The Theory and Modeling of Power Dissipation and Quantum Decoherence in Molecular Quantum-dot Cellular Automata (QCA)

Quantum-dot cellular automata (QCA) is a paradigm for classical computing being developed as an alternative to conventional complimentary metal-oxide semiconductor (CMOS) transistor logic. QCA is motivated by high levels of power dissipation (heat) in modern CMOS devices and the approaching limit of the decades-long trend of transistor scaling to improve computing performance. QCA offers ultra-high device densities, ultra-fast device switching, and low levels of dissipation.

Here, a scheme is provided for the clocking of molecular QCA using a time-varying electric field generated by clocking wires buried beneath the substrate. A worst-case analysis yields an upper limit of power dissipation in clocking wires and demonstrates that the additional power dissipation due to this circuitry is a concern secondary to dissipation in the molecular devices themselves. A model of the energetics of QCA bit packets demonstrates that energy input from the clock required to form a bit packet may be returned to the clock upon erasure of the bit packet. Adiabatic CMOS analogs of QCA circuits are presented, which could yield power benefits even before molecular QCA is fully developed. A model of a QCA molecule interacting with a simple, explicitly-modeled quantum environment is developed to study quantum decoherence in molecular QCA, revealing that environmental interactions tend to stabilize molecular QCA bits. A dissipative model of driven electron transfer coupled to environmentally-damped nuclear displacements in a QCA molecule is developed using the Lindblad equation. Electron transfer rates in the terahertz regime are calculated for a candidate QCA molecule. A calculation of power flow and dissipation to the environment is derived, and a high degree of adiabaticity is demonstrated in some regions of the design space. The models presented here may provide a link in a QCA molecule design loop, in which molecules are conceived, characterized in quantum chemistry, modeled according to our theory and evaluated for operating speed and power dissipation, and, finally, redesigned as needed for superior performance.