  Reservoir computing (RC) is a machine learning paradigm that excels at
dynamical systems analysis. Photonic RCs, which perform implicit computation
through optical interactions, have attracted increasing attention due to their
potential for low latency predictions. However, most existing photonic RCs rely
on a nonlinear physical cavity to implement system memory, limiting control
over the memory structure and requiring long warm-up times to eliminate
transients. In this work, we resolve these issues by demonstrating a photonic
next-generation reservoir computer (NG-RC) using a fiber optic platform. Our
photonic NG-RC eliminates the need for a cavity by generating feature vectors
directly from nonlinear combinations of the input data with varying delays. Our
approach uses Rayleigh backscattering to produce output feature vectors by an
unconventional nonlinearity resulting from coherent, interferometric mixing
followed by a quadratic readout. Performing linear optimization on these
feature vectors, our photonic NG-RC demonstrates state-of-the-art performance
for the observer (cross-prediction) task applied to the R\"ossler, Lorenz, and
Kuramoto-Sivashinsky systems. In contrast to digital NG-RC implementations,
this scheme is easily scalable to high-dimensional systems while maintaining
low latency and low power consumption.
