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Position Papers for the 2024 ASCR Workshop on Analog Computing for Science

Analog computing capabilities have existed since the dawn of science, but modern techniques potentially allow for the construction, verification, and characterization of complicated analog computing systems in a wide variety of contexts, from high-performance computational accelerators to nanorobotics and synthetic biology. In short, advances in analog computing can enable the creation of physical systems with complex behaviors that meet sophisticated requirements. Meeting our nation's needs, from needs in computing and modeling, to needs for advanced materials and energy technologies, continues to motivate pursuing novel kinds of complex systems, and thus analog computing techniques, in all of these spaces.

97 MATHEMATICS AND COMPUTING↗

Brochure on the 2024 ASCR Workshop on Analog Computing for Science

Analog computing fundamentally differs from digital by representing data with fully continuous physical quantities, such as voltages, probabilities, chemical concentrations, or light intensities, rather than encoding values in discrete binary states. While digital computing has historically excelled in precision, scalability, and noise resistance, newer analog approaches are gaining interest for their potential to dramatically improve energy efficiency and processing speed. Analog systems can inherently solve mathematical problems through their physical behavior and offer distinct advantages in scenarios where continuous operations are more effective than Boolean logic.

97 MATHEMATICS AND COMPUTING↗

Analog Computing for Science

Conventional digital computing faces fundamental physical limits: large scale computing systems already con sume tens of Megawatts of power, Dennard scaling has ended, and data movement costs dominate application performance. Next generation experimental facilities generate data at rates that overwhelm conventional pro cessing and demand real-time analysis at the source. Analog computing, which exploits the continuous dynamics of physical systems to perform computation, promises a transformative path toward orders-of-magnitude gains in energy efficiency and time-to-solution for scientific workloads.

97 MATHEMATICS AND COMPUTING↗

Analog simulator of integro-differential equations with classical memristors

An analog computer makes use of continuously changeable quantities of a system, such as its electrical, mechanical, or hydraulic properties, to solve a given problem. While these devices are usually computationally more powerful than their digital counterparts, they suffer from analog noise which does not allow for error control. We will focus on analog computers based on active electrical networks comprised of resistors, capacitors, and operational amplifiers which are capable of simulating any linear ordinary differential equation. However, the class of nonlinear dynamics they can solve is limited. In this work, by adding memristors to the electrical network, we show that the analog computer can simulate a large variety of linear and nonlinear integro-differential equations by carefully choosing the conductance and the dynamics of the memristor state variable. We study the performance of these analog computers by simulating integro-diferential models related to fluid dynamics, nonlinear Volterra equations for population growth, and quantum models describing non-Markovian memory effects, among others. Finally, we perform stability tests by considering imperfect analog components, obtaining robust solutions with up to 13% relative error for relevant timescales.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Modeling Analog Tile-Based Accelerators Using SST

Analog computing has been widely proposed to improve the energy efficiency of multiple important workloads including neural network operations, and other linear algebra kernels. To properly evaluate analog computing and explore more complex workloads such as systems consisting of multiple analog data paths, system level simulations are required. Moreover, prior work on system architectures for analog computing often rely on custom simulators creating signficant additional design effort and complicating comparisons between different systems. To remedy these issues, this report describes the design and implementation of a flexible tile-based analog accelerator element for the Structural Simulation Toolkit (SST). The element focuses on heavily on the tile controller—an often neglected aspect of prior work—that is sufficiently versatile to simulate a wide range of different tile operations including neural network layers, signal processing kernels, and generic linear algebra operations without major constraints. The tile model also interoperates with existing SST memory and network models to reduce the overall development load and enable future simulation of heterogeneous systems with both conventional digital logic and analog compute tiles. Finally, both the tile and array models are designed to easily support future extensions as new analog operations and applications that can benefit from analog computing are developed.

97 MATHEMATICS AND COMPUTING↗

Analog Systems for Edge Optimization

Over the past decade, analog computing has the subject of substantial research interest providing a path toward improved computational efficiency in the post-Dennard era. Analog matrix vector multiplication (MVM) accelerators provide a popular approach given the ubiquity of MVM operations in numerous applications. However, historically analog computing systems can struggle with applications requiring high precision due to the inherent susceptibility of these systems to analog non-idealities. Therefore, prior work on analog systems has focused either on applications known to be tolerant of limited precision (e.g., neural network inference), or using expensive techniques to emulate high-precision using many analog MVM operations. In this work, we propose an alternative approach. Motivated by recent advances in inexact nonlinear solvers and optimizers, we explore the potential of co-designing optimization algorithms which can take full advantage of the fundamentally inexact analog MVM operations. To enable these co-designed algorithms we also develop a general mathematical theory of the precision and energy efficiency of analog operations, and a new system architecture for tightly-coupled analog and digital computation. Finally, we examine the applicability of analog computing to a wider class of symmetric positive definite systems and find potential in using analog operations as a sparse approximate inverse preconditioner. With these core innovations, this project provides a path toward effectively implementing optimization algorithms on power-constrained autonomous and semi-autonomous systems.

97 MATHEMATICS AND COMPUTING↗

Digital-analog quantum computation

Digital quantum computing paradigm offers highly desirable features such as universality, scalability, and quantum error correction. However, physical resource requirements to implement useful error-corrected quantum algorithms are prohibitive in the current era of NISQ devices. As an alternative path to performing universal quantum computation, within the NISQ era limitations, we propose to merge digital single-qubit operations with analog multiqubit entangling blocks in an approach we call digital-analog quantum computing (DAQC). Along these lines, although the techniques may be extended to any resource, we propose to use unitaries generated by the ubiquitous Ising Hamiltonian for the analog entangling block and we prove its universal character. Here, we construct explicit DAQC protocols for efficient simulations of arbitrary inhomogeneous Ising, two-body, and M-body spin Hamiltonian dynamics by means of single-qubit gates and a fixed homogeneous Ising Hamiltonian. Additionally, we compare a sequential approach where the interactions are switched on and off (stepwise DAQC) with an always-on multiqubit interaction interspersed by fast single-qubit pulses (banged DAQC). Finally, we perform numerical tests comparing purely digital schemes with DAQC protocols, showing a remarkably better performance of the latter. The proposed DAQC approach combines the robustness of analog quantum computing with the flexibility of digital methods.

97 MATHEMATICS AND COMPUTING↗