Abstract
We examine the energy dissipated by a two-state quantum system during a switching operation when interacting with a thermal environment. For an isolated system, the excess energy decreases exponentially with switching time. For classically damped systems, the energy dissipation decreases linearly with switching time. We model the quantum system coupled to a thermal environment using a Lindblad equation for the density matrix. For rapid switching, the exponential quantum adiabaticity holds. For slow enough switching, the damping from the bath yields linear dissipation, as in the classical limit. Between these two limits, when the switching time is comparable to the characteristic energy transfer time to the thermal bath, there is an inverted region when dissipation increases with longer switching times. Consequences for the design of molecular quantum-dot cellular automata are discussed.
Highlights
Energy dissipation is the major limiter in achieving scaled highdensity computational devices
The damping from the bath yields linear dissipation, as in the classical limit. Between these two limits, when the switching time is comparable to the characteristic energy transfer time to the thermal bath, there is an inverted region when dissipation increases with longer switching times
Switching of an isolated two-state system shows an exponential decrease in excess energy with increasing switching time the excited state PEx (Ts)
Summary
Energy dissipation is the major limiter in achieving scaled highdensity computational devices. Shrinking lithographically defined transistors has defined generations of computing.[3] The ultimate limit of device size is arguably a single molecule Such device sizes, a nanometer or a tenth of a nanometer, present the promise of extraordinarily high functional densities, but the power dissipation per device must be correspondingly very low. Electron transfer by tunneling from one dot to another enables switching the device state.[8] Power dissipation can be extraordinarily low. Quasi-adiabatically, switching keeps a QCA cell (here, we take the case of just two dots) very close to the instantaneous ground state and so minimizes dissipation. In the switching events considered here, bit information is physically represented in the electrode potentials, not in the electronic state of the two dots alone. We leave for future work addressing the issues of the energy investment required to write a bit or the energy dissipation necessary to truly erasing a bit, each of which in QCA requires consideration of a three-state system
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