Depth dependence of entanglement and circuit complexity in random linear optical networks

arXiv:2604.14277 · quant-ph, math-ph, math.MP, math.PR · Submitted 2026-04-15 · Read on arXiv

quant-ph, math-ph, math.MP, math.PR

Submitted: 2026-04-15

Updated: 2026-10-20

Comments: 54 pages, 14 figures; v2 added Appendices C-E

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Entanglement — 5× in this paper · explained in 4 episodes
• Circuit Depth — 2× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Wasserstein Distance — 1× in this paper · explained in 5 episodes

Sources

• Bosonic coding: introduction and use cases
• Incompressibility and spectral gaps of random circuits
• Parallel Kac's Walk Generates PRU
• Robust quantum computational advantage with programmable 3050-photon Gaussian boson sampling
• Black Holes and Complexity Classes
• Energy-constrained diamond norm with applications to the uniform continuity of continuous variable channel capacities

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