The following are modifications or improvements to original notebooks. Please refer to the authors' models for the published primary work.

ITensor and TeNPy are leading open-source tensor network libraries featured in recent literature, GitHub, and community discussions - allowing for new opportunities regarding high dimensional generative modeling in artificial intelligence. [01-07]

ITensor includes ITensor C++, ITensors.jl, with related contributions to ITensorNetworks.jl and DMRGPy. A 2021 Fishman, M., et al. paper titled "The ITensor Software Library for Tensor Network Calculations" described the platform as being purposed for enhanced connectivity of tensor networks without manually bookkeeping tensor indices, while ruling out "common programming errors and enables rapid prototyping of algorithms". [08-09]

The platform was recently extended by ITensor researchers, Flatiron Institute, and NYU in yielding Tensor Network results significantly more accurate and precise than a 127-qubit quantum computer circuit with high scalability akin "to a quantum computer with an infinite number of qubits", along with many other practical advantages. [10-11] Despite the support and results in literature, Python machine learning library implementations along with other mainstream AI libraries aren't available for direct Python-based LLMs, for example.

TeNPy "is a Python library for the simulation of strongly correlated quantum systems with tensor networks" supported by GitHub repositories. TeNPy v1.0.0 was released March 19, 2024, marking the first official release of the library which is now considered reliable enough for general use. TeNPy was created to achieve a "balance of a good readability and usability for new-comers, and at the same time powerful algorithms and fast development of new algorithms for experts." [12-13]

A main advantage of TeNPy is ease of accessibility with other Python ML platforms such as PyTorch and TensorFlow. At low-moderate run times, Julia-based tensor network software has some speed advantage, as can be expected when using Python. [14] Since its inception in 2018, TeNPy has grown from basic approaches of MPS and MPO to being utilized by leaders in condensed matter physics and quantum information theory. This also includes developments to improve algorithms and detailed demos for increased Tensor Network adoption in High Dimensional Generative AI. [15] Two demos based on ITensor and TeNPy are attached with code. [16-18]

[01] https://lnkd.in/gXJWFNCU
[02] https://lnkd.in/g3Ciyyxs
[03] https://lnkd.in/gceBgBTS
[04] https://lnkd.in/gFpCPqgW
[05] https://lnkd.in/gcjEy6yh
[06] https://lnkd.in/gfVjZ3fd
[07] https://lnkd.in/gW6jMzFE
[08] https://itensor.org/codes/
[09] https://lnkd.in/gDMp-Mkm
[10] https://lnkd.in/g4vVZ6Gg
[11] https://lnkd.in/gX5ZnPnP
[12] https://lnkd.in/gWpavHnd
[13] https://lnkd.in/gnpktcMg
[14] https://lnkd.in/gMSDp-PH
[15] https://lnkd.in/gxMF4kHF
[16] https://lnkd.in/gyNJSY2Z
[17] https://lnkd.in/gsxPFdAq
[18] https://lnkd.in/g5_gkz2G