---
title: "Lectures on Quantum Tensor Networks"
authors:
  - "Jacob Biamonte"
year: 2019
venue: "arXiv:quant-ph"
arxiv: "1912.10049"
doi: null
source: "https://arxiv.org/abs/1912.10049"
topics:
  - "tensor-networks"
  - "category-theory"
  - "quantum"
seed_rank: 937
seed_batch: "user-add-2026-08-13"
reviewed: "2026-08-13"
pool: "maths-foundations"
relevance_score: 8
lineage: categorical-deep-learning
cites:
  - title: "A Survey of Graphical Languages for Monoidal Categories"
    url: "https://arxiv.org/abs/0908.3347"
    year: 2010
    arxiv: "0908.3347"
    doi: "10.1007/978-3-642-12821-9_4"
  - title: "The Geometry of Tensor Calculus, I"
    url: "https://doi.org/10.1016/0001-8708(91)90003-P"
    year: 1991
    doi: "10.1016/0001-8708(91)90003-P"
see:
  - "117-a-survey-of-graphical-languages-for-monoidal-categories"
  - "948-the-geometry-of-tensor-calculus-i"
---

# Lectures on Quantum Tensor Networks

## One-sentence takeaway

Lecture notes that treat tensor networks as a diagrammatic / categorical calculus — the quantum-side ancestor of neural circuit diagrams.

## Why it matters here

String-diagram literacy for anyone reading Weaves. Tensor-network wiring is the older sibling of NCD wires; Joyal–Street plus Penrose is the shared geometry.

## Key ideas

- arXiv:1912.10049, 2019 lecture notes (quant-ph).
- Penrose-style graphical tensor calculus applied to quantum many-body systems and ML-adjacent networks.
- Cited by Weaves as diagrammatic prior art alongside Joyal–Street (card 948) and Selinger’s survey (card 117).
- Methodological citation: quantum tensor networks are not DL broadcasting.

## Caveats

## Links

- arXiv: [1912.10049](https://arxiv.org/abs/1912.10049)
- PDF: https://arxiv.org/pdf/1912.10049