Investigation of the topological quantum phase transition in a superconducting system via quantum walks
Yi-Hao Kang, Qi-Ping Su, Yu Wang, Lijiong Shen, Chui-Ping Yang
DOI 10.1103/7dy8-1g4t · Physical Review A
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Abstract
We study topological quantum phase transition in a superconducting system via quantum walks. The physical model is composed of a superconducting ququart (a four-level system) employed as the coin and two resonators exploited to encode the positions of the walker in two distinct directions. The topological properties of the quantum evolutions in one- and two-dimensional quantum walks are characterized by topological invariants, namely, the winding number and the Chern number, respectively. Through theoretical analysis, we derive explicit expressions for the critical points of the coin-flip angles, where the topological invariants jump from zero to nonzero integers, signaling the occurrences of topological quantum phase transitions. We also present approaches to measure these topological invariants. Under available control parameters, numerical simulations demonstrate that the measured topological invariants are in accordance with theoretical predictions and are insensitive to the influence of imperfections including systematic errors and decoherence. Moreover, this proposal is flexible and can be implemented across various physical systems, offering valuable insights into exploring topological quantum phase transitions.
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