Tensor-train formulation reduces multidimensional inverse Laplace transform cost from exponential to polynomial under low-rank assumptions.
Multiscale interpolative construction of quantized tensor trains
6 Pith papers cite this work, alongside 1 external citations. Polarity classification is still indexing.
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UNVERDICTED 6representative citing papers
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.
A QTT-based solver for multiscale elliptic equations achieves full-field solutions and gradients on meshes up to 10^37 DoFs in 3D via a penalized Helmholtz-Leray formulation solved in Fourier space, with claimed unconditional stability.
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.
The paper investigates the effects of time integrator selection, numerical dissipation, and problem representation on the efficiency and stability of quantized tensor train simulations for advection-dominated test problems.
citing papers explorer
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A tensor-train multidimensional inverse Laplace transform
Tensor-train formulation reduces multidimensional inverse Laplace transform cost from exponential to polynomial under low-rank assumptions.
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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 for multiscale elliptic equations achieves full-field solutions and gradients on meshes up to 10^37 DoFs in 3D via a penalized Helmholtz-Leray formulation solved in Fourier space, with claimed unconditional stability.
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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.
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A practical investigation on time integration in the quantized tensor train format
The paper investigates the effects of time integrator selection, numerical dissipation, and problem representation on the efficiency and stability of quantized tensor train simulations for advection-dominated test problems.