Tracking information flow in quantum networks via new divergence measures

• Applicant: Professor Dr. Christoph Hirche
• Subject Area: Hardware Systems and Architectures for Information Technology and Artificial Intelligence, Quantum Engineering Systems ; Theoretical Computer Science
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 550206990

Many problems regarding quantum information processing can be formulated in a network setting. This includes, in particular, communication networks, quantum circuits and machine learning questions. For all of these, their classical equivalents are well studied and one of the main tools for that, in theoretical computer science, are inequalities between divergence measures. In quantum information theory we lack many of these tools. While we know of quantum generalizations of the classical measures, it is often unclear if they obey the same favorable properties. This proposal is based on a recently formulated new definition of one such divergence measure for which we were able to prove many of the needed properties. This motivates several theoretical questions, but also opens the door to more effectively investigate applications in quantum computing. In particular, we will investigate the contraction properties of these divergences. This means we will quantify how much the quantities decrease under specific noise models. The focus is set on theoretical bounds, but also how to efficiently compute these divergences. Further, we will investigate contraction with respect to other quantum resources beyond information, including entanglement and coherence. In the second, application-oriented, part of the proposal, these results will be applied to specific settings and noise models. Briefly stated, we will investigate three questions: 1) Current implementations of circuits on quantum computing hardware unavoidably experience a certain level of noise. We will explore fundamental limitations using our new tools that bound the overhead incurred by the noise. 2) We will consider quantum communication networks and explore how additional knowledge regarding the noise contraction can lead to more practical and efficient communication strategies. 3) Finally, we will consider machine learning applications. Many structures such as neural networks are heavily influenced by noise. This can both be a benefit or a detriment. With our divergence measure tools we will investigate the information flow in such structures under noise and investigate the resulting possibilities and limitations. The focus here will be on possible advantages compared to classical machine learning.

• DFG Programme: Research Grants