Riemannian optimization for linear optical problems

arXiv:2609.07890 · quant-ph, math-ph, math.MP · Submitted 2026-09-07 · Read on arXiv

quant-ph, math-ph, math.MP

Submitted: 2026-09-07

Updated: 2026-09-17

Code: https://github.com/pablovegan/riemannian-optimization-linear-optics

Terminology

• Riemannian optimization — 34× in this paper · explained in 2 episodes
• Fidelity — 14× in this paper · explained in 2 episodes
• Benchmark — 11× in this paper · explained in 2 episodes
• Adam — 10× in this paper · explained in 2 episodes
• Algebraic Invariants — 8× in this paper · explained in 1 episode
• Entanglement — 8× in this paper · explained in 4 episodes
• Quantum Circuits — 4× in this paper · explained in 2 episodes
• No-Go Theorem — 3× in this paper · explained in 2 episodes
• Benchmarking — 2× in this paper · explained in 3 episodes
• Effective Hamiltonian — 2× in this paper · explained in 2 episodes
• Gradient Flow — 2× in this paper · explained in 2 episodes
• Quantum Physics — 2× in this paper · explained in 11 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Objective Function — 1× in this paper · explained in 2 episodes
• Post-Selection — 1× in this paper · explained in 2 episodes

Sources

• Universal Linear Optics
• Simple rules for two-photon state preparation with linear optics
• Certification of genuine non-Gaussian entanglement
• Exact gradients for linear optics with single photons
• Fock Space Perspective on Optimal Heralding Schemes
• Permanents in linear optical networks
• Creation of Entangled Photonic States Using Linear Optics
• Local controllability of heralded quantum linear optics
• Riemannian Adaptive Optimization Methods
• Momentum-based gradient descent methods for Lie groups
• Orbit dimensions in linear and Gaussian quantum optics
• Invariants in Linear Optics
• Unveiling Hierarchical Invariants in Multiphoton Linear Optics

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