An adaptive patching method exploits block-sparse QTT structures to reduce computational costs for tensor contractions and enables efficient evaluation of bubble diagrams and Bethe-Salpeter equations.
Lindsey, Multiscale interpolative construction of quantized tensor trains 10.48550/ARXIV.2311.12554 (2023)
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A QTT-based solver with Helmholtz-Leray penalization in Fourier space stably computes solutions and gradients for multiscale elliptic PDEs on meshes with up to 10^37 virtual degrees of freedom in 3D.
Tailoring tensor network algorithms to the scale hierarchy in quantics representation produces faster, more robust solvers for high-dimensional linear and eigenvalue PDE problems.
Derives rigorous entanglement scaling laws in MPS for smooth real or complex functions and applies them via tensor cross interpolation to construct and test shallow quantum encoding circuits on up to 156 qubits.
citing papers explorer
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Adaptive Patching for Tensor Train Computations
An adaptive patching method exploits block-sparse QTT structures to reduce computational costs for tensor contractions and enables efficient evaluation of bubble diagrams and Bethe-Salpeter equations.
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Stable full-field simulation of a multiscale elliptic equation by means of Quantized Tensor Trains
A QTT-based solver with Helmholtz-Leray penalization in Fourier space stably computes solutions and gradients for multiscale elliptic PDEs on meshes with up to 10^37 virtual degrees of freedom in 3D.
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Tailoring tensor network techniques to the quantics representation for highly inhomogeneous problems and few body problems
Tailoring tensor network algorithms to the scale hierarchy in quantics representation produces faster, more robust solvers for high-dimensional linear and eigenvalue PDE problems.
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Entanglement scaling in matrix product state representation of smooth functions and their shallow quantum circuit approximations
Derives rigorous entanglement scaling laws in MPS for smooth real or complex functions and applies them via tensor cross interpolation to construct and test shallow quantum encoding circuits on up to 156 qubits.