Universal Logical Quantum Photonic Neural Network Processor via Cavity-Assisted Interactions

Encoding quantum information within bosonic modes offers a promising direction for hardware-efficient and fault-tolerant quantum information processing. However, achieving high-fidelity universal control over the bosonic degree of freedom using native photonic hardware remains a challenge. Here, we propose an architecture to prepare and perform logical quantum operations on arbitrary multimode multi-photon states using a quantum photonic neural network. Central to our approach is the optical nonlinearity, which is realized through strong light-matter interaction with a three-level Lambda atomic system. The dynamics of this interaction are confined to the single-mode subspace, enabling the construction of high-fidelity quantum gates. This nonlinearity functions as a photon-number selective phase gate, which facilitates the construction of a universal gate set and serves as the element-wise activation function in our neural network architecture. Through numerical simulations, we demonstrate the versatility of our approach by executing tasks that are key to logical quantum information processing. The network is able to deterministically prepare a wide array of multimode multi-photon states, including essential resource states. We also show that the architecture is capable of encoding and performing logical operations on bosonic error-correcting codes. Additionally, by adapting components of our architecture, error-correcting circuits can be built to protect bosonic codes. The proposed architecture paves the way for near-term quantum photonic processors that enable error-corrected quantum computation, and can be achieved using present-day integrated photonic hardware.