NonConvex Quantum Verification

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This project is supported by NSF (CCF:FET 1907936)

Collaborators:

Anastasios Kyrillidis (Rice CS - PI)
Amir Kalev (USC CS)
Georgios Kollias (IBM NY)
Jay Gambetta (IBM NY)

Students:
Junhyung Lyle Kim (Rice CS)

We propose the exploration of new theory and algorithms for quantum system characterization. With more qubits, the volume of generated data outgrows our 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 tomography, as well as novel noise-robust validation and certification tools for quantum computing. This research proposes to 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 tomography (QST), \(ii)\) 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 scenaria.

Results by this projects include:

For reproducility, we provide real quantum datasets:

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).

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).

Anastasios Kyrillidis, George Kollias, Amir Kalev, Junhyung Lyle Kim, Tayo Ajayi, '’Fast quantum state tomographyvia momentum-inspired non-convex programming’‘, on-going work, (2020).