Efficient Optimization of Tensor Rings with Low-Rank Environments

arXiv:2610.10027 · cond-mat.str-el · Submitted 2026-10-07 · Read on arXiv

cond-mat.str-el

Submitted: 2026-10-07

Updated: 2026-10-07

Terminology

• Core — 22× in this paper · explained in 2 episodes
• Accuracy — 15× in this paper · explained in 1 episode
• Entanglement — 9× in this paper · explained in 4 episodes
• Trace — 5× in this paper · explained in 2 episodes
• Local Optimization — 4× in this paper · explained in 2 episodes
• Effective Hamiltonian — 3× in this paper · explained in 2 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Alternating Optimization Scheme — 1× in this paper · explained in 1 episode
• Benchmark — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Quantum Physics — 1× in this paper · explained in 10 episodes
• Riemannian optimization — 1× in this paper · explained in 2 episodes
• Singular Value Decomposition (SVD) — 1× in this paper · explained in 2 episodes

Sources

• Changing the topology of Tensor Networks
• Tensor Ring Decomposition
• Sampling-Based Decomposition Algorithms for Arbitrary Tensor Networks
• Quotient geometry of tensor ring decomposition
• A Provably Efficient Method for Tensor Ring Decomposition and Its Applications
• The trouble with tensor ring decompositions
• Tensor network ranks
• Extracting central charge from ground-state overlaps of spatially deformed Hamiltonians
• Replica Tensor Train
• Computing with traceable tensor networks

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