Solving a system of linear equations means finding the unknown vector x which satisfies the equation Ax = b, where A is a matrix of coefficients and b is a known vector. To solve this problem, a conventional digital computer executes an algorithm which takes several operations, thus translating into considerable time and energy consumption.
The new circuit, which has been developed in the frame of the ERC European project RESCUE - Resistive switch computing beyond CMOS, solves systems of linear equations (Ax=b) thanks to an innovative method of in-memory computing, where the coefficients of matrix A are stored in a special device called memristor. The memristor is able to store analogue values, thus a memristor matrix can physically map a coefficient matrix A within the circuit, thus strongly accelerating the computation.
The memristor array has been developed at the Clean Room of the Center for micro and nano fabrication Polifab of Politecnico di Milano. The memristor circuit has been tested and validated on a wide set of algebraic problems, such as the ranking of internet websites and the solution of complicated differential equations, such as the Schrödinger equation for the computation of the quantum wavefunction for an electron. All these problems are solved in a single operation.
These results have been published on the prestigious journalPNASof the National Academy of Science of the USA.