Analog Computer Research Articles

Ultrathin film optical coatings for all-optical mathematical operations with ultrahigh numerical aperture

Optical analog computation is garnering increasing attention due to its innate parallel processing capabilities, swift computational speeds, and minimal energy requirements. However, traditional optical components employed for such computations are usually bulky. Recently, there has been a substantial shift toward utilizing nanophotonic structures to downsize these bulky optical elements. Nevertheless, these nanophotonic structures are typically realized in planar subwavelength nanostructures, demanding intricate fabrication processes and presenting limitations in their numerical apertures. In this study, we present a three-layer thin-film optical coating different from the conventional Fabry–Pérot nanocavity. Our design functions as a real-time Laplacian operator for spatial differentiation, and it remarkably boasts an ultrahigh numerical aperture of up to 0.7, enabling the detected edges to be sharper and have closely matched intensities. We also experimentally demonstrate its capacity for effective edge detection. This ultracompact and facile-to-fabricate thin-film spatial differentiator holds promising prospects for applications in ultrafast optical processing and biomedical imaging.

In-memory analog solution of compressed sensing recovery in one step

Modern analog computing, by gaining momentum from nonvolatile resistive memory devices, deals with matrix computations. In-memory analog computing has been demonstrated for solving some basic but ordinary matrix problems in one step. Among the more complicated matrix problems, compressed sensing (CS) is a prominent example, whose recovery algorithms feature high-order matrix operations and hardware-unfriendly nonlinear functions. In light of the local competitive algorithm (LCA), here, we present a closed-loop, continuous-time resistive memory circuit for solving CS recovery in one step. Recovery of one-dimensional (1D) sparse signal and 2D compressive images has been experimentally demonstrated, showing elapsed times around few microseconds and normalized mean squared errors of 10 −2 . The LCA circuit is one or two orders of magnitude faster than conventional digital approaches. It also substantially outperforms other (electronic or exotically photonic) analog CS recovery methods in terms of speed, energy, and fidelity, thus representing a highly promising technology for real-time CS applications.

The design of adder, subtractor, and derivative circuits without the use of op-amp in CNFET Technology

The complexity of digital circuits is constantly rising. Analog computing can be an excellent alternative to overcome the complexity issue. Operational Amplifiers play a serious role in many analog circuit designs. This paper presents a new implementation approach to an analog subtractor. This design enjoys high speed and low power dissipation using Carbon Nanotube FETs (CNTFETs). We have also achieved a significant improvement in terms of the number of transistors and chip area. The proposed design considerably decreases power consumption and optimizes the chip area. The same performance can be achieved when designing a high-quality Differentiator. It is to remark that there is no need to use a huge number of resistors and capacitors. In this design, no additional voltage or current sources have been used. HSPICE and the Stanford 32 nm CNTFET model are used to simulate the proposed circuit. The comparisons with State-of-the-art prove the performance of this design.

Modeling the Transient Behavior of Ionic Diodes with the Nernst–Planck–Poisson Equations

AbstractIonic circuitry formed from soft charged polymers promises to enable a new kind of analog computing and usher in a new age of human–computer interaction, but devices remain in their infancy. Ionic diodes, created by the interface between two oppositely charged polymers, form one of the most fundamental elements of ionic circuitry. However, it is currently not well understood how the boundary conditions and geometry of a diode influence its transient response and performance. A consistent set of metrics with which to analyze these diodes is first developed, then a continuum model based on the Nernst–Planck–Poisson equations is used to study how device construction and three types of boundary conditions affect performance. This model is solved using the finite volume method and gives insight into transient diode behavior not described by previous analyses. It is demonstrated how different parts of a diode's construction, thickness, and operating voltage act as the limiting factors for different regimes. To conclude, it is demonstrated how blocking electrodes limit both diode lifetime and rectification behavior and how neutral bath boundary conditions play an important role in the performance of some diodes, with recommendations for building higher performance devices in the future.

Analog image processing with nonlinear nonlocal flat optics

Digital signal processing has revolutionized many fields of science and engineering, but it still shows critical limits, mainly related to the complexity, power consumption, and limited speed of analogue-to-digital converters. A long-sought solution to overcome these hurdles is optical analog computing. In this regard, flat optics has been recently unveiled as a powerful platform to perform data processing in real-time, with low power consumption and a small footprint. So far, these explorations have been mainly limited to linear optics. Arguably, significantly more impact may be garnered from pushing this operation towards nonlinear processing of the incoming signals. In this context, we demonstrate here that nonlinear phenomena combined with engineered nonlocality in flat optics devices can be leveraged to synthesize Volterra kernels able to outperform linear optical analog image processing.

Analog monolayer SWCNTs-based memristive 2D structure for energy-efficient deep learning in spiking neural networks

Advances in materials science and memory devices work in tandem for the evolution of Artificial Intelligence systems. Energy-efficient computation is the ultimate goal of emerging memristor technology, in which the storage and computation can be done in the same memory crossbar. In this work, an analog memristor device is fabricated utilizing the unique characteristics of single-wall carbon nanotubes (SWCNTs) to act as the switching medium of the device. Via the planar structure, the memristor device exhibits analog switching ability with high state stability. The device’s conductance and capacitance can be tuned simultaneously, increasing the device's potential and broadening its applications' horizons. The multi-state storage capability and long-term memory are the key factors that make the device a promising candidate for bio-inspired computing applications. As a demonstrator, the fabricated memristor is deployed in spiking neural networks (SNN) to exploit its analog switching feature for energy-efficient classification operation. Results reveal that the computation-in-memory implementation performs Vector Matrix Multiplication with 95% inference accuracy and few femtojoules per spike energy efficiency. The memristor device presented in this work opens new insights towards utilizing the outstanding features of SWCNTs for efficient analog computation in deep learning systems.

Hybrid integrators with predictive overload estimation for analog computers and continuous-time ΔΣ modulators

Abstract. Continuous-time integrators are a central component in ΔΣ modulators, in analog computers, and general analog signal processing. If several integrators are interconnected, scaling plays an important role: In analog computers, scaling is performed with respect to the machine unit (MU). In ΔΣ modulators, scaling is performed in such a way that at maximum input signal the allowable dynamic range of no integrator is exceeded. In both cases the scaling is a compromise limiting the dynamic range. For analog computers, it was proposed early on to extend the dynamic range by hybrid integrators. Here, an analog range overflow is processed digitally and the analog integrator is reduced to its permissible operating range within the machine unit interval. While in earlier proposals for hybrid integrators only the subsequent integrator stage processes the overflow and works with reduced analog values, our hybrid integrator can process the overflow directly, with the analog reset process being continuous-time. In the case of highly dynamical input signals and transients, analog overload handling is further improved by a prediction of the overload that includes the currently applied input signal in the calculation. For example, with continuous-time ΔΣ modulators, overload of the analog integrator can be reliably avoided.

AirNN: Over-the-Air Computation for Neural Networks via Reconfigurable Intelligent Surfaces

Over-the-air analog computation allows offloading computation to the wireless environment through carefully constructed transmitted signals. In this paper, we design and implement the first-of-its-kind convolution that uses over-the-air computation and demonstrate it for inference tasks in a convolutional neural network (CNN). We engineer the ambient wireless propagation environment through reconfigurable intelligent surfaces (RIS) to design such an architecture, which we call ’AirNN’. AirNN leverages the physics of wave reflection to represent a digital convolution, an essential part of a CNN architecture, in the analog domain. In contrast to classical communication, where the receiver must <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">react</i> to the channel-induced transformation, generally represented as finite impulse response (FIR) filter, AirNN <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">proactively</i> creates the signal reflections to emulate specific FIR filters through RIS. AirNN involves two steps: first, the weights of the neurons in the CNN are drawn from a finite set of channel impulse responses (CIR) that correspond to realizable FIR filters. Second, each CIR is engineered through RIS, and reflected signals combine at the receiver to determine the output of the convolution. This paper presents a proof-of-concept of AirNN by experimentally demonstrating convolutions with over-the-air computation. We then validate the entire resulting CNN model accuracy via simulations for an example task of modulation classification.

Polychromatic Dual-Mode Imaging with Structured Chiral Photonic Crystals.

Optical spatial differentiation is a typical operation of optical analog computing and can single out the edge to accelerate the subsequent image processing, but in some cases, overall information about the object needs to be presented synchronously. Here, we propose a multifunctional optical device based on structured chiral photonic crystals for the simultaneous realization of real-time dual-mode imaging. This optical differentiator is realized by self-organized large-birefringence cholesteric liquid crystals, which are photopatterned to encode with a special integrated geometric phase. Two highly spin-selective modes of second-order spatial differentiation and bright-field imaging are exhibited in the reflected and transmitted directions, respectively. Two-dimensional edges of both amplitude and phase objects have been efficiently enhanced in high contrast and the broadband spectrum. This work extends the ingenious building of hierarchical chiral nanostructures, enriches their applications in the emerging frontiers of optical computing, and boasts considerable potential in machine vision and microscopy.

Impact of hypertension on mean transvalvular gradients in aortic stenosis Lessons learned from in silico modelling

Abstract Introduction The influence of hypertension on the diagnostic assessment of aortic stenosis (AS) severity is unclear, yet clinically relevant. To clarify the effect of hypertension on transvalvular gradients, requires a better understanding of the impact that blood pressure change has on mean flow rate. Also, the effect of various degrees of AS severity, the valve geometry and intrinsic left ventricular contractile function (elastance) on this interaction, needs to be clarified. Existing clinical research on this topic is limited by not incorporating the full complement of factors that influences the directionality and magnitude of mean transvalvular gradient change for any given change in blood pressure. Purpose To use validated flow dynamics modelling grounded in fundamental physics principles to create a digital platform where various parameters can be manipulated to quantify the effects of bloodpressure change on mean transvalvular gradients in various pathological states. Methods A validated, zero-dimensional electro-hydraulic analogue computer model of the human cardiovascular circulatory system was generated. It was used to assess the impact of blood pressure changes on left ventricular pressure and transvalvular gradients at various flow rates, left ventricular elastances, a range of aortic valve areas and for different aortic valve morphologies. Results Mean transvalvular gradients are flow dependent. The impact of hypertension on mean flow rate (MFR), and hence on mean gradient (MG), is influenced by the aortic valve area as well as the underlying left ventricular elastance (Figure 1). Subsequently, the relationship between MFR and MG could be modelled (Figure 2). Generally, for a given change in systemic arterial pressure, the impact on MG will be the most marked for lower flow rate states such as is expected in more severe degrees of AS and for worse intrinsic left ventricular (LV) contractility. Furthermore, for a constant hemodynamic valve area, the hydraulic valve orifice area was found to be smaller in rheumatic AS compared to degenerative AS. This results in less susceptibility to blood pressure induced changes in mean transvalvular gradient. Similarly, the size of the aortic root was found to be inversely related to the susceptibility to induce a change in mean gradient for a change in blood pressure. Conclusion The interaction between hypertension and mean gradients in AS is complex. The current work places previous recommendations in perspective by quantifying the magnitude of the effect that a change in blood pressure has on mean gradient in various pathophysiological states. By doing so it provides more granularity into this multifaceted interaction compared to previously oversimplified deductions from clinical studies. The findings of this study creates a basic science framework based on first principles that dictates the scope of parameters that should be considered in future clinical research on the topic.Modelling 1Modelling 2

Multilevel nonvolatile photomemory with long-term robust optical retention based on photoinduced depolarization

Ferroelectric memory is promising for implementing emerging information technologies, including digital storage and analog computing. Two-dimensional (2D) ferroelectric materials retain robust room-temperature ferroelectric characteristics at the single-layer limit, surpassing traditional ferroelectric materials. This characteristic enables further advancements in device miniaturization to meet the growing demand. Herein, we manufactured a metal–insulator–ferroelectric–semiconductor field-effect transistor (MIFSFET) using a 2D ferroelectric material (α-In2Se3), which displayed nonvolatile characteristics. Based on the mechanism of photoinduced depolarization in a ferroelectric semiconductor, the MIFSFET device can be used as a photomemory, capable of storing an optical image for up to 1000 s with minimal information loss and can achieve a multistate photoresponse induced by an optical pulse. Moreover, it can function as a ferroelectric memory, with an on/off ratio exceeding 106, endurance of above 3000 cycles, and stable retention. The proposed MIFSFET demonstrated excellent optical image sensing and memory functions, presenting a feasible approach for developing efficient visual systems in the future.

First demonstration of in-memory computing crossbar using multi-level Cell FeFET

Advancements in AI led to the emergence of in-memory-computing architectures as a promising solution for the associated computing and memory challenges. This study introduces a novel in-memory-computing (IMC) crossbar macro utilizing a multi-level ferroelectric field-effect transistor (FeFET) cell for multi-bit multiply and accumulate (MAC) operations. The proposed 1FeFET-1R cell design stores multi-bit information while minimizing device variability effects on accuracy. Experimental validation was performed using 28 nm HKMG technology-based FeFET devices. Unlike traditional resistive memory-based analog computing, our approach leverages the electrical characteristics of stored data within the memory cell to derive MAC operation results encoded in activation time and accumulated current. Remarkably, our design achieves 96.6% accuracy for handwriting recognition and 91.5% accuracy for image classification without extra training. Furthermore, it demonstrates exceptional performance, achieving 885.4 TOPS/W–nearly double that of existing designs. This study represents the first successful implementation of an in-memory macro using a multi-state FeFET cell for complete MAC operations, preserving crossbar density without additional structural overhead.

Effects of Mg Doping to a LiCoO2 Channel on the Synaptic Plasticity of Li Ion-Gated Transistors.

Artificial synapses with ideal functionalities are essential in hardware neural networks to allow for energy-efficient analog computing. However, the realization of linear and symmetric weight updates in real synaptic devices has proven challenging and ultimately limits the online training capabilities of neural network systems. Herein, we investigate the effect of Mg doping on a LiCoO2 (LCO) channel in a Li ion-gated synaptic transistor, so as to improve long-term and short-term plasticity. Two transistor structures, based on a lithium phosphorus oxynitride electrolyte, were examined by using undoped LCO and Mg-doped LCO as the channel material between the source and drain electrodes. It was found that Mg doping increased the initial channel conductance by 3 orders of magnitude, which is probably due to the substitution of Co3+ by Mg2+ and the compensation of hole creation. It was further found that the doped channel transistor showed good retention characteristics and better linearity of long-term potentiation and depression when voltage pulses were applied to the gate electrode. The improved retention and linearity are attributed to an extended range of the insulator-to-conductor transition by Mg doping and Li-ion extraction/insertion cooperated in the LCO channel. Using the obtained synaptic weight update, artificial neural network simulations demonstrated that the doped channel transistor shows an image recognition accuracy of ∼80% for handwritten digits, which is higher than ∼65% exhibited by the undoped channel transistor. Mg doping also improved short-term plasticity such as paired-pulse facilitation/depression and Hebbian spike timing-dependent plasticity. These results indicate that elemental doping to the channel of Li ion-gated synaptic transistors could be a useful procedure for realizing robust neuromorphic systems based on analog computing.

Switchable optical differentiator using Fano resonance metasurface

Optical differentiation plays a pivotal role in analog computing and image processing, owing to its faster operating speeds and lower power consumption. However, the conventional differentiator encounters a common issue of single and fixed functions due to the lack of effective dynamic modulation means. Here, we proposed a polarization-sensitive differentiator based on a Fano resonance metasurface. The interference between transmitted light and a quasi-guided mode induces Fano resonance, resulting in the leakage of high-frequency component of the p-wave. By adjusting the asymmetry and line width of the Fano resonance line shape, the metasurface can function as a Fourier spatial filter to achieve the differential of an incident beam. Additionally, the direction of the s- and p-wave can be controlled to realize multiple differential functions. We demonstrate the simulation of switchable differential between arbitrary one-dimensional (1D) direction and two-dimensional (2D) directions, with a numerical aperture up to 0.26. It is expected that this switchable optical differentiator will have broad applications in areas such as bioimaging and computer vision.

Evidence of Transport Degradation in 22 nm FD-SOI Charge Trapping Transistors for Neural Network Applications

This article reports on the characterization and analysis of 22 nm FD-SOI CMOS technology-based charge trap transistors (CTT) and their application in neural networks. The working principle of CTT as non-volatile memory depends on trapping and de-trapping of charge in the high-k gate dielectric with the application of voltage pulses on the drain and gate terminals. This programming condition leads to the generation of interfacial traps that can drastically impact device performance. We report degradation in CTT through extractions of subthreshold swing, ON-state current, and mobility. We elucidate transport degradation by correlating effective mobility to interface trap density using a quasi-ballistic transport theory essential for the nanoscale devices under test in this work. Importantly, the trap-induced degradation in CTT transport is not recovered with voltage pulsing at room temperature as our experiments show. We demonstrate the implications of these findings based on analog computation of dot products, an operation of utmost importance to the implementation of artificial neural networks.

Analog Programmable‐Photonic Computation

AbstractDigital electronics is a technological cornerstone in this modern society that has covered the increasing demand for computing power during the last decades thanks to a periodic doubling of transistor density in integrated circuits. Currently, such scaling law is reaching its fundamental limit, leading to the emergence of a large gamut of applications that cannot be supported by digital electronics, specifically, those that involve real‐time multi‐data processing, e.g., medical diagnostic imaging, robotic control, and autonomous driving, among others. In this scenario, an analog computing approach implemented in a real‐time reconfigurable nonelectronic hardware such as programmable integrated photonics (PIP) can be more efficient than digital electronics to perform these emerging applications. However, actual analog computing models such as quantum and neuromorphic computation were not conceived to extract the unique benefits of PIP (and integrated photonics in general). Here, the foundations of a new computation theory are presented, termed Analog Programmable‐Photonic Computation (APC), explicitly designed to unleash the full potential of PIP technology. Interestingly, APC enables overcoming basic theoretical and technological limitations of existing computational models and can be implemented in other technologies (e.g., in electronics, acoustics or using metamaterials), consequently exhibiting the potential to spark a ground‐breaking impact on the information society.

State dependence of Krylov complexity in 2d CFTs

We compute the Krylov Complexity of a light operator O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}L in an eigenstate of a 2d CFT at large central charge c. The eigenstate corresponds to a primary operator O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}H under the state-operator correspondence. We observe that the behaviour of K-complexity is different (either bounded or exponential) depending on whether the scaling dimension of O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}H is below or above the critical dimension hH = c/24, marked by the 1st order Hawking-Page phase transition point in the dual AdS3 geometry. Based on this feature, we hypothesize that the notions of operator growth and K-complexity for primary operators in 2d CFTs are closely related to the underlying entanglement structure of the state in which they are computed, thereby demonstrating explicitly their state-dependent nature. To provide further evidence for our hypothesis, we perform an analogous computation of K-complexity in a model of free massless scalar field theory in 2d, and in the integrable 2d Ising CFT, where there is no such transition in the spectrum of states.

Preparation of (ZrTiCoNiNb)Ox high-entropy oxide powders by microwave heating with thermal field modulation

High entropy oxide powders (ZrTiCoNiNb)Ox were successfully synthesised using microwave heating with a TE666 resonant mode at temperatures ranging from 700 °C to 900 °C. X-ray diffraction (XRD) and Scanning electron microscopy (SEM) techniques were carried out to characterize the samples, and the behavior of the samples when they undergo microwave heating was investigated. The mechanism of thermal field modulation (TFM) was explored to reduce the temperature gradients and improve heating efficiency. The temperature field distribution was simulated using COMSOL software. The process of synthesising (ZrTiCoNiNb)Ox using microwave heating was found to comprise four stages: thermal accumulation, local solid-phase reaction, synchronous reaction and grain growth. A phase transition from multi-phase mixing to a fixed high entropy phase was observed. The effectiveness of the mechanism of thermal field modulation was confirmed via analogue computation and experimentation.

Symplectic gauge group on the Lens space

We compute the Lens space index for 4d supersymmetric gauge theories involving symplectic gauge groups. This index can distinguish between different gauge groups from a given algebra and it matches across theories related by supersymmetric dualities. We provide explicit calculations for mathcal{N} = 4 SYM and for classes of mathcal{N} = 2 and mathcal{N} = 1 Lagrangian quivers related by S-duality. In these cases the index matches across the S-dual phases, while models in different S-duality orbits have a different Lens index. We provide analogous computations for a 4d mathcal{N} = 1 toric quiver gauge theory corresponding to a ℤ7 orbifold of ℂ3. This SU(n)7 gauge theory becomes interesting in the case of n = 2 because it is conformally dual to other two models, with symplectic and unitary gauge groups, bifundamentals and antisymmetric tensors. We explicitly check this triality at the level of the Lens space index.

Solving ordinary and partial differential equations using an analog computing system based on ultrasonic metasurfaces

Wave-based analog computing has recently emerged as a promising computing paradigm due to its potential for high computational efficiency and minimal crosstalk. Although low-frequency acoustic analog computing systems exist, their bulky size makes it difficult to integrate them into chips that are compatible with complementary metal-oxide semiconductors (CMOS). This research paper addresses this issue by introducing a compact analog computing system (ACS) that leverages the interactions between ultrasonic waves and metasurfaces to solve ordinary and partial differential equations. The results of our wave propagation simulations, conducted using MATLAB, demonstrate the high accuracy of the ACS in solving such differential equations. Our proposed device has the potential to enhance the prospects of wave-based analog computing systems as the supercomputers of tomorrow.