# MPO construction and compression principles (or: how does OpSum work?)

**URL:** <https://itensor.discourse.group/t/mpo-construction-and-compression-principles-or-how-does-opsum-work/1898>\
**Category:** General Discussion\
**Created:** [July 26, 2024, 9:23am UTC](https://itensor.discourse.group/t/mpo-construction-and-compression-principles-or-how-does-opsum-work/1898 "2024-07-26T09:23:29Z")\
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**Author:** ![ryanlevy](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/ryanlevy/32/150_2.png) [@ryanlevy](https://itensor.discourse.group/u/ryanlevy)\
**Post date:** [July 26, 2024, 11:25am UTC](https://itensor.discourse.group/t/mpo-construction-and-compression-principles-or-how-does-opsum-work/1898/2 "2024-07-26T11:25:46Z")

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For construction, I would recommend checking out if you haven’t

- [[0708.1221] Finite automata for caching in matrix product algorithms](https://arxiv.org/abs/0708.1221)
- [[0804.2509] Infinite size density matrix renormalization group, revisited](https://arxiv.org/abs/0804.2509)

And this paper on MPO compression

- [[1909.06341] Local Matrix Product Operators: Canonical Form, Compression, & Control Theory](https://arxiv.org/abs/1909.06341)

I’ll have to let others comment on the exact compression techniques that are in ITensors

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