Holographic isoTNS represent volume-law entangled states including arbitrary fermionic Gaussian states, Clifford states, and certain short-time evolved states using an extra network dimension with isometric constraints.
Pymanopt: A Python toolbox for optimization on manifolds using automatic differentiation
5 Pith papers cite this work, alongside 108 external citations. Polarity classification is still indexing.
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representative citing papers
A new isometric form for 2D tensor network states uses auxiliary tensors on a 45-degree rotated lattice, enabling a local Yang-Baxter move and a TEBD algorithm that captures area-law ground states and short-time dynamics.
A robust Riemannian Levenberg-Marquardt algorithm is formulated in block-wise form, with convergence results carried over from prior work and demonstrated via an open-source Manopt.jl implementation on tasks including geodesic regression and Procrustes analysis.
On the random-field XY model, Riemannian Monotonic Basin Hopping finds lower-energy states than MultiStart at lower computational cost in the tested L=10–32 instances.
The monograph organizes and derives classical Riemannian geometry structures explicitly in coordinate and matrix form for direct use in optimization algorithms on nonlinear manifolds.
citing papers explorer
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Holographic Representation of One-Dimensional Many-Body Quantum States via Isometric Tensor Networks
Holographic isoTNS represent volume-law entangled states including arbitrary fermionic Gaussian states, Clifford states, and certain short-time evolved states using an extra network dimension with isometric constraints.
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Diagonal Isometric Form for Tensor Network States in Two Dimensions
A new isometric form for 2D tensor network states uses auxiliary tensors on a 45-degree rotated lattice, enabling a local Yang-Baxter move and a TEBD algorithm that captures area-law ground states and short-time dynamics.
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A modified Riemannian Levenberg-Marquardt Algorithm for robust or constraint optimization on manifolds
A robust Riemannian Levenberg-Marquardt algorithm is formulated in block-wise form, with convergence results carried over from prior work and demonstrated via an open-source Manopt.jl implementation on tasks including geodesic regression and Procrustes analysis.
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Nonconvex optimization methods for ground states in disordered continuous-spin models
On the random-field XY model, Riemannian Monotonic Basin Hopping finds lower-energy states than MultiStart at lower computational cost in the tested L=10–32 instances.
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Foundations of Riemannian Geometry for Riemannian Optimization: A Monograph with Detailed Derivations
The monograph organizes and derives classical Riemannian geometry structures explicitly in coordinate and matrix form for direct use in optimization algorithms on nonlinear manifolds.