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

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.