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Fig. 7. A dissipation zone, including placement of boundaries, for circuits designed
according to the design rules of this work. For such circuits, all dissipation zones result-
ing from modular dissipation analyses performed according to the decomposition rules
of this work will have this form. The design rules preclude irreversibility in all circuit
structures other than majority gates.
Such a decomposition is always possible for circuits designed according to the
design rules presented above. Use of the decomposition rules presented here
greatly simplifies dissipation analysis, as shown below.
Dissipation Analysis. Recall that the modular approach aims to simplify eval-
uation of the fundamental dissipation bounds obtained via the general approach
by partitioning the circuit into smaller zones - once and for all at the beginning
of the analysis - and applying the general approach piecemeal to determine the
dissipative contributions from each zone. The partitioning process can, however,
introduce an artifact that will cause the modular approach to overestimate the
dissipative contributions from the individual zones, and thus from the circuit as a
whole when the individual contributions are summed. We now describe the origin
of this artifact, and show that it is avoided in circuits that are designed according
to the above design rules and partitioned according to the above decomposition
rules.
Information propagation in Landauer-clocked QCA is not dissipative under
paradigmatic operation. Information lost from a block of adjacent, identically
clocked cells in a QCA wire during the “relax” phase of the clocking cycle are
always erased in the presence of (and in interaction with) an identical copy that
has already been transferred to - and is locked in - an adjacent block of cells
that is immediately “downstream.” This is the reversible
erase with copy
operation. If the block of cells being erased belongs to a particular circuit zone,
but the downstream copy does not, then the erasure will appear irreversible -
and thus dissipative - in a dissipation analysis that treats the zone including the
erased cells as independent and isolated. Neglect of the cross-boundary interac-
tions that renders the erasure reversible are lost, causing the simplified modular
analysis to fail.
If the decomposition rules stated above are followed, however, any group of
identically clocked cells is necessarily a wire segment that belongs to two circuit
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