Building Blocks for Fluctuation Based Calculation in Single Electron Tunneling Technology

Safiruddin, Saleh; Cotofana, Sorin; Peper, Ferdinand; Lee, Jia

doi:10.1109/nano.2008.111

Cited by 6 publications

(4 citation statements)

References 8 publications

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“…Here we present novel consequences obtained by integrating theories explained in the previous sections. The reduced transition rate matrix (37)…”

Section: E Reversible Tmmentioning

confidence: 99%

“…Although the token-based Brownian circuit was introduced as a theoretical model for asynchronous computation, several efforts have been conducted to realize them by integrated quantum devices. For example, primitive circuit elements of Brownian circuits implemented by single-electron-tunneling circuits have been proposed [37,38]. In another technology, one of the circuit elements, the Hub, was experimentally realized in a ferromagnetic thin film in which magnetic skyrmions represent tokens [39].…”

Section: Introductionmentioning

confidence: 99%

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Computation time and thermodynamic uncertainty relation of Brownian circuits

Utsumi¹,

Ito²,

Golubev³

et al. 2022

Preprint

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We analyze a token-based Brownian circuit in which Brownian particles, coined 'tokens,' move randomly by exploiting thermal fluctuations, searching for a path in multi-token state space corresponding to the solution of a given problem. The circuit can evaluate a Boolean function with a unique solution. However, its computation time varies with each run. We numerically calculate the probability distributions of Brownian adders' computation time, given by the first-passage time, and analyze the thermodynamic uncertainty relation and the thermodynamic cost based on stochastic thermodynamics. The computation can be completed in finite time without environment entropy production, i.e., without wasting heat to the environment. The thermodynamics cost is paid through error-free output detection and the resets of computation cycles. The signal-to-noise ratio quantifies the computation time's predictability, and it is well estimated by the mixed bound, which is approximated by the square root of the number of token detections. The thermodynamic cost tends to play a minor role in token-based Brownian circuits in computation cycles. This contrasts with the logically reversible Brownian Turing machine, in which the entropy production increases logarithmically with the size of the state space, and thus worsens the mixed bound.

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“…Here we present novel consequences obtained by integrating theories explained in the previous sections. The reduced transition rate matrix (37)…”

Section: E Reversible Tmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Computation time and thermodynamic uncertainty relation of Brownian circuits

Utsumi¹,

Ito²,

Golubev³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

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“…In the original Hub functionality, previously implemented in SET in [8], where three channels are connected to a node, tokens enter one channel and randomly exit from one channel, which could also be the one it just came from. To provide support for stigmergic search the Hub functionality has to be extended such that it does not have a static behavior anymore, but it is adaptable.…”

Section: B Extended Hub Functionalitymentioning

confidence: 99%

Stigmergic search with single electron tunneling technology based memory enhanced hubs

Safiruddin

Cotöfană

Peper

2012

Proceedings of the 2012 IEEE/ACM International Symposium on Nanoscale Architectures

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Fluctuations have recently been recognized as powerful resources that can be exploited to drive computations, but their use has mostly been limited to logic circuits. This paper goes further and explores a more general framework, in which computation is modeled as a process with a multitude of fluctuating tokens that interact with each other directly or via stigmergy. For the implementation of these concepts Single Electron Tunneling (SET) technology is a strong candidate, since it combines a key element of fluctuation-driven systems, i.e., fluctuating tokens, with the potential for manufacturing in traditional materials (silicon) as well as alternatives, such as molecules. We propose computational elements, i.e., Memory Enhanced Hubs (MEHs), that contain functionality to pass fluctuating signals through them, as well as stigmergic functionality to store a state temporarily and reset it. We introduce a SET based design of such a memory enhance hub instance and demonstrate by means of simulations that it function correctly and that MEHs networks operating according to the stigmergic paradigm can be constructed.

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“…Asynchronous systems, like Petri net [11], usually suffer from the issue of deadlocks. Since Brownian motion provides a natural way to backtrack from deadlock situations, the fluctuation-driven computing scheme promises more effective circuit constructions [34,20] and offers the potential for physical implementation by future nano-electronics [37]. As a result, our novel NCCA model requires merely 11 cell states as well as a simple binary function, and is able to implement any arbitrary logic circuit in its cellular space, thereby it is computationally universal.…”

Section: Introductionmentioning

confidence: 99%

Fluctuation-driven computing on number-conserving cellular automata

Lee

Imai

Zhu

2012

Information Sciences

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A number-conserving cellular automaton (NCCA) is a cellular automaton where the states of cells are denoted by integers, and the sum of all numbers in a configuration is conserved throughout its evolution. It has been widely used to model physical systems ruled by conservation law of mass or energy. Imai et al. (2002) showed that an NCCA's local transition function can be effectively translated into sum of a binary flow function over pairs of neighboring cells. In this paper, we explore the computability of NCCAs where the pairwise number flows are performed at fully asynchronous timings. Despite the randomness associated with asynchronous transition, useful computation still can be accomplished efficiently in cellular automata, through active exploitation of fluctuations (Lee, et al., 2008). In particular, certain numbers may flow randomly fluctuating between forward and backward directions in the cellular space, as if they were subject to Brownian motion. Since random fluctuation promises a powerful resource for searching through the computational state space, the Brownianlike flow of numbers allows efficient embedding of logic circuits into our novel asynchronous NCCA.

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Building Blocks for Fluctuation Based Calculation in Single Electron Tunneling Technology

Cited by 6 publications

References 8 publications

Computation time and thermodynamic uncertainty relation of Brownian circuits

Computation time and thermodynamic uncertainty relation of Brownian circuits

Stigmergic search with single electron tunneling technology based memory enhanced hubs

Fluctuation-driven computing on number-conserving cellular automata

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