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arXiv:2507.07684

Phase-Space Framework for Noisy Intermediate-Scale Quantum Optical Neural Networks

Stanisław Świerczewski, Wouter Verstraelen, Piotr Deuar, Barbara Piętka, T. C. H. Liew, Michał Matuszewski, Andrzej Opala

Published Jul 10, 2025• 0 citations
arXivHTMLPDF

Abstract

Quantum optical neural networks (QONNs) enable information processing beyond classical limits by exploiting the advantages of classical and quantum optics. However, simulation of large-scale bosonic lattices remains a significant challenge due to the exponential growth of the Hilbert space required to describe a quantum network accurately. Consequently, previous theoretical studies have been limited to small-scale systems, leaving the behaviour of multimode QONNs largely unexplored. This work presents an efficient computational framework based on the phase-space positive-P method for simulating bosonic neuromorphic systems. This approach provides a view to previously inaccessible regimes, allowing the validation of large-scale bosonic networks in various quantum machine learning tasks such as quantum state classification and quantum state feature prediction. Our results show that the performance of a large quantum reservoir does not improve monotonously with the number of bosonic modes, instead following a complex dependence driven by the interplay of nonlinearity, reservoir size, and the average occupation of the input mode. These findings are essential for designing and optimising optical bosonic reservoirs for future quantum neuromorphic computing devices.

DOI
10.48550/arxiv.2507.07684

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Abstract Physically motivated quantum algorithms for specific near-term quantum hardware will likely be the next frontier in quantum information science. Here, we show how many of the features of neural networks for machine learning can naturally be mapped into the quantum optical domain by introducing the quantum optical neural network (QONN). Through numerical simulation and analysis we train the QONN to perform a range of quantum information processing tasks, including newly developed protocols for quantum optical state compression, reinforcement learning, black-box quantum simulation, and one-way quantum repeaters. We consistently demonstrate that our system can generalize from only a small set of training data onto inputs for which it has not been trained. Our results indicate that QONNs are a powerful design tool for quantum optical systems and, leveraging advances in integrated quantum photonics, a promising architecture for next-generation quantum processors.
The simulation of quantum many-body systems poses a significant challenge in physics due to the exponential scaling of Hilbert space with the number of particles. Traditional methods often struggle with large system sizes and frustrated lattices. In this research article, we present a novel algorithm that leverages the power of deep neural networks combined with Markov Chain Monte Carlo simulation to address these limitations. Our method introduces a neural network architecture specifically designed to represent bosonic quantum states on a 1D lattice chain. We successfully achieve the ground state of the Bose-Hubbard model, demonstrating the superiority of the adaptive momentum optimizer for convergence speed and stability. Notably, our approach offers flexibility in simulating various lattice geometries and potentially larger system sizes, making it a valuable tool for exploring complex quantum phenomena. This work represents a substantial advancement in the field of quantum simulation, opening new possibilities for investigating previously challenging systems.
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Advances in quantum technologies are accelerating the demand for optical quantum state sensors that combine high precision, versatility, and scalability within a unified hardware platform. Quantum reservoir computing offers a powerful route toward this goal by exploiting the nonlinear dynamics of quantum systems to process and interpret quantum information efficiently. Photonic neural networks are particularly well suited for such implementations, owing to their intrinsic sensitivity to photon-encoded quantum information. However, the practical realisation of photonic quantum reservoirs remains constrained by the inherently weak optical nonlinearities of available materials and the technological challenges of fabricating densely coupled quantum networks. To address these limitations, we introduce a hybrid quantum-classical detection protocol that integrates the advantages of quantum reservoirs with the adaptive learning capabilities of analogue neural networks. This synergistic architecture substantially enhances information-extraction accuracy and robustness, enabling low-cost performance improvements of quantum light sensors. Based on the proposed approach, we achieved significant improvements in quantum state classification, tomography, and feature regression, even for reservoirs with a relatively small nonlinearity-to-losses ratio U/γ≈0.02U/γ\approx 0.02U/γ≈0.02 in a network of only five nodes. By reducing reliance on material nonlinearity and reservoir size, the proposed approach facilitates the practical deployment of high-fidelity photonic quantum sensors on existing integrated platforms, paving the way toward chip-scale quantum processors and photonic sensing technologies.