Non-Hermitian topological ohmmeter

Measuring large electrical resistances forms an essential part of common applications such as insulation testing, but suffers from a fundamental problem: the larger the resistance, the less sensitive a canonical ohmmeter is. Here we develop a conceptually different electronic sensor by exploiting the topological properties of non-Hermitian matrices, whose eigenvalues can show an exponential sensitivity to perturbations. The ohmmeter is realized in an multi-terminal, linear electric circuit with a non-Hermitian conductance matrix, where the target resistance plays the role of the perturbation. We inject multiple currents and measure a single voltage in order to directly obtain the value of the resistance. The relative accuracy of the device increases exponentially with the number of terminals, and for large resistances outperforms a standard measurement by over an order of magnitude. Our work paves the way towards leveraging non-Hermitian conductance matrices in high-precision sensing.