photonic-variational-trainability

name

photonic-variational-trainability

description

Pre-asymptotic trainability analysis for photonic variational quantum circuits under postselection. Covers barren plateau dynamics in passive linear-optical circuits, Lie algebra dimension scaling, postselection-induced gradient concentration (allow-bunching, collision-free, dual-rail), and design guidance for near-term photonic variational architectures. Use when: analyzing photonic QNN trainability, designing variational photonic circuits, understanding gradient concentration under postselection, or comparing postselection regimes for optical quantum computing. Trigger keywords: photonic barren plateau, variational photonic circuits, postselection gradient concentration, linear optical quantum computing, dual-rail postselection, collision-free filtering, photonic QNN trainability.

Photonic Variational Trainability

From arXiv:2605.11879 "Pre-Asymptotic Trainability in Photonic Variational Circuits under Postselection" (Xie, Notton, Senellart, 2026).

Core Problem

Barren plateaus in variational quantum circuits cause gradient variance to vanish exponentially with system size. Passive photonic circuits challenge this picture: although their Hilbert space is exponentially large, dynamics are constrained to a Lie algebra of dimension O(m²) where m = number of modes.

Key Finding: Postselection Determines Trainability

Gradient concentration is governed not by Hilbert-space dimension but by how postselection reshapes the effective observable.

Three Postselection Regimes

Regime	Gradient Scaling	Trainability
Allow-bunching	Polynomial decay	✅ Trainable
Collision-free filtering	Polynomial decay	✅ Trainable
Dual-rail postselection	Exponential concentration	❌ Barren plateau