Quantum Dot Cellular Automata

Quantum dot cellular automata (QDCA, 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.

Background

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.

Cellular automata

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.

Quantum-dot cells

Origin

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.

Modern cells

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.

Cell design

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.

QCA wire

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.

There are two types of wires possible in QCA: A simple binary wire as shown in Figure 4 and an inverter chain, which is constituted by placing 45-degree inverted QCA cells side by side.

Logic gates

Majority gate

Majority gate and inverter (NOT) gate are considered as the two most fundamental building blocks of QCA. Figure 5 shows a majority gate with three inputs and one output. In this structure, the electrical field effect of each input on the output is identical and additive, with the result that whichever input state ("binary 0" or "binary 1") is in the majority becomes the state of the output cell — hence the gate's name. For example, if inputs A and B exist in a “binary 0” state and input C exists in a “binary 1” state, the output will exist in a “binary 0” state since the combined electrical field effect of inputs A and B together is greater than that of input C alone.

Other gates

Other types of gates, namely AND gates and OR gates, can be constructed using a majority gate with fixed polarization on one of its inputs. A NOT gate, on the other hand, is fundamentally different from the majority gate, as shown in Figure 6. The key to this design is that the input is split and both resulting inputs impinge obliquely on the output. In contrast with an orthogonal placement, the electric field effect of this input structure forces a reversal of polarization in the output.

State transition

There is a connection between quantum-dot cells and cellular automata. Cells can only be in one of 2 states and the conditional change of state in a cell is dictated by the state of its adjacent neighbors. However, a method to control data flow is necessary to define the direction in which state transition occurs in QCA cells. The clocks of a QCA system serve two purposes: powering the automaton, and controlling data flow direction. QCA clocks are areas of conductive material under the automaton's lattice, modulating the electron tunneling barriers in the QCA cells above it.

Four stages

A QCA clock induces four stages in the tunneling barriers of the cells above it. In the first stage, the tunneling barriers start to rise. The second stage is reached when the tunneling barriers are high enough to prevent electrons from tunneling. The third stage occurs when the high barrier starts to lower. And finally, in the fourth stage, the tunneling barriers allow electrons to freely tunnel again. In simple words, when the clock signal is high, electrons are free to tunnel. When the clock signal is low, the cell becomes latched.

Figure 7 shows a clock signal with its four stages and the effects on a cell at each clock stage. A typical QCA design requires four clocks, each of which is cyclically 90 degrees out of phase with the prior clock. If a horizontal wire consisted of say, 8 cells and each consecutive pair, starting from the left were to be connected to each consecutive clock, data would naturally flow from left to right. The first pair of cells will stay latched until the second pair of cells gets latched and so forth. In this way, data flow direction is controllable through clock zones

Wire-crossing

Wire-crossing in QCA cells can be done by using two different quantum dot orientations (one at 45 degrees to the other) and allowing a wire composed of one type to pass perpendicularly "through" a wire of the other type, as shown schematically in figure 8. The distances between dots in both types of cells are exactly the same, producing the same Coulombic interactions between the electrons in each cell. Wires composed of these two cell types, however, are different: one type propagates polarization without change; the other reverses polarization from one adjacent cell to the next. The interaction between the different wire types at the point of crossing produces no net polarization change in either wire, thereby allowing the signals on both wires to be preserved.

Fabrication problems

Although this technique is rather simple, it represents an enormous fabrication problem. A new kind of cell pattern potentially introduces as much as twice the amount of fabrication cost and infrastructure; the number of possible quantum dot locations on an interstitial