# Dimension-adaptive machine-learning-based quantum state reconstruction

arXiv: https://arxiv.org/abs/2205.05804 · HTML: https://mlsanity.com/paper/2205.05804/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 77 references that are in the map.
- First posted on arXiv 11 May 2022.

## Builds on (most cited first, 13 of 13)

- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [A Mathematical Theory of Deep Convolutional Neural Networks for Feature Extraction](https://mlsanity.com/paper/1512.06293/) (2015)
- [Quantum State Tomography with Conditional Generative Adversarial Networks](https://mlsanity.com/paper/2008.03240/) (2020)
- [Experimental neural network enhanced quantum tomography](https://mlsanity.com/paper/1904.05902/) (2019)
- [Classification and reconstruction of optical quantum states with deep neural networks](https://mlsanity.com/paper/2012.02185/) (2020)
- [Adaptive Quantum State Tomography with Neural Networks](https://mlsanity.com/paper/1812.06693/) (2018)
- [Machine learning assisted quantum state estimation](https://mlsanity.com/paper/2003.03441/) (2020)
- [Experimental quantum homodyne tomography via machine learning](https://mlsanity.com/paper/1907.06589/) (2019)
- [On the experimental feasibility of quantum state reconstruction via machine learning](https://mlsanity.com/paper/2012.09432/) (2020)
- [Quantum Pattern Recognition in Photonic Circuits](https://mlsanity.com/paper/2107.09961/) (2021)
- [Data-Centric Machine Learning in Quantum Information Science](https://mlsanity.com/paper/2201.09134/) (2022)
- [Generative Machine Learning for Robust Free-Space Communication](https://mlsanity.com/paper/1909.02249/) (2019)
- [Improving application performance with biased distributions of quantum states](https://mlsanity.com/paper/2107.07642/) (2021)

## Built on by (most cited first, 2 of 2)

- [Tomography of Quantum States from Structured Measurements via quantum-aware transformer](https://mlsanity.com/paper/2305.05433/) (2023)
- [ShadowNet for Data-Centric Quantum System Learning](https://mlsanity.com/paper/2308.11290/) (2023)

## Abstract (arXiv)

We introduce an approach for performing quantum state reconstruction on systems of n qubits using a machine-learning-based reconstruction system trained exclusively on m qubits, where m≥ n. This approach removes the necessity of exactly matching the dimensionality of a system under consideration with the dimension of a model used for training. We demonstrate our technique by performing quantum state reconstruction on randomly sampled systems of one, two, and three qubits using machine-learning-based methods trained exclusively on systems containing at least one additional qubit. The reconstruction time required for machine-learning-based methods scales significantly more favorably than the training time; hence this technique can offer an overall savings of resources by leveraging a single neural network for dimension-variable state reconstruction, obviating the need to train dedicated machine-learning systems for each Hilbert space.