions corresponding to the general component ψ(k) · e −i·k·x , then one has to solve the differential equation for η(t, k) and µ(t, k), and finally compute the inverse Fourier Transform.Here I present an algorithm which can be used in solving the Schrődinger equation for a general form of the time and position dependence of potential energy, without referring to the Fourier Transform. One can test Schrődinger equation using the following explicit Euler substitution:I used the series expansion of the potential energy w.r.t.x:The initial conditions are given by:Expanding in power series, Schrődinger equation gives:One can easily note that if one has non-zero initial coefficients only for n < n 0 (which includes(0, t)), all coefficients for n < 2·n 0 have to remain zero at every subsequent moment (one can perform any-order time derivations in (7) at t = 0 and obtain null values). Relation (7) can be very useful, either for analytical calculations, or for numerical (finite difference) calculus algorithms:In (8) a finite time step t 0 was chosen . It is obvious that one can iterate (8) in order to estimate {α n,p } n for every moment p · t 0 as functions of the initial coefficients {α n,0 } n given by (6).[1] I. Guedes, Phys. Rev. A, 63, 034102 (2001).
We present a numerical study of fault tolerance properties in quantum-dot cellular automata (QCA) devices. A full-basis quantum method is used for calculations of the Hamiltonian, and a statistical model has been introduced to simulate the influence of position defects of the dots within cells on the logical output. Combined effects of temperature and cell defects on a shift register have been studied. Uniform and normal distributions have been used for the cell defect simulations. Normal distribution simulations produce realistic results compared to the uniform distribution. In order to show the operational limit of a device, parameters such as “displacement factor” and “success rate” are introduced. Results show that the fault tolerance of a QCA device is strongly dependent on temperature as well as on the cell defects. The robustness of a shift register is also dependent on the size of the device.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.