Retinamorphic bichromatic Schrödinger metamedia

A complex number is formed by a real part and an imaginary part, the latter being composed of a real number multiplied by the imaginary unit “i,” defined as the square root of . For this reason, imaginary numbers cannot be placed on the real number line. The geometric representation of complex numbers is done in the so-called complex plane, composed of a real axis and an imaginary axis, orthogonal to the real line. However, from a philosophical point of view, the fact that the imaginary axis is not identified with any axis in three-dimensional Euclidean space raises ontological questions that transcend the well-established mathematical formalism of the set of complex numbers: are imaginary numbers just a sophism, an arbitrary invention, or a true mathematical discovery? Are imaginary numbers a glimpse of a parallel reality that is beyond our perception? In this article, I seek to demonstrate that the imaginary unit can be interpreted as an algebraic ambiguity that arises when representing certain vectors in the real plane as one-dimensional variables. Consequently, we will see how it is possible to express complex numbers in terms of real numbers.

In the past few years, CMOS semiconductor has been a growing and evolving technology in VLSI. However, due to the scaling issue and some other constraints like heat generation, high power consumption QCA (quantum cellular automata) emerged as an alternate and enhanced solution that provides a new technique of computing than CMOS in recent years. QCA is highly effective in implementing both Irreversible and Reversible logic, which has been shown to be incredibly efficient in terms of power consumption. A novel technique to data encryption called as SCV (select, cross, and variation) is demonstrated in this paper, which is based on ASCII to binary conversion and uses reversible logic. The data security procedure is aided by implementing SCV logic in reversible logic. Using Fredkin gate, it is built in QCA. QCADesigner tool has been used here for design and verification purposes. Total 80 cell counts and 0.14 μm 2 area are required. The theoretical data and the simulation results are the same as the intended circuit. Comparison to previous QCA architectural features is featured.

Quantum Cellular Automata (QCA) offers a new approach to building computer circuits. In the light of these global research led to the development are found. Since memory is one of the most applicable basic units in digital circuits, but Its smaller components, which are called by filip-flop is created. Although there are some QCA structures for a memory cell in the literature, however, QCA characteristics may be used in designing a more optimized memory cell than blindly modeling CMOS logics in QCA. It is trying to propose a new design of the D-ff be paid within QCA. It is designed to lower the number of cells used to build D-ff. Also, to prove the correctness of implementation in routine simulator (QCADesigner) is used and the result schema is also expressed.

Recently, P. Shor (1994) has shown that quantum computers (computers which can operate simultaneously on a quantum superposition of inputs) permit efficient (i.e. polynomial-time) solutions of problems for which no efficient classical-mechanical solution is known. This has led to renewed interest in the question of whether or not quantum computers can be physically realized. One kind of quantum computer, quantum cellular automata, can be described by relatively simple Hamiltonians that resemble the Hamiltonians of spin systems. In this paper, we report a quantum cellular automaton which, though not itself computation-universal, forms an essential part of any quantum cellular automaton which is synchronized using Feynman's technique. This quantum cellular automaton has as its Hamiltonian the one-dimensional XY Hamiltonian, which is exactly solvable. Furthermore, there is experimental evidence from low-temperature measurements of the heat capacity and electric susceptibility that the Hamiltonian of the quantum cellular automaton is realized in nature by the rare-earth compound praseodymium ethyl sulfate near 1 K. >

This paper compares the three possible types of complex number. These provide a very concise means for representing certain geometric transformations of the points of a plane. The first type considered is the ordinary complex number, a + ib (where i2 = −1). This is used in the exponential form exp(iα) to rotate the plane through the angle α. The second type is the dual number, a + ∈b (where ∈2 = 0), and exp(∈τ) shears the plane parallel to the y-axis through the shear τ. The third type is the double number, a + jb (where j2 = +1), and exp(jβ) represents another type of shear transformation, known as a Lorentz transformation, which shears the plane through the rapidity β.

We construct a novel three-dimensional quantum cellular automaton (QCA) based on a system with short-range entangled bulk and chiral semion boundary topological order. We argue that either the QCA is nontrivial, i.e. not a finite-depth circuit of local quantum gates, or there exists a two-dimensional commuting projector Hamiltonian realizing the chiral semion topological order (characterized by $U(1)_2$ Chern-Simons theory). Our QCA is obtained by first constructing the Walker-Wang Hamiltonian of a certain premodular tensor category of order four, then condensing the deconfined bulk boson at the level of lattice operators. We show that the resulting Hamiltonian hosts chiral semion surface topological order in the presence of a boundary and can be realized as a non-Pauli stabilizer code on qubits, from which the QCA is defined. The construction is then generalized to a class of QCAs defined by non-Pauli stabilizer codes on ${2^n}$-dimensional qudits that feature surface anyons described by $U(1)_{2^n}$ Chern-Simons theory. Our results support the conjecture that the group of nontrivial three-dimensional QCAs is isomorphic to the Witt group of non-degenerate braided fusion categories.

We study a quantum cellular automaton (QCA) whose time-evolution is defined from global transition function of classical cellular automata (CA). In order to investigate natural transformations from CA to QCA, the present QCA includes CA with Wolfram's rule 150 and 105 as special cases. We firstly compute the time-evolution of the QCA and examine its statistical properties. As a basic statistical value, the probability of finding an active cell averaged over a spatial-temporal space is introduced, and the difference between CA and QCA is considered. In addition, it is shown that statistical properties in QCA are related to the classical trajectory in the configuration space.

Missing-cell defects in QCA wires: The ground and excited electronic states perspectives

Quantum Cellular Automata (QCA) represents an emerging technology at the nanotechnology level. The effects of space radiations in QCA inverter gate are investigated in this paper. Single Electron Fault (SEF) is a fault which may happen during operation of QCA circuits. A detailed simulation based logic level modelling of Single Electron Fault for QCA inverter gate is represented in this paper. It will be shown that the behaviour of single electron fault in QCA devices is not similar to either previously investigated faults or conventional CMOS logic

Quantum cellular automata (QCA) technology is a nanotechnology provides a very different computation platform than traditional CMOS, in which polarization of electrons indicates the digital information. This paper discusses about the quantum cellular automata complex gate structure consist of 3, 4 and 5 input majority gates. Multi input complex gates can be constructed with the single QCA structure that can be configured in to Boolean functions and logic gates. We have also constructed product of sum and sum of product representation and other different Boolean functions. QCA circuits are simulated using QCAdesinger tool and waveforms are presented. We also validate the constructed structure by building combination al circuits like comparators etc. A single fixed QCA structure is useful for building module in QCA FPGA and ASIC applications.

Computer operations involving complex numbers, essential in such applications as digital signal processing and image processing, are usually performed in a divide-and-conquer approach dealing separately with the real and imaginary parts and then accumulating the results. There have been several proposals to treat complex numbers as a single unit but all seem to have floundered on the basic problem of the division process without which, of course, it is impossible to carry out all but the most basic arithmetic. This paper resurrects an early proposal to express complex numbers in a single binary representation and provides a fail-safe procedure for obtaining the quotient of two complex numbers expressed in this representation.

We show that by using complex, double, and dual numbers one can find the invariant one-forms employed in the metrics of the Bianchi cosmological models. The result is equivalent to find, locally, all the Lie groups of dimension three.

A QCA in 2 + 1 and 3 + 1 dimensions

In this paper, we propose an alternative heterostructure device geometry to realize a semiconductor quantum cellular automata (QCA) cell. This device, called a split current quantum cellular automata (SCQCA) cell, has some attractive features which may enable the fabrication and circuit realization of QCA systems with current fabrication technologies. We present the device model and simulation results by incorporating this model in QCADesigner, a design and simulation tool for QCA. The simulations consist of the two cell interaction, showing the nonlinear cell-cell response function, a short wire, as well as the majority gate created with a cross pattern of five QCA cells.

We present results to show the effects of device scaling on the relativeperformance of three device technologies, namely resonant tunnellingdiodes (RTD), electronic quantum cellular automata (QCA) andcomplementary metal-oxide-semiconductor (CMOS) transistortechnology. The minimumfeature size (MOSFET or HFET gate lengths λ) is scaled from 250 to50 nm, while QCA inter-dot separations of 20 to 2 nm are examined. Thecomparison is made using a standard digital circuit architecture, namely amemory-adder model. Our aim is to compare these device technologies on thesystem level rather than individual device level. The results show that theRTDs offer speed advantages over CMOS, but improvements in the circuit densityare limited. The electronic QCAs will suffer both from effectively low packingdensity and low operating speeds in comparison to CMOS if conventional designsand a 2D architecture are used.