Alternating cross interpolation performs elementwise operations on tensor trains in O(χ³) time with error control, improving on the standard O(χ⁴) scaling when output ranks are controlled.
Shinaoka , author M
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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.
Derives an explicit stability criterion for parquet fixed-point iterations showing convergence issues arise independently of vertex divergences and demonstrates a controlled stabilization method that reaches the physical solution across multiple divergence lines.
A quantics tensor train solver resolves the Gross-Pitaevskii equation across seven orders of magnitude in length scale in one dimension and on grids larger than a trillion points in two dimensions.
NESSi 2.0 reduces nonequilibrium Green's function simulation cost from O(N_t^3) to O(N_t N_c^2) via memory cutoff and adds tools for nonequilibrium steady states relevant to transport and prethermal dynamics.
citing papers explorer
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Fast elementwise operations on tensor trains with alternating cross interpolation
Alternating cross interpolation performs elementwise operations on tensor trains in O(χ³) time with error control, improving on the standard O(χ⁴) scaling when output ranks are controlled.
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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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Stabilizing the parquet problem
Derives an explicit stability criterion for parquet fixed-point iterations showing convergence issues arise independently of vertex divergences and demonstrates a controlled stabilization method that reaches the physical solution across multiple divergence lines.
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Solving the Gross-Pitaevskii equation on multiple different scales using the quantics tensor train representation
A quantics tensor train solver resolves the Gross-Pitaevskii equation across seven orders of magnitude in length scale in one dimension and on grids larger than a trillion points in two dimensions.