# Parametric Quantum State Tomography with HyperRBMs

arXiv: https://arxiv.org/abs/2601.20950 · HTML: https://mlsanity.com/paper/2601.20950/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 57 references that are in the map.
- First posted on arXiv 28 Jan 2026.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Continual learning with hypernetworks](https://mlsanity.com/paper/1906.00695/) (2019)
- [Meta Networks](https://mlsanity.com/paper/1703.00837/) (2017)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [Efficient quantum tomography II](https://mlsanity.com/paper/1612.00034/) (2016)
- [HyperGAN: A Generative Model for Diverse, Performant Neural Networks](https://mlsanity.com/paper/1901.11058/) (2019)
- [Quantum State Tomography with Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2008.03240/) (2020)
- [Improved machine learning algorithm for predicting ground state properties](https://mlsanity.com/paper/2301.13169/) (2023)
- [Fast and robust quantum state tomography from few basis measurements](https://mlsanity.com/paper/2009.08216/) (2020)
- [Predicting Ground State Properties: Constant Sample Complexity and Deep Learning Algorithms](https://mlsanity.com/paper/2405.18489/) (2024)

## Built on by (most cited first, 1 of 1)

- [Apparent Compression, Real Stability: The Intrinsic Dimension of Learning a Quantum Wavefunction](https://mlsanity.com/paper/2609.33193/) (2026)

## Abstract (arXiv)

Quantum state tomography (QST) is essential for validating quantum devices but suffers from exponential scaling in system size. Neural-network quantum states, such as Restricted Boltzmann Machines (RBMs), can efficiently parameterize individual many-body quantum states and have been successfully used for QST. However, existing approaches are point-wise and require retraining at every parameter value in a phase diagram. We introduce a parametric QST framework based on a hypernetwork that conditions an RBM on Hamiltonian control parameters, enabling a single model to represent an entire family of quantum ground states. Applied to the transverse-field Ising model, our HyperRBM achieves high-fidelity reconstructions from local Pauli measurements on 1D and 2D lattices across both phases and through the critical region. Crucially, the model accurately reproduces the fidelity susceptibility and identifies the quantum phase transition without prior knowledge of the critical point. These results demonstrate that hypernetwork-modulated neural quantum states provide an efficient and scalable route to tomographic reconstruction across full phase diagrams.