Probing Tensor Singularities and Their Euler-Class Descendants via Non-Abelian Quantum Geometry Measurement

TL;DR

This work predicts and observes new 4D tensor singularities and their 3D Euler-class descendants using superconducting circuits, revealing complex topological structures and a novel measurement protocol for non-Abelian quantum geometry.

Contribution

It introduces the first experimental realization of 4D tensor singularities and their Euler-class descendants, employing a hybrid analog-digital measurement protocol in superconducting qubits.

Findings

Observation of 4D tensor monopoles characterized by Dixmier-Douady class

Identification of 3D Euler and Euler curvature dipoles with nontrivial topology

Development of a hybrid measurement protocol for non-Abelian quantum geometry

Abstract

We report the theoretical prediction and experimental observation of a new class of four-dimensional (4D) tensor singularities and their three-dimensional (3D) Euler-class descendants, protected by chiral and spacetime inversion symmetries on a superconducting circuit platform. The 4D point-like singularity/monopole, characterized by the Dixmier-Douady class of a real bundle gerbe associated with tensor gauge fields, is observed to evolve into a nodal ring carrying an additional first Euler class charge under symmetry-preserving perturbations. Dimensional reduction reveals 3D Euler and Euler curvature dipoles, exhibiting nontrivial Euler topology and a topological sum rule that ensures zero-energy flat bands inherit nontrivial topology even without interactions. Crucially, these high-dimensional degenerate systems are mapped and reconstructed using a hybrid analog-digital protocol designed for non-Abelian quantum geometry measurement within a superconducting qubit array. Our work not only expands the family of topological monopoles but also establishes a robust experimental framework for exploring high-order gauge theory and real-bundle topology across diverse quantum platforms.