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arXiv:2602.17440

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

Çağın Ekici

quant-phSubmitted Feb 19, 2026• Announced Feb 20, 2026• 0 citations
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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.

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We investigate quantum reservoir computing (QRC) using a hybrid qubit-boson system described by the Jaynes-Cummings (JC) Hamiltonian and its dispersive limit (DJC). These models provide high-dimensional Hilbert spaces and intrinsic nonlinear dynamics, making them powerful substrates for temporal information processing. We systematically benchmark both reservoirs through linear and nonlinear memory tasks, demonstrating that they exhibit an unusual superior nonlinear over linear memory capacity. We further test their predictive performance on the Mackey-Glass time series, a widely used benchmark for chaotic dynamics, and show comparable forecasting ability. We also investigate how memory and prediction accuracy vary with reservoir parameters and show the role of higher-order bosonic observables and time multiplexing in enhancing expressivity, even in minimal spin-boson configurations. Our results establish JC- and DJC-based reservoirs as versatile platforms for time-series processing and as elementary units that overcome the setting of equivalent qubit pairs and offer pathways toward tunable, high-performance quantum machine learning architectures.
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Quantum reservoir computing (QRC) is a highly promising computational paradigm that leverages quantum systems as a computational resource for nonlinear information processing. While its application to time-series analysis is eagerly anticipated, prevailing approaches suffer from the collapse of the quantum state upon measurement, resulting in the erasure of temporal input memories. Neither repeated initializations nor weak measurements offer a fundamental solution, as the former escalates the time complexity while the latter restricts the information extraction from the Hilbert space. To address this issue, we propose the feedback-driven QRC framework. This methodology employs projective measurements on all qubits for unrestricted access to the quantum state, with the measurement outcomes subsequently fed back into the reservoir to restore the memory of prior inputs. We demonstrate that our QRC successfully acquires the fading-memory property through the feedback connections, a critical aspect in time-series processing. Notably, analysis of measurement trajectories reveals three distinct phases depending on the feedback strength, with the memory performance maximized at the edge of chaos. We also evaluate the predictive capabilities of our QRC, demonstrating its suitability for forecasting signals originating from quantum spin systems. Published by the American Physical Society 2024
Quantum reservoir computing (QRC) leverages the nonlinearity and correlations of quantum systems to enhance machine learning tasks. We explore continuous-variable (CV) photonic platforms for QRC using frequency- and pulse-multiplexed squeezed states generated via nonlinear waveguides, enabling scalable, room-temperature architectures without single-photon sources or detectors. We introduce a novel, measurement-based QRC protocol that uses a neural network of cluster states and local operations, in which input data are encoded through measurement via quantum teleportation. In this design, measurements enable input injection, information processing, and continuous monitoring for time-series tasks. The architecture’s power and versatility are demonstrated through benchmark tasks, showing that the protocol exhibits internal memory and is suitable for both static and temporal information processing without hardware modifications. Additionally, we report a proof-of-principle experimental realization of QRC based on pump-phase encoding and electronic feedback, demonstrating temporal data processing capabilities.
Quantum Reservoir Computing (QRC) leverages quantum systems to perform complex computational tasks with exceptional efficiency and reduced energy consumption. We introduce a minimalistic QRC framework utilizing as few as five atoms in a single-mode optical cavity, combined with continuous quantum measurement. The system is conveniently scalable, as newly added atoms naturally couple with existing ones via the shared cavity field. To achieve high computational expressivity with a minimal reservoir, we include two critical elements: reservoir feedback and polynomial regression. Reservoir feedback modifies the reservoir’s dynamics without altering its internal quantum hardware, while polynomial regression nonlinearly enhances output resolution. We demonstrate significant QRC performance in memory retention and nonlinear data processing through two tasks: predicting chaotic time-series data via the Mackey-Glass task and classifying sine-square waveforms. This framework fulfills QRC’s objectives to minimize hardware size and energy consumption, marking a significant advancement in integrating quantum physics with machine learning technology.
Quantum reservoir computing (QRC) exploits the information-processing capabilities of quantum systems to tackle time-series forecasting tasks, which is expected to be superior to their classical counterparts. By far, many QRC schemes have been theoretically proposed. However, most of these schemes involve long-time evolution of quantum systems or networks with quantum gates. This poses a challenge for practical implementation of these schemes, as precise manipulation of quantum systems is crucial, and this level of control is currently hard to achieve with the existing state of quantum technology. Here we propose a different QRC scheme, which is friendly to experimental realization. It implements the quantum version of nonlinear vector autoregression, extracting linear and nonlinear features of quantum data by measurements. Thus, the evolution of complex networks of quantum gates can be avoided. Compared to other QRC schemes, our proposal also achieves an advance by effectively reducing the necessary training data for reliable predictions in time-series forecasting tasks. Furthermore, we experimentally verify our proposal by performing the forecasting tasks, and the observation matches well with the theoretical ones. Our work opens up a different way for complex tasks to be solved by using QRC, which can herald the next generation of QRC.