REVIEW 5 cited by
Chebyshev approximation and composition of functions in matrix product states for quantum-inspired numerical analysis
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Chebyshev approximation and composition of functions in matrix product states for quantum-inspired numerical analysis
read the original abstract
This work explores the representation of univariate and multivariate functions as matrix product states (MPS), also known as quantized tensor-trains (QTT). It proposes an algorithm that employs iterative Chebyshev expansions and Clenshaw evaluations to represent analytic and highly differentiable functions as MPS Chebyshev interpolants. It demonstrates rapid convergence for highly-differentiable functions, aligning with theoretical predictions, and generalizes efficiently to multidimensional scenarios. The performance of the algorithm is compared with that of tensor cross-interpolation (TCI) and multiscale interpolative constructions through a comprehensive comparative study. When function evaluation is inexpensive or when the function is not analytical, TCI is generally more efficient for function loading. However, the proposed method shows competitive performance, outperforming TCI in certain multivariate scenarios. Moreover, it shows advantageous scaling rates and generalizes to a wider range of tasks by providing a framework for function composition in MPS, which is useful for non-linear problems and many-body statistical physics.
Forward citations
Cited by 5 Pith papers
-
Local tensor-train surrogates for quantum learning models
Local tensor-train surrogates approximate quantum machine learning models via Taylor polynomials and tensor networks, delivering polynomial parameter scaling and explicit generalization bounds controlled by patch radius.
-
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.
-
Tensor-network approach to quantum optical state evolution beyond the Fock basis
A tensor-network (MPS/MPO) solver simulates SPDC quantum dynamics directly in the continuous quadrature representation, compressing the state >3,000× at α=100.
-
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.
-
SeeMPS: A Python-based Matrix Product State and Tensor Train Library
SeeMPS is a Python MPS/TT library offering a BLAS/LAPACK-style API for compressed linear algebra, from DMRG and time evolution to PDE solving and Fourier transforms.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.