Stochastic Gate Research Articles

Local model of a qubit in the interferometric setup

We consider a typical realization of a qubit as a single particle in two-path interferometric circuits built from phase shifters, beam splitters and detectors. This framework is often taken as a standard example illustrating various paradoxes and quantum effects, including non-locality. In this paper we show that it is possible to simulate the behaviour of such circuits in a classical manner using stochastic gates and two kinds of particles, real ones and ghosts, which interact only locally. The model has built-in limited information gain and state disturbance in measurements which are blind to ghosts. We demonstrate that predictions of the model are operationally indistinguishable from the quantum case of a qubit, and allegedly ‘non-local’ effects arise only on the epistemic level of description by the agent whose knowledge is incomplete due to the restricted means of investigating the system.

Noise Tolerant Stochastic Logic Gate Circuits Synthesis using Genetic Algorithms

In this paper we propose a method for synthesis of combinational networks using non conventional logic gates. The logic components considered are Stochastic Logic Gates (SLGs) able to change their logic functionality by means of a single control parameter and the environmental level of noise. SLGs are able to adapt their computed logic function depending on the environmental conditions. Circuits composed of SLGs are thus sensitive to changes in the environment which alter the computed logic function. We propose a solution for the synthesis of SLGs combinational networks able to produce a network operating fault tolerant in different environmental conditions, i.e. different levels of noise. Given a description of the problem, in form of a truth table, the synthesis of the network is performed by means of genetic algorithms. The proposed solution is tested with a half-adder and compared to the optimal solution found with an exhaustive search.

Probabilistic analysis of dynamic and temporal fault trees using accurate stochastic logic gates

This paper presents accurate models for the analysis of fault trees based on stochastic logic. To produce the models, probabilistic analysis of static, dynamic and temporal gates is carried out and the probability models are converted to their equivalent stochastic logic gates. A hardware template is also designed for each stochastic logic gate. In the proposed method, users provide fault rates of basic events and immediately evaluate system reliability. Experimental results show that the proposed method is more accurate than previous methods using the proposed stochastic logic gates for dynamic and temporal fault trees. The formula was validated using the Markov model for exponential failure distribution events. The proposed model is applicable for both exponential and non-exponential distributions.

Stochastic gate dynamics regulate the catalytic activity of ubiquitination enzymes.

Initiation of the DNA damage and innate immune responses is dependent upon the flow of chemical information through coupled protein-protein interaction networks and driven by the synthesis and recognition of Lys 63 linked polyubiquitin (polyUb) chains on adaptor proteins. The central chemical step in Lys 63-linked protein ubiquitination involves the reaction of a specific lysine on a target protein with Ub that is covalently attached as a thioester conjugate to the Ub conjugating enzyme (E2) Ubc13. The active site cysteine of Ubc13, and E2 enzymes in general, is buttressed by a flexible loop. The role of loop dynamics in catalysis was investigated by mutating the central and hinge residues to glycine. The loop dynamics were experimentally characterized through measurement of enzyme kinetics, main chain NMR relaxation, X-ray crystallographic studies, and in vivo studies in yeast. The experimental data were complemented by analysis of MD simulations of the dynamics and kinetics for the loop motion. The results show that fast pico- to nanosecond time scale active site loop fluctuations play a crucial role in regulating the catalytic activity of Ubc13 by functioning as a stochastic active site gate, which is characterized by precisely balanced rates of opening and closing. In vivo functional complementation assays in yeast demonstrate that defects within this regulatory mechanism can have profound biological consequences, given that Ubc13 is the only E2 dedicated to synthesizing Lys 63-linked polyUb chains.

Boundary induced phase transition with stochastic entrance and exit

.We study an open-chain totally asymmetric exclusion process (TASEP) with stochastic gates present at the two boundaries. The gating dynamics has been modeled with the physical system of ion-channel gating in mind. These gates can randomly switch between an open state and a closed state. In the open state, the gates are highly permeable such that any particle arriving at the gate immediately passes through. In the closed state, a particle becomes trapped at the gate and cannot pass through until the gate switches open again. We calculate the phase-diagram of the system and find important and non-trivial differences with the phase-diagram of a regular open-chain TASEP. In particular, depending on the switching rates of the two gates, the system may or may not admit a maximal current phase. Our analytic calculations within mean-field theory capture the main qualitative features of our Monte Carlo simulation results. We also perform a refined mean-field calculation where the correlations at the boundaries are taken into account. This theory shows significantly better quantitative agreement with our simulation results.

Low-power asynchronous digital pipeline based on mismatch-tolerant logic gates

We present design of an asynchronous digital pipeline based on stochastic resonance gates (SR gates). These gates allow mismatch-tolerant and low-power designs by utilizing the beneficial role of noise (stochastic resonance effect). However, unpredictable delays appear in SR gates due to their dependence on stochastic processes. Therefore, applications are found in asynchronous circuits. We demonstrate the performance of a three-stage-asynchronous pipeline with dual-rail data encoding. Electrical simulations were done for a 0.18μm CMOS technology, and confirmed the pipeline performance regardless of transistor mismatches and consuming low power (100 picowatts). Moreover, experimental results based on a macrosystem confirmed the pipeline performance.

All-Optical Stochastic Logic Gate Based on a VCSEL With Tunable Optical Injection

We study the dynamics of a vertical-cavity surface-emitting laser with continuous-wave orthogonal optical injection from a tunable laser. We use the dynamical properties of polarization bistability and the interplay with internal or external noise to demonstrate numerically a reliable logic output to two logic inputs encoded in the optical frequency of the injected light. This all-optical configuration is more than ten times faster than the electro-optical implementation and has the advantage of operating at constant injection power.

Stochastic logic gate that exploits noise and polarization bistability in an optically injected VCSEL

We study numerically the dynamics of a vertical-cavity surface-emitting laser (VCSEL) with optical injection and show that the interplay of polarization bistability and noise yields a reliable logic output to two logic inputs. Specifically, by encoding the logic inputs in the strength of the light injected into the suppressed polarization mode of the VCSEL (the so-called 'orthogonal' injection), and by decoding the output logic response from the polarization state of the emitted light, we demonstrate an all-optical stochastic logic gate that exploits the ubiquitous presence of noise. It gives the correct logic output response for as short as 5 ns bit times when the dimensionless spontaneous emission coefficient, β(sp), is within the range 10(-4)-10(-1). Considering that typical values of β(sp) in semiconductor lasers are in the range 10(-5)-10(-4), the VCSEL-based logic gate can be implemented with nowadays commercially available VCSELs, exploiting either their intrinsic noise, or external and background noise sources.

Numerical implementation of a VCSEL-based stochastic logic gate via polarization bistability

We study the interplay of polarization bistability, spontaneous emission noise and aperiodic current modulation in vertical cavity surface emitting lasers (VCSELs). We demonstrate the phenomenon of logic stochastic resonance (LSR), by which the laser gives robust and reliable logic response to two logic inputs encoded in an aperiodic signal directly modulating the laser bias current. The probability of a correct response is controlled by the noise strength, and is equal to 1 in a wide region of noise strengths. LSR is associated with optimal noise-activated polarization switchings (the so-called "inter-well" dynamics if one considers the VCSEL as a bistable system described by a double-well potential) and optimal sensitivity to spontaneous emission in each polarization (the "intra-well" dynamics in the double-well potential picture). The robust nature of LSR in VCSELs offers interesting perspectives for novel applications and provides yet another example of a driven nonlinear optical system where noise can be employed constructively.

A Fuzzy Optimization Approach for Variation Aware Power Minimization During Gate Sizing

Technology scaling in the nanometer era has increased the transistor's susceptibility to process variations. The effects of such variations are having a huge impact on the yield of the integrated circuits and need to be considered early in the design flow. Traditional corner based deterministic methods are no longer effective and circuit optimization methods require reinvention with a statistical perspective. In this paper, we propose a new gate sizing algorithm using fuzzy linear programming in which the uncertainty due to process variations is modeled using fuzzy numbers. The variations in gate delay which is a function of the gate sizes and the fan-outs of the gates are represented using triangular fuzzy numbers with linear membership functions. Initially, as a preprocessing step for fuzzy optimization, we perform deterministic optimizations by fixing the fuzzy parameters to the worst and the average case values, the results of which are used to convert the fuzzy optimization problem into a crisp nonlinear problem. The crisp problem with delay and power as constraints is then formulated to maximize the robustness, i.e., the variation resistance of the circuit. The fuzzy optimization approach was tested on ITC'99 benchmark circuits and the results were validated for timing yield using Monte Carlo simulations. The proposed approach is shown to achieve better power reduction than the worst case deterministic optimization as well as the stochastic programming based gate sizing methods, while having comparable runtimes.

A heuristic approach for airport gate assignments for stochastic flight delays

To make good flight to gate assignments, not only do all the relevant constraints have to be considered, but stochastic flight delays that occur in actual operations also have to be taken into account. In past research, airport gate assignments and stochastic disturbances have often been handled in the planning and the real-time stages separately, meaning that the interrelationship between these stages, as affected by such delays, has been neglected. In this research, we develop a heuristic approach embedded in a framework designed to help the airport authorities make airport gate assignments that are sensitive to stochastic flight delays. The framework includes three components, a stochastic gate assignment model, a real-time assignment rule, and two penalty adjustment methods. The test results are based on data supplied by a Taiwan international airport, and show that the proposed framework performs better than the current manual assignment process and the traditional deterministic model.

Molecular motion under stochastic gating

We investigate molecular passage through a geometrical barrier. We assume that the barrier is a stochastic gate so that the passage rate depends on its fluctuating nature and on the molecular size. We calculate the dependence of the passage rate Keff on relaxation rate of the gate radius and therefore on the solvent viscosity η. Two cases are solved: an open-or-closed gate and an harmonic gate. The latter is shown to lead to the experimentally observed fractional power law dependence of Keff on η.