Optically Writable Atomic Vapor Memory as a Substrate for Optical Reservoir Computing

Universal approximation in reservoir computing is typically associated with a class of reservoirs. We show that universality can be associated with a single reservoir, considering a minimal setup of a single atom in front of a mirror. In its linear-transducer limit, our reservoir is a universal approximator of fading-memory maps under an operating class of checkable conditions, with a rate constant measured at the operating point. A given reservoir can reach arbitrary accuracy by changing measurement settings. The proof gives an explicit recipe: for a target accuracy, it specifies the required physical resources and resonator modes. Enlarging the number of accessible modes increases the matchable kernel span without reducing capability. Beyond the linear limit, the atom's saturation replaces high-order polynomial readouts, and the device operates on real-world tasks alongside classical baselines. Our results highlight an example of universality with a minimal quantum setup.

Photonic reservoir computing is a promising physical machine-learning approach for time-series prediction. Quantization of the reservoir response signal is an important consideration in the implementation of photonic reservoir computing, and the number of quantization bits and sampling frequency need to be optimized to achieve high prediction performance and low energy consumption. However, few studies have investigated the effects of the number of quantization bits and sampling frequency on both prediction performance and energy consumption. In this study, we introduce the concept of approximate reservoir computing with a semiconductor laser by quantizing the reservoir node states and output weights. We numerically evaluate the performance of a chaotic time-series prediction task and estimate the energy consumption per sample using a component-level model. By optimizing the number of quantization bits, the sampling frequency, and the injection current of the semiconductor laser, we achieve a significant reduction in the estimated energy consumption per sample while maintaining prediction performance. We also obtain model-based estimates of the throughput, energy efficiency, and energy per operation of the proposed reservoir-computing system.

Reservoir Computing (RC) designs Recurrent Neural Networks around a fixed, i.e., untrained, recurrent layer, and is a natural candidate for neuromorphic hardware. Memristive-friendly reservoirs derive the neuron dynamics from memristive-device kinetics, but still rely on dense recurrent matrices, which are expensive to realize physically. In this paper, we replace the dense matrix with a structured orthogonal operator, built from sign diagonals, a permutation, and a fast Walsh-Hadamard transform. The operator is multiplier-free, requires $O(N)$ parameters and $O(N\log N)$ operations per step, and is never materialized as a matrix. We instantiate it in a standard and in a memristive-friendly Echo State Network, with one binary input connection per unit. Our mathematical analysis shows that exact orthogonality yields an echo state condition that is tight in the recurrent scaling, and a noise response that is predictable at design time. Moreover, the operator mixes the whole state in a single application. Experiments on twenty classification and seven regression benchmarks, at reservoir sizes up to $N = 8192$, show that the structured models match dense orthogonal reservoirs, and achieve better mean performance than the cycle reservoir by a margin that widens with size. Furthermore, we time the recurrent step on three hardware platforms, where it is up to $50\times$ faster than a dense product and $10^4\times$ smaller in memory. Finally, we ablate the operator and measure the response to noise, quantization, device mismatch and discrete faults.