Probing symmetry-protected topological states on noisy quantum computers

  Daniel Azses [1,2]  ,  Yehuda Naveh [3]  ,  Eran Sela [4]  ,  Emanuele G. Dalla Torre [1,2]  
[1] Department of Physics, Bar-Ilan University, Ramat Gan 5290002, Israel
[2] Center for Quantum Entanglement Science and Technology, Bar-Ilan University, Ramat Gan 5290002, Israel
[3] IBM Research Haifa
[4] School of Physics and Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel

One of the key properties of topological states is their insensitivity to local probes. Ironically, this
also means that it is extremely hard to check whether a state is topological, without performing
a full-state tomography. Here, we perform this task using the properties of symmetry-resolved
entanglement measures. We exemplify this protocol for a one-dimensional symmetry-protected
topological state and implement it on an IBM quantum computer. The comparison between the
simulated result and the experimental one allows us to address the stability of topological phases
of matter to realistic noise sources. We find that while fluctuating noise sources do not affect
topological degeneracies, the latter are affected by systematic errors in the measurement protocol.