Certifying steady-state properties of open quantum systems

• URL: http://arxiv.org/abs/2410.13646v2
• Date: Tue, 17 Jun 2025 15:17:09 GMT
• Title: Certifying steady-state properties of open quantum systems
• Authors: Luke Mortimer, Donato Farina, Grazia Di Bello, David Jansen, Andreas Leitherer, Pere Mujal, Antonio Acín,
• Abstract summary: Estimating the steady-state properties of open many-body quantum systems is a fundamental challenge in quantum science.<n>We present a scalable approach based on semi-definite programming to derive certified bounds.<n>Our method introduces the first general numerical tool for bounding steady-state properties of open quantum dynamics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Estimating the steady-state properties of open many-body quantum systems is a fundamental challenge in quantum science and technologies. In this work, we present a scalable approach based on semi-definite programming to derive certified bounds on the expectation value of an arbitrary observable in the steady state of Lindbladian dynamics. We illustrate our method on a series of many-body systems, including paradigmatic spin-1/2 chains and two-dimensional ladders, considering both equilibrium and nonequilibrium steady-states. We benchmark our method with state-of-the-art tensor-network approaches that, unlike our method, are only able to provide estimates, with no guarantee, on steady-state quantities. For the tested models, only modest computational effort is needed to obtain certified non-trivial bounds for system sizes intractable by exact methods. Our method introduces the first general numerical tool for bounding steady-state properties of open quantum dynamics, opening a new avenue in the understanding of stable configurations in many-body systems.

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