Real-Time Boundary Criticality in Superconducting Circuits

Shen et al. (2024) predicted exotic boundary criticalities (e.g., BKT transitions) in topological insulators, but these remain unobserved due to measurement limitations. We propose implementing their edge-mode-bulk coupling model in superconducting quantum circuits (Xue & Hu 2021), where parametric couplings enable in situ tuning of boundary interactions. Unlike static phase-diagram studies, circuits allow real-time tracking of boundary fermion dynamics during transitions, directly testing Shen's predictions about defect-mediated BKT transitions. This leverages Dai et al.'s (2023) strain-tuning concepts but replaces mechanical control with quantum-circuit modulation for higher precision. The approach could also explore non-Hermitian extensions (Zhou et al. 2021) by adding engineered dissipation, probing whether boundary criticality survives in open systems. This bridges theoretical boundary physics with experimental quantum simulation, offering a testbed for dynamical topological phenomena.

References:

1. Strain-tuned topological phase transition and unconventional Zeeman effect in ZrTe5 microcrystals. Apurva Gaikwad, Song-Gen Sun, Peipei Wang, Liyuan Zhang, Jennifer Cano, X. Dai, Xu Du (2022). Communications Materials.
2. Non-Hermitian topological phases and dynamical quantum phase transitions: a generic connection. Longwen Zhou, Qianqian Du (2021).
3. New boundary criticality in topological phases. Xiaoyang Shen, Zhengzhi Wu, Shao-Kai Jian (2024).
4. Topological Photonics on Superconducting Quantum Circuits with Parametric Couplings. Z. Xue, Yong Hu (2021). Advanced Quantum Technologies.