David Aram Korbany

---

In this talk, we will discuss [arxiv:2502.19504] and subsequent work: Long-range nonstabilizerness can be defined as the amount of nonstabilizerness which cannot be removed by shallow local quantum circuits (QCs). We study long-range nonstabilizerness in the context of many-body quantum physics, a task with possible implications for quantum-state preparation protocols and implementation of quantum-error correcting codes. After presenting a simple argument showing that long-range nonstabilizerness is a generic property of many-body states, we restrict to the class of ground states of gapped local Hamiltonians. We focus on one and two dimensional systems and present rigorous results in the context of translation-invariant matrix product states (MPSs) and topologically ordered phases in 2d. By analyzing the fixed points of the MPS renormalization-group flow, we provide a sufficient condition for long-range nonstabilizerness, which depends entirely on the local MPS tensors. For a large class of 2d topologically ordered systems, we can extend the results through compactification to 1d. As an application, we prove no-go theorems for approximating universal gate sets (logical algebras) with local shallow QCs, extending some results of the Bravyi-König classification [PRL 110.17 (2013): 170503] beyond stabilizer codes and including approximations. An introduction to the mathematical tools, stabilizer states, MPS fixed points, shallow QCs and phases of matter, will be provided.

---

Università di Bologna
0.03
Contact: Markus Heinrich