  On-chip microring resonators (MRRs) have been proposed to construct the
time-delayed reservoir computing (RC), which offers promising configurations
available for computation with high scalability, high-density computing, and
easy fabrication. A single MRR, however, is inadequate to supply enough memory
for the computational task with diverse memory requirements. Large memory needs
are met by the MRR with optical feedback waveguide, but at the expense of its
large footprint. In the structure, the ultra-long optical feedback waveguide
substantially limits the scalable photonic RC integrated designs. In this
paper, a time-delayed RC is proposed by utilizing a silicon-based nonlinear MRR
in conjunction with an array of linear MRRs. These linear MRRs possess a high
quality factor, providing sufficient memory capacity for the entire system. We
quantitatively analyze and assess the proposed RC structure's performance on
three classical tasks with diverse memory requirements, i.e., the Narma 10,
Mackey-Glass, and Santa Fe chaotic timeseries prediction tasks. The proposed
system exhibits comparable performance to the MRR with an ultra-long optical
feedback waveguide-based system when it comes to handling the Narma 10 task,
which requires a significant memory capacity. Nevertheless, the overall length
of these linear MRRs is significantly smaller, by three orders of magnitude,
compared to the ultra-long feedback waveguide in the MRR with optical feedback
waveguide-based system. The compactness of this structure has significant
implications for the scalability and seamless integration of photonic RC.
