| The Quantum-dot cellular automata (QCA) concept is an approach to computing at the nanoscale. Information is encoded in the charge configuration of closed cells comprised of several dots. Current does not flow between the cells, instead the coulomb interaction between cells enables computation to occur. Here, a theoretical approach, based on the density matrix formalism, is used to examine energy flow in QCA devices. An equation of motion well suited to modelling dissipative dynamics in quasi-adiabatic systems is developed, by using a simple two-state model to describe the cell and an energy-relaxation time to describe the coupling to the environment. Calculations are performed to show that QCA cells can exhibit true signal-power gain, where the energy lost to dissipative processes is restored by the clock. The power dissipated to the environment in QCA circuits is also calculated to show that it is possible to achieve the ultralow levels of power dissipation required at molecular device densities.; An analysis is performed with three-state QCA cells to quantitatively explore the relationship between computation and energy dissipation. The results support the connection made by Landauer between logical reversibility and physical reversibility. Computation always involves some dissipation, but there is no fundamental lower limit on how much energy must be dissipated in performing a logically reversible computation. The amount of energy dissipated to the environment in both logically irreversible “erase” and logically reversible “copy-then-erase” operations is calculated for finite times and at nonzero temperatures. The “copy” operation is performed by a QCA cell, which plays the role of Maxwell's demon. The QCA shift-register can then be viewed as a sequence of “copy-then-erase” operations where the role of the demon cell shifts down the cell chain. |
