Gr.IV seminar: Donato Farina - "Convex optimization for quantum science and technology"

Wednesday 11 Mar 2026, 16:00 → 17:00 Europe/Rome

0M04

Convex optimization and, in particular, semidefinite programming (SDP) represent fundamental multidisciplinary tools for science and engineering, as they allow one to perform projections on convex sets and obtain certified bounds for quantities of interest. The scope of this presentation is to provide an overview of their usefulness in quantum information and many-body physics. 

In open quantum systems, projective methods can regularize important master equations that lack complete positivity, replacing unphysical Choi states with their closest physical ones. This mimics recent work on quantum process tomography (see [1] and references therein), and enables preserving non-Markovian effects while improving the description of the transient dynamics [2]. 

For many-body systems, scalable SDP approaches (NPA hierarchy) can bound ground-state properties, and detect quantum phase transitions [3]. In open settings, they enable certifying steady-state properties [4], with an efficacy demonstrated in equilibrium and non-equilibrium thermodynamic configurations. Besides, these methods can be naturally enhanced leveraging information coming from accessible measurements, resulting in tighter confidence bounds [5-7]. 

All this highlights the relevance of convex optimization as a rigorous tool for quantum science and technology. In this regard, we conclude with a discussion on the difference between estimating with an ansatz (e.g., using tensor networks) and certifying with SDP methods the properties of many-body quantum systems, clarifying how the two approaches provide complementary information. 

[1] J. Barberà-Rodriguez, L. Zambrano, A. Acin, and D. Farina, “Boosting projective methods for quantum process and detector tomography”, Phys. Rev. Research 7, 013208 (2025). 

[2] A. D’Abbruzzo, D. Farina, and V. Giovannetti, “Recovering Complete Positivity of Non-Markovian Quantum Dynamics with Choi-Proximity Regularization”, Phys. Rev. X 14, 031010 (2024). 

[3] D. Jansen, D. Farina, ..., J. Wang, and A. Acín, “Mapping phase diagrams of quantum spin systems through semidefinite-programming relaxations”, Phys. Rev. Letters 136, 050401 (2026). 

[4] L. Mortimer, D. Farina, G. Di Bello, D. Jansen, A. Leitherer, P. Mujal, and A. Acin, “Certifying steady-state properties of open quantum systems”, Phys. Rev. Research 7, 033237 (2025). 

[5] L. Zambrano, D. Farina, E. Pagliaro, M. M. Taddei, and A. Acin, “Certification of quantum state functions under partial information”, Quantum 8, 1442 (2024). 

[6] L. Mortimer, L. Zambrano, A. Acín, and D. Farina, “Bounding many-body properties under partial information and finite measurement statistics”, arXiv preprint arXiv:2601.10408 (2026). 

[7] L. Zambrano, T. Parella-Dilmé, A. Acín, and D. Farina, “Certification of quantum properties with imperfect measurements”, arXiv preprint arXiv:2601.16570 (2026).