Modular Dissipation Analysis for QCA - Field-Coupled Nanocomputing: Paradigms, Progress, and Perspectives - page 368

Fig. 8. Dissipation zones identified by application of the circuit decomposition rules to
the QCA half adder of this work.

and evaluating the five required conditional entropies, we have

Δ↕E B ≤ d 1 ≥

1 . 1887 k B T ln(2)

Δ↕E B ≤ d 2 ≥ 0 . 6887 k B T ln(2)

Δ↕E B ≤ d 3 ≥

0 . 6887 k B T ln(2)

Δ↕E B ≤ d 4 ≥ 0 . 5 k B T ln(2)

Δ↕E B ≤ d 5 ≥

0 . 6887 k B T ln(2)

for the five dissipation zones. Summing these results, we obtain the bound

ΔE diss ≥ (3 . 76) k B T ln(2) (8)

on the dissipative cost of processing one adder input, which is indeed identical
to that obtained from the general approach.
Evaluation of this dissipation bound, which was shown in Sect. 3.1 to be
somewhat involved even for this simple circuit in general approach (and is labo-
rious in more complex circuits like the > 10 5 -cell QCA ALU studied in [ 11 ]), is
straightforward and simple in the modular approach. The vast analytical sim-
plification was enabled by the consistency of the circuit structure with stated
design rules, and the identification and formulation of an appropriate set of cir-
cuit decomposition rules specific to these design rules. With decomposition rules
in hand for our design rules, modular dissipation analyses could be performed
in exactly the same manner for any Landauer-clocked QCA circuit constructed
according to the same design rules.