Connection between memory performance and optical absorption in quantum reservoir computing

TL;DR

This work investigates how dissipation in quantum reservoir computers (QRCs) affects time-series memory, by linking memory capacity to optical absorption via a coherently driven fully-connected TFIM. The dynamics are modeled with a GKSL master equation and tunable decay $\gamma$, and memory is quantified by linear short-term memory capacity (STMC) using Legendre targets $P_i$, while absorption is computed from linear response as $\alpha_{s,\gamma}(\omega)$. A key finding is that both the mean absorption $\bar{\alpha}_\gamma$ and the linear STMC peak at an intermediate dissipation $\gamma$, forming a sweet spot that optimizes memory via input susceptibility. This physically grounded link provides a tunable route to optimize QRC across platforms such as photonics and Rydberg arrays and motivates physics-based benchmarks alongside information-theoretic metrics.

Abstract

The fading memory property is a key requirement for reservoir computers -- a specific type of recurrent neural network with fixed internal weights. While mostly undesired in gate-based quantum computing, dissipation due to material imperfections or coupling to the environment acts as a natural mechanism intrinsically providing fading memory to reservoir computers based on dynamical open quantum systems. In this work, we unravel a connection between the physical metric of optical absorption and the performance of quantum reservoir computers in terms of their short-term memory capacity. We establish this link by considering a coherent input encoding in conjunction with tunable qubit decay, giving precise control over the fading memory in the quantum reservoir computer. Our analysis enables us to identify a sweet-spot regime for the dissipation strength at which memory performance is maximized.

Figures (8)

• Figure 1: Illustration of the QRC paradigm using a three-qubit reservoir with the coupling matrix elements $J_{ij}$, individual qubit decay $\gamma$, and a coherent input-injection pump encoding the signal strength $s_k$. Throughout this work, qubit decay and the pump strength are equal for all qubits. For the 3-qubit case depicted here, we obtain a three-dimensional output function $x(t)$.
• Figure 2: Time evolution of the $\sigma_{\text{z}}$ expectation value of the first qubit in a three-qubit TFIM for different qubit decay strengths $\gamma$. In light red (right axis) the input signal is displayed.
• Figure 3: First three degrees of the stmc of 15 randomly sampled 3-qubit systems for different qubit decays.
• Figure 4: Resonant absorption $\alpha_{s, \gamma}(0)$ of the same 15 randomly sampled 3-qubit system as in Fig. \ref{['fig:stmc']} for different signal strengths $s$ and qubit decays $\gamma$. The thick blue line marks the average over all light curves.
• Figure 5: Absorption spectra for qubit decays $\gamma \in \{10^{-2}, 10^0, 10^2\}$ and an input signal strength of $s=1$. The zero-frequency components correspond to points on the absorption curve for $s=1$ in Fig. \ref{['fig:absorption']}