A Programmable Linear Optical Quantum Reservoir with Measurement Feedback for Time Series Analysis

TL;DR

The paper presents a programmable linear optical quantum reservoir computing (QRC) platform for time-series analysis, implemented as an $M$-mode interferometer mesh driven by a scalar input with a measurement-conditioned feedback loop. It uses threshold detectors to produce coarse-grained coincidence features and updates only a budgeted subset of MZI phases in a Galton wedge, enabling recurrence without training internal weights. By sweeping the feedback gain $\alpha_{\mathrm{fb}}$, the study identifies three dynamical regimes and shows that memory capacity peaks near the stability boundary, in line with edge-of-chaos ideas, while nonlinear forecasting is validated on Mackey–Glass, NARMA-$n$, and non-integrable 1-D Ising dynamics. The approach is compatible with current photonic technology and demonstrates competitive predictive performance under finite measurement budgets, highlighting a scalable path to photonic QRC for temporal learning.

Abstract

Feedback-driven quantum reservoir computing has so far been studied primarily in gate-based architectures, motivating alternative scalable, hardware-friendly physical platforms. Here we investigate a linear-optical quantum reservoir architecture for time-series processing based on multiphoton interference in a reconfigurable interferometer network equipped with threshold detectors and measurement-conditioned feedback. The reservoir state is constructed from coarse-grained coincidence features, and the feedback updates only a structured, budgeted subset of programmable phases, enabling recurrence without training internal weights. By sweeping the feedback strength, we identify three dynamical regimes and find that memory performance peaks near the stability boundary. We quantify temporal processing via linear memory capacity and validate nonlinear forecasting on benchmarks, namely Mackey-Glass series, NARMA$-n$ and non-integrable Ising dynamics. The proposed architecture is compatible with current photonic technology and lowers the experimental barrier to feedback-driven QRC for time-series analysis with competitive accuracy.

Figures (6)

• Figure 1: Feedback-driven linear optical reservoir for temporal processing. Schematic at cycle $k$: the input sample $x_k$ is encoded in a small input block of MZIs (green), cross-mode coincidence statistics from the most recent coincidence measurement in lexicographic order ($C_{12,k-1}, C_{13,k-1}, \dots, C_{(M-1) M ,k-1}$) program the Galton wedge of MZIs (orange) through the feedback. The downstream static layers (black) provide fixed output mixing and can be considered as the reservoir part of the architecture. MZIs in the upper-left and lower-left corners that remain unilluminated for this input configuration are shown in gray. Crossings denote MZIs with yellow triangles representing phase shifters.
• Figure 2: Linear memory performance of the feedback-driven reconfigurable linear optics as a function of delay for different feedback strengths for a fixed device size $(M,N)=(16,4)$ and fixed input strength $\alpha_{\mathrm{in}}$. a$\alpha_{\mathrm{fb}} = 1.5$ (blue), $\alpha_{\mathrm{fb}}=1.8$ (orange), $\alpha_{\mathrm{fb}} = 2.25$ (green) and $\alpha_{\mathrm{fb}}=2.75$ (red) b Total linear capacity, MC$^{^{\text{tot}}}_1$, as a function of feedback strength $\alpha_{\mathrm{fb}}$.
• Figure 3: Mackey--Glass prediction performance. Mean normalized mean-square error (NMSE, log scale) as a function of the prediction horizon $\tau_f$. Each curve corresponds to a different feedback gain $\alpha_{\mathrm{fb}}$ and reports the mean over 30 different realizations.
• Figure 4: NMSE for NARMA-7 (circles) and NARMA-10 (squares) as a function of feedback strength $\alpha_{\mathrm{fb}}$. The input strength is fixed to $\alpha_{\mathrm{in}} = 0.001$.
• Figure 5: Non-integrable quantum Ising forecasting. Mean NMSE (log scale) versus prediction horizon $\tau_f$ for the central-spin signal $\langle \sigma_3^{z}(t)\rangle$ (mapped to $x_k\in[0,1]$). Each curve corresponds to a feedback gain $\alpha_{\mathrm{fb}}$ and shows the mean over 30 realizations.