  Noise is expected to play an important role in the dynamics of analog systems
such as coupled oscillators which have recently been explored as a hardware
platform for application in computing. In this work, we experimentally
investigate the effect of noise on the synchronization of relaxation
oscillators and their computational properties. Specifically, in contrast to
its typically expected adverse effect, we first demonstrate that a common white
noise input induces global frequency synchronization among uncoupled
oscillators. Experiments show that the minimum noise voltage required to induce
synchronization increases linearly with the amplitude of the oscillator output
whereas it decreases with increasing number of oscillators. Further, our work
reveals that in a coupled system of oscillators - relevant to solving
computational problems such as graph coloring, the injection of white noise
helps reduce the minimum required capacitive coupling strength. With the
injection of noise, the coupled system demonstrates frequency synchronization
along with the desired phase-based computational properties at 5x lower
coupling strength than that required when no external noise is introduced.
Consequently, this can reduce the footprint of the coupling element and the
corresponding area-intensive coupling architecture. Our work shows that noise
can be utilized as an effective knob to optimize the implementation of coupled
oscillator-based computing platforms.
