Quantum dot cellular automaton

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 - A simplified diagram of a four-dot QCA cell.

Figure 3 - The two possible states of a four-dot QCA cell.

Figure 2 shows a simplified diagram of a quantum-dot cell.[1] 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.

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.

Figure 5 - QCA Majority Gate

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.

Figure 6 - Standard Implementation of a NOT gate. Note that the labeling of the input and output values follows a convention exactly opposite to that of the rest of this article.

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

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 grid is doubled and an overall increase in geometric design complexity is inevitable. Yet another problem this technique presents is that the additional space between cells of the same orientation decreases the energy barriers between a cell's ground state and a cell’s first excited state. This degrades the performance of the device in terms of maximum operating temperature, resistance to entropy, and switching speed.

A different wire-crossing technique, which makes fabrication of QCA devices more practical, was presented by Christopher Graunke, David Wheeler, Douglas Tougaw, and Jeffrey D. Will, in their paper “Implementation of a crossbar network using quantum-dot cellular automata”. The paper not only presents a new method of implementing wire-crossings, but it also gives a new perspective on QCA clocking.

Their wire-crossing technique introduces the concept of implementing QCA devices capable of performing computation as a function of synchronization. This implies the ability to modify the device’s function through the clocking system without making any physical changes to the device. Thus, the fabrication problem stated earlier is fully addressed by: a) using only one type of quantum-dot pattern and, b) by the ability to make a universal QCA building block of adequate complexity, which function is determined only by its timing mechanism (i.e., its clocks).

Quasi-adiabatic switching, however, requires that the tunneling barriers of a cell be switched relatively slowly compared to the intrinsic switching speed of a QCA. This prevents ringing and metastable states observed when cells are switched abruptly. Therefore, the switching speed of a QCA is limited not by the time it takes for a cell to change polarization, but by the appropriate quasi-adiabatic switching time of the clocks being used.

Adding a second serial line to the device, and adding another latching region would allow for the latching of two input values at the two different outputs. To perform computation, a gate that takes as inputs both serial lines at their respective outputs is added. The gate is placed over a new latching region configured to process data only when both latching regions at the end of the serial lines hold the values of interest at the same instant. Figure 10 shows such an arrangement. If correctly configured, latching regions 5 and 6 will each hold input values of interest to latching region 7. At this instant, latching region 7 will let the values latched on regions 5 and 6 through the AND gate, thus the output could be configured to be the AND result of any two inputs (i.e. R and Q) by merely configuring the latching regions 5, 6 and 7.

This represents the flexibility to implement 16 functions, leaving the physical design untouched. Additional serial lines and parallel inputs would obviously increase the number of realizable functions. However, a significant drawback of such devices is that, as the number of realizable functions increases, an increasing number of clocking regions is required. As a consequence, a device exploiting this method of function implementation may perform significantly slower than its traditional counterpart.

Figure 10 – Multifunction QCA Device.

The metal-island implementation was the first fabrication technology created to demonstrate the concept of QCA. It was not originally intended to compete with current technology in the sense of speed and practicality, as its structural properties are not suitable for scalable designs. The method consists of building quantum dots using aluminum islands. Earlier experiments were implemented with metal islands as big as 1 micrometer in dimension. Because of the relatively large-sized islands, metal-island devices had to be kept at extremely low temperatures for quantum effects (electron switching) to be observable.

Semiconductor (or solid state) QCA implementations could potentially be used to implement QCA devices with the same highly advanced semiconductor fabrication processes used to implement CMOS devices. Cell polarization is encoded as charge position, and quantum-dot interactions rely on electrostatic coupling. However, current semiconductor processes have not yet reached a point where mass production of devices with such small features (≈20 nanometers) is possible. Serial lithographic methods, however, make QCA solid state implementation achievable, but not necessarily practical. Serial lithography is slow, expensive and unsuitable for mass-production of solid-state QCA devices. Today, most QCA prototyping experiments are done using this implementation technology.

A proposed but not yet implemented method consists of building QCA devices out of single molecules.[2] The expected advantages of such a method include: highly symmetric QCA cell structure, very high switching speeds, extremely high device density, operation at room temperature, and even the possibility of mass-producing devices by means of self-assembly. A number of technical challenges, including choice of molecules, the design of proper interfacing mechanisms, and clocking technology remain to be solved before this method can be implemented.

Magnetic QCA, commonly referred to as MQCA (or QCA: M), is based on the interaction between magnetic nanoparticles. The magnetization vector of these nanoparticles is analogous to the polarization vector in all other implementations. In MQCA, the term “Quantum” refers to the quantum-mechanical nature of magnetic exchange interactions and not to the electron-tunneling effects. Devices constructed this way could operate at room temperature.