Automated discovery of high-probability heralded schemes for path-entangled states

Generating large multiphoton entangled states is a fundamental challenge in quantum optics due to the lack of strong, deterministic photon-photon interactions. While linear optics can be used to create these states, existing schemes are often inefficient. This paper investigates whether AI-driven automated discovery can identify new, more efficient linear-optical circuits for generating path-entangled states (such as NOON states) and whether these solutions can be generalized into a scalable, transferable physical framework.

The researchers employed a fast JAX-based simulator to model universal multiport interferometers, using stochastic gradient descent to optimize circuit parameters. By searching over various input product states and target output states, the team identified a new "modular comb" family of circuits. They analyzed the scaling laws of this family, compared its performance against established benchmarks (such as the Pryde-White and Zou-Pahlke-Mathis schemes), and extended the framework to multi-mode NOON states.

The study demonstrates that the discovered modular comb family provides exponential and super-exponential improvements in success probability compared to previous state-of-the-art constructions. For example, a newly discovered NOON9 circuit achieves a 1440% increase in success probability over the best known previous scheme. Beyond the general family, the AI also identified specific, highly efficient circuits for smaller target states that do not fit the general modular pattern. The authors further show that these circuits are robust to detector inefficiencies, partly because they avoid the reliance on "vacuum heralding" (detecting the absence of photons), which is experimentally unreliable.

This work provides a concrete roadmap for generating large-scale photonic entanglement, which is critical for quantum communication, sensing, and metrology. By moving beyond manual design, the authors show that AI can act as an agent of scientific discovery, revealing new physical mechanisms and transferable design principles that outperform human-derived intuition. The proposed circuits are compact and experimentally feasible with current technology, offering a viable path toward a substantial leap in accessible multiphoton entanglement.