Solving matrix equations in one step with cross-point resistive arrays

TLDR

Conventional digital computers perform advanced operations through sequences of Boolean functions, making tasks like solving linear systems or differential equations computationally intensive and memory‑heavy. The authors aim to accelerate such tasks by using in‑memory computing with resistive memories, enabling a cross‑point array to directly solve linear equations or compute matrix eigenvectors. The cross‑point array performs the computation in a single step by exploiting Ohm’s and Kirchhoff’s laws together with a negative‑feedback connection, leveraging analog data storage. Hardware demonstrations confirm that the array can solve algebraic problems in one step, including ranking webpages and solving the Schrödinger equation.

Abstract

Conventional digital computers can execute advanced operations by a sequence of elementary Boolean functions of 2 or more bits. As a result, complicated tasks such as solving a linear system or solving a differential equation require a large number of computing steps and an extensive use of memory units to store individual bits. To accelerate the execution of such advanced tasks, in-memory computing with resistive memories provides a promising avenue, thanks to analog data storage and physical computation in the memory. Here, we show that a cross-point array of resistive memory devices can directly solve a system of linear equations, or find the matrix eigenvectors. These operations are completed in just one single step, thanks to the physical computing with Ohm's and Kirchhoff's laws, and thanks to the negative feedback connection in the cross-point circuit. Algebraic problems are demonstrated in hardware and applied to classical computing tasks, such as ranking webpages and solving the Schrödinger equation in one step.