CMT Forum: Lorenzo Piroli

Long-range nonstabilizerness in many-body physics

In this talk, I will discuss long-range nonstabilizerness (LRN), which can be defined as the obstruction to remove nonstabilizerness by local quantum circuits (nonstabilizerness is the degree to which a state differs from a stabilizer state). I will discuss in particular LRN in the context of many-body quantum physics, a task with possible implications for quantum-state preparation protocols. After presenting a simple argument showing that LRN is a generic property of many-body states and dynamics, I will restrict to the class of ground states of gapped local Hamiltonians in 1D and 2D. I will present an elementary approach to diagnose LRN based on the analysis of the mutual information between separated regions. I will first exemplify this approach in the context of translation-invariant matrix product states (MPSs). By analyzing the fixed points of the MPS renormalization-group flow, I will provide a sufficient condition for LRN, which depends entirely on the local MPS tensors. Next, I will illustrate our approach in the context of 2D topologically ordered lattice Hamiltonians. In the case of the 2D toric code, I will show that our approach provides a full classification of LRN, certifying it for all encoded non-stabilizer states. I will also discuss generalizations for non-abelian string-net models, briefly touching upon the double Fibonacci model.