RTNI swMATH ID: 28081 Software Authors: Motohisa Fukuda, Robert Koenig, Ion Nechita Description: RTNI - A symbolic integrator for Haar-random tensor networks. We provide a computer algebra package called Random Tensor Network Integrator (RTNI). It allows to compute averages of tensor networks containing multiple Haar-distributed random unitary matrices and deterministic symbolic tensors. Such tensor networks are represented as multigraphs, with vertices corresponding to tensors or random unitaries and edges corresponding to tensor contractions. Input and output spaces of random unitaries may be subdivided into arbitrary tensor factors, with dimensions treated symbolically. The algorithm implements the graphical Weingarten calculus and produces a weighted sum of tensor networks representing the average over the unitary group. We illustrate the use of this algorithmic tool on some examples from quantum information theory, including entropy calculations for random tensor network states as considered in toy models for holographic duality. Mathematica and Python implementations are supplied. Homepage: https://arxiv.org/abs/1902.08539 Source Code: https://github.com/MotohisaFukuda/RTNI Dependencies: Mathematica; Python Keywords: Quantum Physics; arXiv_quant-ph; arXiv_hep-th; arXiv_math-ph; arXiv_math.PR; tensor network; Mathematica; Python; Haar-random Related Software: Python; Mathematica; QuantumInformation.jl; OEIS; IntHaar Cited in: 4 Documents Standard Articles 2 Publications describing the Software, including 1 Publication in zbMATH Year RTNI – a symbolic integrator for Haar-random tensor networks. Zbl 1509.68341Fukuda, Motohisa; König, Robert; Nechita, Ion 2019 RTNI - A symbolic integrator for Haar-random tensor networks Motohisa Fukuda, Robert Koenig, Ion Nechita 2019 all top 5 Cited by 8 Authors 3 Nechita, Ion 2 Fukuda, Motohisa 2 König, Robert 1 Kukulski, Ryszard 1 Pawela, Łukasz 1 Puchała, Zbigniew 1 Singh, Satvik 1 Życzkowski, Karol Cited in 3 Serials 2 Journal of Mathematical Physics 1 Linear Algebra and its Applications 1 Journal of Physics A: Mathematical and Theoretical all top 5 Cited in 8 Fields 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Quantum theory (81-XX) 2 Computer science (68-XX) 1 Combinatorics (05-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year