Modular Dissipation Analysis for QCA - Field-Coupled Nanocomputing: Paradigms, Progress, and Perspectives - page 364

of information loss associated with the specific circuit structure and clocking
scheme.

3.2 Analysis via Modular Approach

Design Rules. We begin discussion of our modular approach by articulating
an example set of QCA design rules, since circuit decomposition rules defined
for a set of design rules can be applied to modular dissipation analysis of any
circuit designed according to these rules. Our example design rules, which are
specific to Landauer-clocked combinational QCA circuits with no wire crossings,
are as follows:

1. Wires: All wires are linear arrays of “90-degree” wires, i.e. with adjacent
cells oriented as in Fig. 4 2 , and with right-angle corners. Wire segments cor-
responding to individual clock zones are of length

2 N exp[ E k /k B T ]

(in units of cells), where E k is the kink energy and k B is Boltzmann's con-

stant. The minimum allowable wire pitch is three cells.
2. Inverters: Inverters are of the “complex” form shown in Fig. 5 , with identi-
cally clocked, two-cell input leg and an identically-clocked two-cell output leg
as shown.
3. Majority Gates: Majority gates are of the standard three-input configuration
in Fig. 6 . The four input and output legs adjacent to the central cell - hereafter
the “device cell” - are identically clocked, and the four identically clocked
input and output legs are of equal length.

Fig. 4. Three example sections of QCA wires with “90-degree” cell orientation, two of
which include right angle corners.

Fig. 5. A complex inverter with two-cell input and output legs and specified clock
zones.

2 We do not consider “45-degree” wires since the design rules we propose are not
intended for wire crossings in a plane.