Geometric phase of a transmon in a dissipative quantum circuit

Abstract

Superconducting circuits reveal themselves as promising physical devices with multipleuses. Within those uses, the fundamental concept of the geometric phase accumulated by the stateof a system shows up recurrently, as, for example, in the construction of geometric gates. Giventhis framework, we study the geometric phases acquired by a paradigmatic setup: a transmoncoupled to a superconductor resonating cavity. We do so both for the case in which the evolutionis unitary and when it is subjected to dissipative effects. These models offer a comprehensivequantum description of an anharmonic system interacting with a single mode of the electromagneticfield within a perfect or dissipative cavity, respectively. In the dissipative model, the non-unitaryeffects arise from dephasing, relaxation, and decay of the transmon coupled to its environment.Our approach enables a comparison of the geometric phases obtained in these models, leading to athorough understanding of the corrections introduced by the presence of the environment.