This repository contains the source code of the ML quantum state tomography experiment in the paper "Fast minimization of expected logarithmic loss via stochastic dual averaging" accepted by AISTATS 2024.

How to run

• Tested on Julia Version 1.9.2
• Set the dimension and the number of samples in settings.jl

Install Packages

$ cd mlqst/
$ julia ./install.jl

Run

$ julia ./main.jl

Implemented Algorithms

Batch Algorithms

1. Iterative MLE: A. I. Lvovsky, Iterative maximum-likelihood reconstruction in quantum homodyne tomography, J. opt., B Quantum semiclass. opt., 2004 (link)
2. Diluted iMLE with Armijo line search: D. S. Gonçalves, M. A. Gomes-Ruggiero, and C. Lavor, Global convergence of diluted iterations in maximum-likelihood quantum tomography, Quantum Inf. Comput., 2014 (link)
3. NoLips: Heinz H. Bauschke, Jérôme Bolte, Marc Teboulle, A descent lemma beyond Lipschitz gradient continuity: first-order methods revisited and applications, Math. Oper. Res., 2017 (link)
4. Entropic mirror descent with Armijo line search (EMD): Yen-Huan Li and Volkan Cevher, Convergence of the exponentiated gradient method with Armijo line search, J. Optim. Theory Appl., 2019 (link)
5. Monotonous Frank-Wolfe (M-FW): A. Carderera, M. Besançon, and S. Pokutta, Simple steps are all you need: Frank-Wolfe and generalized self-concordant functions, Adv. Neural Information Processing Systems (NeurIPS), 2021 (link)
6. QEM: Chien-Ming Lin, Hao-Chung Cheng, and Yen-Huan Li, Maximum-likelihood quantum state tomography by Cover's method with non-asymptotic analysis, Int. Conf. Quantum Information Processing (QIP), 2022 (link)
7. Frank-Wolfe (FW): Renbo Zhao and Robert M. Freund, Analysis of the Frank–Wolfe method for convex composite optimization involving a logarithmically-homogeneous barrier, Math. Program., 2023 (link)

Stochastic Algorithms

1. Stochastic Q-Soft-Bayes (SQSB): Chien-Ming Lin, Yu-Ming Hsu, and Yen-Huan Li, Maximum-likelihood quantum state tomography by Soft-Bayes, arXiv preprint, 2022 (link)
2. Stochastic Q-LB-OMD (SQLBOMD): Chung-En Tsai, Hao-Chung Cheng, and Yen-Huan Li, Faster stochastic first-order method for maximum-likelihood quantum state tomography, Int. Conf. Quantum Information Processing (QIP), 2023 (link)
3. 1-sample LB-SDA: this work
4. $d$-sample LB-SDA: this work