  Accelerating computational tasks with quantum resources is a widely-pursued
goal that is presently limited by the challenges associated with high-fidelity
control of many-body quantum systems. The paradigm of reservoir computing
presents an attractive alternative, especially in the noisy intermediate-scale
quantum era, since control over the internal system state and knowledge of its
dynamics are not required. Instead, complex, unsupervised internal trajectories
through a large state space are leveraged as a computational resource. Quantum
systems offer a unique venue for reservoir computing, given the presence of
interactions unavailable in analogous classical systems, and the potential for
a computational space that grows exponentially with physical system size. Here,
we consider a reservoir comprised of a single qudit ($d$-dimensional quantum
system). We demonstrate a robust performance advantage compared to an analogous
classical system accompanied by a clear improvement with Hilbert space
dimension for two benchmark tasks: signal processing and short-term memory
capacity. Qudit reservoirs are directly realized by current-era quantum
hardware, offering immediate practical implementation, and a promising outlook
for increased performance in larger systems.
