CSDNN is a protocol based on the combination of Compressed Sensing (CS) and a deep neural network model, to improve the performance of CS. The goal is twofolds:

1. Thanks to CS algorithm, we can use at most $r d\log d$ correlators (tensor produt of single qubit Pauli operators) to estimate a quantum state with high precision. We improve the CS algorithm adding a deep neural network that trains on the CS estimation outputs, in a supervised learning strategy, and improve them. In our job, we focused on 4 qubit random Haar states and employ 30-45 correlators only, instead of the CS theoretical upper bound of 64, or the full informational amount of 256.

2. We want to extend the supervised denoising approach to a more general usecase, that would allow us to reconstruct states of unknwon mixedness witout any prior information about them. To achieve this goal, we make use of the out-of-distribution (OOD) paradigm. In OOD we study the generalization ability of a network by using it in inference on data different from the ones used during training. In our case, a quantum state estimation task, our DNN model is trained on pure states only, and we analyze how efficient it is in reconstructring state afflicted by depolarization noise of different strength.

All information and details can be found in the article

• The git contains all the main codes used for the article realization. In the AttentionModel.ipynb file, the whole train (valid)-test of the models is provided in a python notebook, to make its use and understanding handier; the model class and other utilities can be found in the /utils. In /fixed point inference a .py file for inferring the OOD esitmations with the fixed point strategy, as described in the article.

• Last, in the folder /article model, a .ph file of the model used throghout all the experiment is provided. In /CS analysis the code to produce Fig.5.

• torch 2.0.1
• cvxpy 1.4.
• cuda-version 12.0
• cudnn 8.8.0.121
• mosek 10.1.20
• pandas 2.1.3
• tqdm 4.66.1

(painting, Brecht Evens)