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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UNVERDICTED 6representative citing papers
Time-scale entanglement, quantified by bond dimensions in quantics tensor trains of n-particle correlators, is enhanced near phase transitions and scale-invariant at quantum critical points across multiple models.
Tailoring tensor network algorithms to the scale hierarchy in quantics representation produces faster, more robust solvers for high-dimensional linear and eigenvalue PDE problems.
Tensor-network fractional-step method simulates incompressible flows in curvilinear coordinates with up to 20x field compression and 1000x operator compression while keeping errors below 0.3% versus finite differences.
A quantum solver for PDEs is introduced via flexible matrix product operator representations with mid-circuit measurements and state-dependent norm correction to handle non-unitary dynamics.
A survey of variational quantum algorithms, quantum neural networks, and tensor networks for addressing scalability challenges in computational fluid 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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Diagnosing phase transitions through time-scale entanglement
Time-scale entanglement, quantified by bond dimensions in quantics tensor trains of n-particle correlators, is enhanced near phase transitions and scale-invariant at quantum critical points across multiple models.
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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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Quantum-Inspired Tensor-Network Fractional-Step Method for Incompressible Flow in Curvilinear Coordinates
Tensor-network fractional-step method simulates incompressible flows in curvilinear coordinates with up to 20x field compression and 1000x operator compression while keeping errors below 0.3% versus finite differences.
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Tensor-Programmable Quantum Circuits for Solving Differential Equations
A quantum solver for PDEs is introduced via flexible matrix product operator representations with mid-circuit measurements and state-dependent norm correction to handle non-unitary dynamics.
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A review of quantum machine learning and quantum-inspired applied methods to computational fluid dynamics
A survey of variational quantum algorithms, quantum neural networks, and tensor networks for addressing scalability challenges in computational fluid dynamics.