We propose the exploration of new theory and algorithms for quantum system characterization. With more qubits, the volume of generated data outgrows the computational capacity of classical tomography methods, posing major challenges. The goal of this project is to close this gap by investigating ways to accelerate such protocols with guarantees.

This project focuses on benchmarking and testing quantum computation systems through efficient, robust, and provable quantum state and process tomography, as well as novel noise-robust validation and certification tools for quantum computing. We investigate new theoretical and practical approaches, via the following three paths: \(i)\) by provably distributing computations in a non-convex way for large-scale quantum state and process tomography (QST and QPT), \(ii)\) by robustifying state of the art validation methods using robust optimization and techniques, and finally, \(iii)\) by designing efficient and robust schemes for validating and certifying specific experimentally-relevant quantum operations.

We propose to evaluate the theoretical studies with experiments on available prototypes of quantum processors in order to assess their practicality in real scenarios.

The results by this project include:

• Projected FGD for QST.
• Momentum-Inspired FGD for QST.
• Using non-convex optimization in quantum process tomography: Factored gradient descent is tough to beat

For reproducibility, we provide real quantum datasets:

• Real QST data.

Publications

Anastasios Kyrillidis, Amir Kalev, Dohyung Park, Srinadh Bhojanapalli, Constantine Caramanis, Sujay Sanghavi, ``Provable compressed sensing quantum state tomography via non-convex methods’‘, npj Quantum Information volume 4, Article number: 36 (2018).

Kelly Geyer, Anastasios Kyrillidis, Amir Kalev, '’Low-rank regularization and solution uniqueness in over-parameterized matrix sensing’‘, Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:930-940, 2020.

Mitchell Roddenberry, Santiago Segarra, Anastasios Kyrillidis, '’Rank-One Measurements of Low-Rank PSD Matrices Have Small Feasible Sets’‘, Arxiv Preprint, arXiv preprint arXiv:2012.09768 (2020).

Junhyung Lyle Kim, George Kollias, Amir Kalev, Ken X. Wei, Anastasios Kyrillidis '’Fast quantum state reconstruction via accelerated non-convex programming’‘, Sumitted, Arxiv Preprint, arXiv preprint arXiv:2104.07006, (2021).

Junhyung Lyle Kim, Jose Antonio Lara Benitez, Mohammad Taha Toghani, Cameron Wolfe, Zhiwei Zhang, Anastasios Kyrillidis '’Momentum-inspired Low-Rank Coordinate Descent for Diagonally Constrained SDPs’‘, Sumitted, Arxiv Preprint, arXiv preprint arXiv:2106.08775, (2021).

David Quiroga and Anastasios Kyrillidis '’Using non-convex optimization in quantum process tomography: Factored gradient descent is tough to beat’‘, 2023 IEEE International Conference on Rebooting Computing (ICRC) (best student poster award), (2023).