Paula I. Villar

Geometric Phase of a Transmon in a Dissipative Quantum Circuit

  1. Ludmila Viotti,
  2. Fernando C. Lombardo,
  3. and Paula I. Villar
Superconducting circuits reveal themselves as promising physical devices with multiple uses. Within those uses, the fundamental concept of the geometric phase accumulated by the state
of a system shows up recurrently, as, for example, in the construction of geometric gates. Given this framework, we study the geometric phases acquired by a paradigmatic setup: a transmon coupled to a superconductor resonating cavity. We do so both for the case in which the evolution is unitary and when it is subjected to dissipative effects. These models offer a comprehensive quantum description of an anharmonic system interacting with a single mode of the electromagnetic field within a perfect or dissipative cavity, respectively. In the dissipative model, the non-unitary effects 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 a thorough understanding of the corrections introduced by the presence of the environment.
arxiv pdf

Corrections to the Berry phase in a solid-state qubit due to low-frequency noise

  1. Fernando C. Lombardo,
  2. and Paula I. Villar
We present a quantum open-system approach to analyze the nonunitary dynamics of a superconducting qubit when it evolves under the influence of external noise. We consider the presence
of longitudinal and transverse environmental fluctuations affecting the system’s dynamics and model these fluctuations by defining their correlation function in time. By using a Gaussian-like noise correlation, we can study low- and high-frequency noise contribution to decoherence and implement our results in the computation of geometric phases in open quantum systems. We numerically study when the accumulated phase of a solid-state qubit can still be found close to the unitary (Berry) one. Our results can be used to explain experimental measurements of the Berry phase under high-frequency fluctuations and design experimental future setups when manipulating superconducting qubits.
arxiv pdf