Realistic quantum information processing devices are inherently imperfect, leading to computational errors that require quantum error correction. Likewise, random bits generated by such devices are flawed and must be enhanced to be usable for applications such as generating cryptographic keys. This enhancement of randomness quality is achieved through a protocol known as randomness amplification1. Here we report on an experiment that implements such a protocol. Randomness amplification is device-independent, making no assumptions about the internal workings of the quantum devices. It requires executing a loophole-free Bell test2–4 within a specific parameter regime that involves both a high Bell violation and a high repetition rate. The experimental demonstration is made possible by a combination of theoretical advances, which allow for protocols with an experimentally realistic parameter regime, and experimental progress that achieves this regime with superconducting circuits. Crucially, randomness amplification has been proven to be impossible by purely classical means5. This experiment therefore demonstrates a definitive quantum advantage—leveraging quantum technology to accomplish a task unattainable by classical information processing.