The Development of Quantum-Dot Cellular Automata - Field-Coupled Nanocomputing: Paradigms, Progress, and Perspectives - page 5

applied by another wire, forming a three-input majority gate [ 14 ]. Inverters could be
formed from diagonal interactions between cells. With these basic elements, any
logical or arithmetic function can be formed.
With a year of the first QCA publication, other implementations were suggested.
Small metal islands could serve as dots and form QCA cells if they were coupled by
tunnel junctions [ 15 ]. One advantage of metal-dot QCA is that the electric field lines
from the dot can be guided by the conductors to influence the neighboring dots; in the
semiconductor depletion dots, the field spreads out in all directions. It was also natural
to envision molecular versions of QCA where the role of the quantum dot was played
by a part of the molecule that could localize charge [ 14 ]. A magnetic model of QCA
was constructed from three-inch magnets held in Lucite blocks which rotated on low-
friction jeweled pivots. These magnetic cells were used during talks and lectures by
both of the present authors to demonstrate QCA wires and gates. They prefigured (at
enormous scale) the nanomagnetic QCA under active research today and discussed in
other contributions to this volume.
A detailed examination of QCA dynamics and the development of several levels of
quantum description of QCA arrays [ 16 ], were prompted by another observation of
Landauer [ 17 ]. While encouraging QCA exploration, he expressed concern that a weak
link in a QCA wire would cause a switching error because the incorrect ''old'' state
downstream would have more influence than the upstream cells with the new state.
By treating the whole wire quantum mechanically it could be shown that this would
only be a temporary problem. But the exercise focused attention on the nature
of computation in QCA systems, which were designed from the beginning to map
the ground state onto the computationally correct state. This mapping can be robust,
while the details of the transient response of the system are inherently more fragile.
We wanted to avoid computing with the transient. A byproduct of these calcula-
tions was the development of several approximate treatments for both equilibrium and
dynamic calculations. The mapping between QCA and the Ising model in a transverse
field was also made precise.
Clocking of QCA arrays arose out of the detailed consideration of switching
dynamics and the desire to retain the robustness of the mapping between the ground
state and the computationally correct state for large systems. Clocking QCA entails
gradually moving cells between a neutral state and an active state with a clocking
signal. The active state can be either a binary 0 or 1; the neutral state is usually
denoted as a ''null'' state that carries no information. The first version of clocking,
proposed the year following the initial QCA papers, contemplated raising and low-
ering the inter-dot tunneling barriers [ 18 , 19 ]. This would gradually (adiabatically)
transition the cell between a delocalized electron configuration (null) and the localized
configuration of the active state. Koroktov and Likharev subsequently suggested a
version of metal-dot QCA called the single electron parametron which used a com-
plicated rotating electric field as a clock [ 20 ]. This had several drawbacks (e.g.,
information could only move in one direction in an array), but the idea of using as the
null state a localized state on an intermediate dot was adopted for clocking QCA,
particularly for molecular implementations. It is much easier to change the potential
on the intermediate dot than to directly influence the tunnel barriers between dots, and
the effect is the same. Adiabatic clocking QCA [ 21 ] solved the problem of switching