Speaker
Description
Photonic quantum systems are a promising platform for near-term quantum technologies, combining low noise, high-fidelity linear-optical operations, and scalability to large numbers of optical modes. In this work, we develop the first general framework for computing second moments of particle-number-preserving bosonic observables under Haar-random passive linear-optical transformations. Exploiting representation-theoretic tools for the unitary group, we derive closed-form expressions valid for arbitrary number of photons and modes. We identify a class of observables, which we call generalised parity operators, that can evade concentration while seemingly remaining beyond the reach of currently known simulation techniques, suggesting a regime in which trainability and classical hardness may coexist. Moreover, we further establish anti-concentration of Boson Sampling output probabilities in the experimentally relevant regime, resolving an open conjecture and taking a step closer to a rigorous proof of the hardness of boson sampling.
| Topic | Theoretical foundations of quantum learning |
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