Quantum dot cellular automaton

Quantum dot cellular automata (sometimes referred to simply as quantum cellular automata, or QCA) are a proposed improvement on conventional computer design (CMOS), which have been devised in analogy to conventional models of cellular automata introduced by John von Neumann. Quantum dot cellular automata (sometimes referred to simply as quantum cellular automata, or QCA) are a proposed improvement on conventional computer design (CMOS), which have been devised in analogy to conventional models of cellular automata introduced by John von Neumann. Any device designed to represent data and perform computation, regardless of the physics principles it exploits and materials used to build it, must have two fundamental properties: distinguishability and conditional change of state, the latter implying the former. This means that such a device must have barriers that make it possible to distinguish between states, and that it must have the ability to control these barriers to perform conditional change of state. For example, in a digital electronic system, transistors play the role of such controllable energy barriers, making it extremely practical to perform computing with them. A cellular automaton (CA) is a discrete dynamical system consisting of a uniform (finite or infinite) grid of cells. Each cell can be in only one of a finite number of states at a discrete time. As time moves forward, the state of each cell in the grid is determined by a transformation rule that factors in its previous state and the states of the immediately adjacent cells (the cell's 'neighborhood'). The most well-known example of a cellular automaton is John Horton Conway's 'Game of Life', which he described in 1970. Cellular automata are commonly implemented as software programs. However, in 1993, Lent et al. proposed a physical implementation of an automaton using quantum-dot cells. The automaton quickly gained popularity and it was first fabricated in 1997. Lent combined the discrete nature of both cellular automata and quantum mechanics, to create nano-scale devices capable of performing computation at very high switching speeds (order of Terahertz) and consuming extremely small amounts of electrical power. Today, standard solid state QCA cell design considers the distance between quantum dots to be about 20 nm, and a distance between cells of about 60 nm. Just like any CA, Quantum (-dot) Cellular Automata are based on the simple interaction rules between cells placed on a grid. A QCA cell is constructed from four quantum dots arranged in a square pattern. These quantum dots are sites electrons can occupy by tunneling to them. Figure 2 shows a simplified diagram of a quantum-dot cell. If the cell is charged with two electrons, each free to tunnel to any site in the cell, these electrons will try to occupy the furthest possible site with respect to each other due to mutual electrostatic repulsion. Therefore, two distinguishable cell states exist. Figure 3 shows the two possible minimum energy states of a quantum-dot cell. The state of a cell is called its polarization, denoted as P. Although arbitrarily chosen, using cell polarization P = -1 to represent logic “0” and P = +1 to represent logic “1” has become standard practice. Grid arrangements of quantum-dot cells behave in ways that allow for computation. The simplest practical cell arrangement is given by placing quantum-dot cells in series, to the side of each other. Figure 4 shows such an arrangement of four quantum-dot cells. The bounding boxes in the figure do not represent physical implementation, but are shown as means to identify individual cells. If the polarization of any of the cells in the arrangement shown in figure 4 were to be changed (by a 'driver cell'), the rest of the cells would immediately synchronize to the new polarization due to Coulombic interactions between them. In this way, a 'wire' of quantum-dot cells can be made that transmits polarization state. Configurations of such wires can form a complete set of logic gates for computation.