Wave function networks for correlated quantum matter

• Applicant: Professor Dr. Markus Philip Ludwig Heyl
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 550495627

Recent impressive advancements in quantum simulator experiments and numerical methods such as neural quantum states are generating increasingly large datasets of “snapshots”. Such snapshots result from a joint projective measurement on each quantum degree of freedom yielding as measurement outcomes full many-body configurations. These snapshots, akin to images in computer science, offer unprecedented opportunities to probe complex quantum states, but present significant challenges in data processing and interpretation. Current analytical approaches often rely on simplifying the snapshot data information through dimensional reduction, potentially discarding crucial information. This project aims to address this challenge through the framework of wave function networks - network representations of snapshot datasets -. to extract physically meaningful insights from these large-scale observations and to characterize complex quantum matter. The core idea is to leverage the maximal information content of these snapshots. Initial work demonstrated the potential of wave function networks built upon imposing a metric structure on the snapshot dataset, revealing scale-free properties near quantum phase transitions and enabling cross-certification of experimental and theoretical data. However, existing wave function networks also face key limitations, including a deficiency to include symmetries, information loss through binarization in the construction of the network, and an inability to capture genuine quantum features such as entanglement. This project aims at overcoming these limitations through three interconnected objectives. First, we will develop weighted wave function networks by replacing the previously utilized metric with a more general similarity measure learned through kernel methods. This will allow for the incorporation of system symmetries and a richer representation of the data. Second, we will expand wave function networks beyond the limitations of occupation-based snapshots by incorporating data from measurements of phase coherences and utilizing symmetric informationally complete measurements to access broader Hilbert space information with the final goal to even quantify quantum entanglement. Finally, we will apply these advanced wave function networks to characterize complex quantum many-body systems, focusing on systems with topological properties such as quantum spin liquids, which are challenging to experimentally detect by means of traditional local measurement probes. By harnessing the power of machine learning and network analysis, this project aims at developing a new approach to understanding and characterizing complex quantum systems. A successful completion of these objectives will allow to establish wave function networks as a versatile tool for analyzing large-scale quantum datasets from both theory and experiment potentially enabling so far hidden insights into the behavior of complex quantum matter.

• DFG Programme: Research Units
• Subproject of: FOR 5919: Machine learning for complex quantum states
• International Connection: Switzerland
• Co-Investigators: Professorin Dr. Annabelle Bohrdt; Dr. Markus Schmitt
• Cooperation Partner: Professor Dr. Giuseppe Carleo