> 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/born-machines.md).

# Born machines: sampling from |ψ|²

A Born machine is a generative model that defines a probability distribution from a quantum-style wavefunction. Sampling follows the Born rule: the probability of an outcome is the squared magnitude of its amplitude. This page explains the idea and Quantaria's Born research line.

## The rule

For a state with amplitude ψ(x) for outcome x, the probability of x is |ψ(x)|². A quantum measurement samples outcomes this way. A Born machine uses the same rule as a model.

## Why an MPS

An MPS defines a wavefunction ψ(x) through its cores. Because the cores form a chain, the probabilities can be sampled one site at a time. Each site's conditional distribution is computed from the cores already chosen, so sampling is exact and sequential.

## What this offers

* Sampling is exact for the distribution the MPS defines, with no separate sampler to train.
* The bond dimension controls how much correlation the distribution can carry.

## What is open

* It is not established that Born machines match diffusion models on image quality. That is what the research line tests.
* Sampling cost grows with the number of sites and the bond dimension.

## Quantaria's use

Born heads are a research line. They are not part of Hilbert-1, as stated in [Quantum Path](https://github.com/bhavy2908/dataai_docs/tree/main/architecture/quantum-path.md#born-machines). The aim is to test whether images can be sampled directly from tensor cores, without a separate diffusion process.

## Related

* [Diffusion on image patches](/deep-dives/diffusion-on-patches.md)
* [Models](https://github.com/bhavy2908/dataai_docs/tree/main/overview/models.md#born)


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