Quantum complexity of topological phases. Or lack thereof
Alberto Giuseppe Catalano, Sven Benjamin Kožić, Gianpaolo Torre, Carola Ciaramelletti, Simone Paganelli, Fabio Franchini, Salvatore Marco Giampaolo
公開日: 2025/9/9
Abstract
Topological phases are expected to carry enhanced computational power, stemming from the long-range entanglement that characterizes them. Here we investigate whether this advantage is reflected in quantum magic, quantified through stabilizer R\'enyi entropies (SREs). We analyze one-dimensional models with an exact duality between a symmetry-protected topological phase and a trivial one. Surprisingly, a finite (parameters dependent) asymmetry appears only when boundary conditions break the duality, and emerges as well in the transverse-field Ising chain, which lacks topological order. These results show that magic is unable to detect topological phases, indicating that either an additional resource is required to capture their unique quantum contribution, or that not all forms of long-range entanglement constitute a genuine computational resource.