> For the complete documentation index, see [llms.txt](https://docs.quantaria.xyz/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.quantaria.xyz/deep-dives/mera-and-disentanglers.md).

# MERA and disentanglers

The multi-scale entanglement renormalization ansatz (MERA) is a tensor network built in layers, with each layer removing short-range correlations before coarse-graining. Its disentanglers are the part Quantaria's hybrid layers rely on. This page explains both.

## The structure

A MERA alternates two kinds of tensor:

* **Disentanglers**, which act on pairs of neighbouring sites and remove short-range entanglement between them.
* **Isometries**, which combine neighbouring sites into one coarser site.

Stacking these layers gives a network whose depth grows with the logarithm of the system size.

## Why disentanglers matter

Disentanglers are unitary. Because they can be built from quantum gates, they are the natural place where a tensor network meets a quantum circuit. Moving a disentangler from the tensor side to the circuit side is the step the quantum path depends on.

## The published result

The paper behind Quantaria's hybrid-layer idea ([arXiv:2410.17397](https://arxiv.org/abs/2410.17397)) describes MERA-style disentanglers that move correlations out of an MPO and into parameterized circuits. It reports that one SmolLM2 attention layer was cut to about 3,000× fewer classical parameters at +0.26% perplexity, with part of inference run on an IBM Heron processor. This is the paper's result on its own model, not a Quantaria measurement.

## What is still open

* The disentangler layers in the paper are small. Scaling them to full Hilbert-1 layers is not established.
* Running them on hardware adds noise. The results depend on how much of the circuit runs on the device and how much on a simulator.

## Quantaria's use

The Dirac line builds hybrid layers from a circuit, an MPO, and a circuit. Disentanglers are the circuit pieces. The line is in research, and results are published on simulators first. See [Dirac](https://github.com/bhavy2908/dataai_docs/tree/main/overview/models.md#dirac) and [Quantum Path](https://github.com/bhavy2908/dataai_docs/tree/main/architecture/quantum-path.md).

## Related

* [Staircase circuits](/deep-dives/staircase-circuits.md)
* [Cayley transform and unitary adapters](/deep-dives/cayley-unitary-adapters.md)


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