The Development of Quantum-Dot Cellular Automata - Field-Coupled Nanocomputing: Paradigms, Progress, and Perspectives - page 4

A study of few-electron systems under bias showed a threshold behavior for single
electron transfer that is very nonlinear [ 9 ]. The origin of this nonlinearity is funda-
mentally the quantization of charge. If a region of space is surrounded by barriers that
are appropriately high, but still possibly leaky, then the expectation value of the
enclosed charge will be very close to an integer multiple of the fundamental charge.
When the equilibrium value of the charge changes because of a tunneling event, it will
necessarily be a rather abrupt jump between two integers.
Finally, the QCA architecture was inspired by classical cellular automata (CA)
architectures [ 10 ], of the type popularized by Conway's Game of Life. These are
mathematical models of evolution that proceed from discrete generation to generation
according to specified rules. The state of each cell is determined by the state of the
neighboring cells in a previous generation. The neighbor-to-neighbor coupling is a
natural match for nano-devices, since one expects that one very small device may
influence its neighbors, but not distant devices. CA's represent a means of compu-
tation that departs from the current-switch paradigm of transistors. But cellular
automata are mathematical models that can operate with any set of evolution rules.
The question for device architecture was not simply what local CA rules will produce
computational behavior, but what rules does the actual physics of cellular interaction
support.
The original QCA idea was the result of the confluence of these four ideas: (1) the
ability to create configurations of quantum dots which localize charge, (2) the con-
vincing argument by Landauer that any practical device would need bistable satura-
tion in the information transfer function, (3) the nonlinearity of charge tunneling
between such dots because of charge quantization, and (4) the notion of a locally-
coupled architecture in analogy to cellular automata.
It is worth noting that the connection to cellular automata is by analogy. Classical
CA's are almost always regular one or two-dimensional arrays of cells. The physics of
the interaction between QCA cells does not yield very interesting results for regular
arrays. QCA circuits look more like wires connecting devices; highly non-regular
layouts of cells provide the specific function. Mathematical model CA's evolve in
discrete generations, but physical systems interact continuously.

3 Developments

The first QCA paper demonstrated the bistability of a QCA cell using a multi-electron
Hamiltonian and a direct solution of the Schrödinger equation [ 11 ]. This direct
approach avoided the problems of sorting out exchange and correlation effects; within
the site model it was exact. This bistability remains a key feature of QCA. Though it is
somewhat appealing to explore a multi-state QCA cell and multi-state logic, only a
bistable system can truly saturate in both logic states. An intermediate state is always
subject to drifting off from stage to stage.
It was soon realized that a line of QCA cells acted like a binary wire and a junction
of two or three wires could form a logic gate [ 12 ]. The first proposal was to have a
special cell at the junction which could be internally biased to the 1 or 0 state and
thereby act as an OR gate or an AND gate [ 13 ]. It was soon clear that the bias could be