analiza aiqbench
This release introduces `torch_vn_algebra`, an open-source PyTorch library designed to accelerate numerical experiments with finite-dimensional Type I von Neumann algebras using GPU hardware. The framework enables efficient Monte Carlo simulations of random block-diagonal operators and unitary ensembles, bridging advanced operator algebra theory with practical deep learning infrastructure for quantum physics research.
Finite-Dimensional Type I von Neumann Algebras in PyTorch: A GPU-Accelerated Framework for Random Block-Diagonal Operators
arXiv:2606.15882v1 Announce Type: cross Abstract: We present \texttt{torch\_vn\_algebra}, an open-source Python library built on PyTorch for numerical experiments with finite-dimensional Type I von Neumann algebras (direct sums of matrix algebras). The library provides: $\bullet$ a compact batched tensor representation $(B,C,k_{\max},k_{\max})$ that handles both Monte Carlo samples and multiple direct summands; $\bullet$ lazy evaluation of operators to avoid unnecessary memory allocation; $\bullet$ generation of random operators with arbitrary eigenvalue distributions (user-provided samplers) and various unitary ensembles (Haar, $\mathrm{SU}(n)$, COE, CSE, diagonal phases); $\bullet$ functional calculus via SVD (absolute value, square root, inverse, entropy) and a hybrid method for extreme eigenvalues (exact diagonalisation for $k_{\max}\le256$, otherwise power iteration); $\bullet$ three trace functionals (blunt, normalised subspace trace, and the von Neumann tracial state); $\bullet$ GPU-accelerated batched linear algebra for moderate-scale Monte Carlo studies (e.g., $2\times10^4$ samples of $100\times100$ operators). The library is validated against analytical expectations (Haar moments, trace properties). Performance benchmarks on a Tesla P100 GPU are presented and discussed. Limitations and future work are outlined. The code is open-source.
Abstract:We present \texttt{torch\_vn\_algebra}, an open-source Python library built on PyTorch for numerical experiments with finite-dimensional Type I von Neumann algebras (direct sums of matrix algebras). The library provides: $\bullet$ a compact batched tensor representation $(B,C,k_{\max},k_{\max})$ that handles both Monte Carlo samples and multiple direct summands; $\bullet$ lazy evaluation of operators to avoid unnecessary memory allocation; $\bullet$ generation of random operators with arbitrary eigenvalue distributions (user-provided samplers) and various unitary ensembles (Haar, $\mathrm{SU}(n)$, COE, CSE, diagonal phases); $\bullet$ functional calculus via SVD (absolute value, square root, inverse, entropy) and a hybrid method for extreme eigenvalues (exact diagonalisation for $k_{\max}\le256$, otherwise power iteration); $\bullet$ three trace functionals (blunt, normalised subspace trace, and the von Neumann tracial state); $\bullet$ GPU-accelerated batched linear algebra for moderate-scale Monte Carlo studies (e.g., $2\times10^4$ samples of $100\times100$ operators). The library is validated against analytical expectations (Haar moments, trace properties). Performance benchmarks on a Tesla P100 GPU are presented and discussed. Limitations and future work are outlined. The code is open-source.
Mathematical Software (cs.MS); Numerical Analysis (math.NA); Operator Algebras (math.OA); Quantum Algebra (math.QA); Spectral Theory (math.SP); Quantum Physics (quant-ph)
G.4; G.1.3; G.3; D.2.13; I.6.5
arXiv:2606.15882 [cs.MS]
(or arXiv:2606.15882v1 [cs.MS] for this version)
https://doi.org/10.48550/arXiv.2606.15882 arXiv-issued DOI via DataCite (pending registration)
From: Andrei Novikov Dr. [view email] [v1] Sun, 14 Jun 2026 16:06:26 UTC (11,394 KB)
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