Modular Dissipation Analysis for QCA - Field-Coupled Nanocomputing: Paradigms, Progress, and Perspectives - page 370

been determined. The fourth and final step, is simply to sum the zone contribu-
tions to obtain a dissipation bound for the full circuit. None of these steps pose
formulation or implementation diculties. We leave implementation of modular
dissipation analysis in a QCA simulator for future work.
5 Conclusion
In this work, we have described a modular approach for determination of funda-
mental lower bounds on heat dissipation in Landauer-clocked QCA circuits. This
approach can provide dramatic analytical simplification over a much more gen-
eral approach to dissipation analysis introduced previously, provided that circuits
are designed according to specified design rules and are “modularized” through
proper application of corresponding circuit decomposition rules. We described
both the general and modular approaches to dissipation analysis, illustrated
their application to a QCA adder circuit designed according to a specified set of
example design rules, and verified that they yield identical results. The circuit
decomposition rules used in the illustrative modular analysis were presented,
and their necessity and physical justification was discussed in detail. We finally
argued that the modular dissipation analysis is well suited to automation, which
could enable determination of fundamental lower bounds on dissipation for large
and complex QCA circuits such as full processors.
Acknowledgments. This work was supported in part by NSF under Grant CCF-
0916156.
References
1. Landauer, R.: Irreversibility and heat generation in the computing process. IBM
J. Res. Dev. 5 , 183-191 (1961)
2. Anderson, N.G.: On the physical implementation of logical transformations: gen-
eralized L-machines. Theoret. Comput. Sci. 411 , 4179-4199 (2010)
3. Ercan, I., Anderson, N.G.: Heat dissipation bounds for nanocomputing: theory and
application to QCA. In: Proceedings of the 11th IEEE International Conference
on Nanotechnology, pp. 1289-1294 (2011)
4. Hanninen, I., Takala, J.: Irreversibility induced density limits and logical reversibil-
ity in nanocircuits. In: Proceedings of the 2012 IEEE/ACM International Sympo-
sium on Nanoscale Architectures, pp. 50-54 (2012)
5. Ercan, I., Anderson, N.G.: Heat dissipation in nanocomputing: lower bounds from
physical information theory. IEEE Trans. Nanotechnol. 12 , 1047-1060 (2013)
6. Walus, K., Mazur, M., Schulhof, G., Jullien, G.A.: Simple 4-bit processor based on
quantum-dot cellular automata. In: Proceedings of the 16th IEEE International
Conference on Application-Specific Systems, Architectures, and Processors, pp.
288-293 (2005)
7. Anderson, N.G., Ercan, I., Ganesh, N.: Toward nanoprocessor thermodynamics.
IEEE Trans. Nanotechnol. 12 , 902-909 (2013)