InterJournal Complex Systems, 18 Status: Accepted |
Manuscript Number: [18] Submission Date: 963011 |
Can metastable states affect ground state computing? |
Subject(s): CX.07
Category: Brief Article
Abstract:
A class of computing architectures comprising locally-coupled arrays of quantum dots has recently been proposed as a novel paradigm for nanoelectronic computation and has attracted considerable attention. These schemes possess several characteristics suited to nanoelectronic implementations, including the absence of explicit interconnects, and the apparent convenience of edge-driven" computation where input/output interactions are confined only to the boundaries of the arrays. The process of computation, however, is predicated on the assumption that the arrays will always relax to their respective ground states. Unlike other energy-based models of computation (e.g., the Ising spin-glass systems and the Hopfield networks), where the ground state corresponds to an optimal solution for the problem under consideration and metastable states correspond to approximate solutions, the metastable states in the proposed models do not have any useful computational interpretation. This critical requirement of relaxation to the ground state has led to speculations that the metastable states might play a dominant role and may indeed invalidate the hypothesis of ground-state computation. We study, for the first time, the issues related to metastable states in such coupled arrays of quantum dots, and answer some of the related computational questions. The orthodox theory of single electron tunneling coupled with the Monte Carlo simulation method is used. Our results show that at zero temperature, the computing system will be trapped in metastable states over the entire parameter regime. As the temperature increases, there indeed exists a small parameter and temperature regime where the system can escape from metastable states and reach the ground state, and the dynamical process almost emulates a domino-type effect, as has been hypothesized by some of the proponents of ground-state computation. While the narrow parameter regime translates to stringent fabrication requirements, our results also determine that for physically relevant parameters, the time taken to reach the ground state is so large that the viability of ground state computing by a coupled array of quantum dots is questionable, even for the most advantageous choices of array parameters.
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