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This research investigates how postselection mechanisms in passive photonic circuits influence trainability and mitigate barren plateaus compared to standard mixing dynamics. The study provides closed-form scaling predictions for gradient variance, demonstrating that specific filtering methods like allow-bunching maintain polynomial consistency while others induce exponential degradation. These findings offer critical theoretical guidance for optimizing variational quantum algorithms using linear optics architectures.
Pre-Asymptotic Trainability in Photonic Variational Circuits under Postselection
arXiv:2605.11879v2 Announce Type: replace Abstract: Barren plateaus (BP) in variational quantum circuits are commonly attributed to strong mixing dynamics that cause gradient variance to vanish exponentially with system size. Passive photonic circuits challenge this picture. Because observables and postselection maps generically extend beyond the algebra's reachable image, we show that trainability is governed by how postselection redistributes weight across the full irreducible decomposition of the operator space. Building on recent representation-theoretic second-moment techniques for passive linear optics, we express postselection through the pulled-back observable and obtain a closed-form Haar-averaged gradient variance, exact for fixed observables. The resulting scaling predictions are tested by statevector simulation of the nonlinear Bhattacharyya loss across allow-bunching, collision-free, and dual-rail postselection, using a four-test protocol (AICc, sliding-window, crossover, and truncation analyses) to separate polynomial from exponential scaling in finite data. Allow-bunching and collision-free filtering remain polynomial-consistent across all tested sizes and initializations, while dual-rail postselection induces a genuine BP at a rate roughly an order of magnitude below the 2-design value.
Abstract:Barren plateaus (BP) in variational quantum circuits are commonly attributed to strong mixing dynamics that cause gradient variance to vanish exponentially with system size. Passive photonic circuits challenge this picture. Because observables and postselection maps generically extend beyond the algebra's reachable image, we show that trainability is governed by how postselection redistributes weight across the full irreducible decomposition of the operator space. Building on recent representation-theoretic second-moment techniques for passive linear optics, we express postselection through the pulled-back observable and obtain a closed-form Haar-averaged gradient variance, exact for fixed observables. The resulting scaling predictions are tested by statevector simulation of the nonlinear Bhattacharyya loss across allow-bunching, collision-free, and dual-rail postselection, using a four-test protocol (AICc, sliding-window, crossover, and truncation analyses) to separate polynomial from exponential scaling in finite data. Allow-bunching and collision-free filtering remain polynomial-consistent across all tested sizes and initializations, while dual-rail postselection induces a genuine BP at a rate roughly an order of magnitude below the 2-design value.
8 pages, 2 figures. Accepted for publication in the proceedings of the 2026 IEEE International Conference on Quantum Computing and Engineering (QCE26)
arXiv:2605.11879 [quant-ph]
(or arXiv:2605.11879v2 [quant-ph] for this version)
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