I found a layman's explanation at Quanta Magazine: https://www.quantamagazine.org/new-quantum-algorithms-finally-crack-nonlinear-equations-20210105/ https://www

I found a layman's explanation at Quanta Magazine: https://www.quantamagazine.org/new-quantum-algorithms-finally-crack-nonlinear-equations-20210105/ https://www.quantamagazine.org/new-quantum-algorithms-finall... The two caveats are 1. Only works for "mildly" nonlinear equations 2. Results are in quantum world and have to be translated back into normal deterministic world results, and this hasn't been figured out yet