Power gain and dissipation in quantum-dot cellular automata

Quantum-dot cellular automata (QCA) may provide a novel way to bypass the transistor paradigm to form molecular-scale computing elements. In the QCA paradigm information is represented by the charge configuration of a QCA cell. We develop a theoretical approach, based on the density matrix formalism, which permits examination of energy flow in QCA devices. Using a simple two-state model to describe the cell, and an energy relaxation time to describe the coupling to the environment, we arrive at an equation of motion well suited to the quasi-adiabatically switched regime. We use this to examine the role of power gain and power dissipation in QCA cells. We show that QCA cells can exhibit true signal power gain. The energy lost to dissipative processes is restored by the clock. We calculate the power dissipated to the environment in QCA circuits and show that it is possible to achieve the ultralow levels of power dissipation required at molecular densities.