QRecoupling.jl: numerical and exact computation of classical and quantum recoupling coefficients
Abstract
QRecoupling.jl is a Julia package for numerical, exact and symbolic evaluation of classical and quantum recoupling coefficients and generic finite sums of quantum factorials, with one interface across the classical limit, principal unitary levels and real or complex deformation. A compact factorial rule and its cyclotomic exponents expose factor cancellation, polynomial structure and level support. The package covers quantum Clebsch-Gordan coefficients, 3j and 6j symbols and user-defined sums. Its adaptive numerical evaluation is combined with exact decisions for sums that cancel to zero. Classical 3j and 6j symbols are evaluated at a speed comparable to that of WIGXJPF, which is based on prime factorization tables, at the smallest spins, and about 6 and 10 times faster at spin cutoff 500. Under real, root-of-unity and complex deformation, the largest relative error measured against independent high-precision references is 3.5 × 10−14 for spins up to 400. Fusion matrices with 401 channels are computed about 100 times faster than by loops over their entries.
Related
- Computation of leading coefficients in asymptotics of relative quantum invariants
- Optimization-based numerical methods for the two-and three-dimensional time harmonic Maxwell problem with sign-changing coefficients
- Generators of stability-preserving semigroups, spectral gaps, and classical ground-state computation
- Cost-Accuracy Trade-offs: Neural Operator vs Classical Numerical Solver
- Formality theorem with coefficients in a module
BibTeX
@misc{asante2026qrecouplingjl,
title = {{QRecoupling.jl: numerical and exact computation of classical and quantum recoupling coefficients}},
author = {Seth K. Asante},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24074},
eprint = {2610.24074},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24074},
}
RIS
TY - UNPB
TI - QRecoupling.jl: numerical and exact computation of classical and quantum recoupling coefficients
AU - Seth K. Asante
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.24074
UR - https://arxiv.org/abs/2610.24074
AB - QRecoupling.jl is a Julia package for numerical, exact and symbolic evaluation of classical and quantum recoupling coefficients and generic finite sums of quantum factorials, with one interface across the classical limit, principal unitary levels and real or complex deformation. A compact factorial rule and its cyclotomic exponents expose factor cancellation, polynomial structure and level support. The package covers quantum Clebsch-Gordan coefficients, 3j and 6j symbols and user-defined sums. Its adaptive numerical evaluation is combined with exact decisions for sums that cancel to zero. Classical 3j and 6j symbols are evaluated at a speed comparable to that of WIGXJPF, which is based on prime factorization tables, at the smallest spins, and about 6 and 10 times faster at spin cutoff 500. Under real, root-of-unity and complex deformation, the largest relative error measured against independent high-precision references is 3.5 × 10^−14 for spins up to 400. Fusion matrices with 401 channels are computed about 100 times faster than by loops over their entries.
ER -