8,061 research outputs found
Making Classical Ground State Spin Computing Fault-Tolerant
We examine a model of classical deterministic computing in which the ground
state of the classical system is a spatial history of the computation. This
model is relevant to quantum dot cellular automata as well as to recent
universal adiabatic quantum computing constructions. In its most primitive
form, systems constructed in this model cannot compute in an error free manner
when working at non-zero temperature. However, by exploiting a mapping between
the partition function for this model and probabilistic classical circuits we
are able to show that it is possible to make this model effectively error free.
We achieve this by using techniques in fault-tolerant classical computing and
the result is that the system can compute effectively error free if the
temperature is below a critical temperature. We further link this model to
computational complexity and show that a certain problem concerning finite
temperature classical spin systems is complete for the complexity class
Merlin-Arthur. This provides an interesting connection between the physical
behavior of certain many-body spin systems and computational complexity.Comment: 24 pages, 1 figur
Error-power tradeoffs in QCA design
In this work we present an error-power tradeoff study in a Quantum-dot Cellular Automata (QCA) circuit design. Device parameter variation to optimize performance is a very crucial step in the development of a technology. In this work we vary the maximum kink energy of a QCA circuit to perform an error-power tradeoff study in QCA design. We make use of graphical probabilistic models to estimate polarization errors and non-adiabatic energy dissipated in a clocked QCA circuit and demonstrate the tradeoff studies on the basic QCA circuits such as majority gate and inverter. We also show how this study can be used by comparing two single bit adder designs. The study will be of great use to designers and fabrication scientists to choose the most optimum size and spacing of QCA cells to fabricate QCA logic designs
Hierarchical probabilistic macromodeling for QCA circuits
With the goal of building an hierarchical design methodology for quantum-dot cellular automata (QCA) circuits, we put forward a novel, theoretically sound, method for abstracting the behavior of circuit components in QCA circuit, such as majority logic, lines, wire-taps, cross-overs, inverters, and corners, using macromodels. Recognizing that the basic operation of QCA is probabilistic in nature, we propose probabilistic macromodels for standard QCA circuit elements based on conditional probability characterization, defined over the output states given the input states. Any circuit model is constructed by chaining together the individual logic element macromodels, forming a Bayesian network, defining a joint probability distribution over the whole circuit. We demonstrate three uses for these macromodel-based circuits. First, the probabilistic macromodels allow us to model the logical function of QCA circuits at an abstract level - the "circuit" level - above the current practice of layout level in a time and space efficient manner. We show that the circuit level model is orders of magnitude faster and requires less space than layout level models, making the design and testing of large QCA circuits efficient and relegating the costly full quantum-mechanical simulation of the temporal dynamics to a later stage in the design process. Second, the probabilistic macromodels abstract crucial device level characteristics such as polarization and low-energy error state configurations at the circuit level. We demonstrate how this macromodel-based circuit level representation can be used to infer the ground state probabilities, i.e., cell polarizations, a crucial QCA parameter. This allows us to study the thermal behavior of QCA circuits at a higher level of abstraction. Third, we demonstrate the use of these macromodels for error analysis. We show that low-energy state configurations of the macromodel circuit match those of the layout level, thus allowing us to isolate weak p- oints in circuits design at the circuit level itsel
On the decomposition of stochastic cellular automata
In this paper we present two interesting properties of stochastic cellular
automata that can be helpful in analyzing the dynamical behavior of such
automata. The first property allows for calculating cell-wise probability
distributions over the state set of a stochastic cellular automaton, i.e.
images that show the average state of each cell during the evolution of the
stochastic cellular automaton. The second property shows that stochastic
cellular automata are equivalent to so-called stochastic mixtures of
deterministic cellular automata. Based on this property, any stochastic
cellular automaton can be decomposed into a set of deterministic cellular
automata, each of which contributes to the behavior of the stochastic cellular
automaton.Comment: Submitted to Journal of Computation Science, Special Issue on
Cellular Automata Application
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