Calculus of Variations and Geometric Measure Theory

D. Mazzoleni - C. Muratov - B. Ruffini

An optimal design problem for a charge qubit

created by mazzoleni on 17 May 2024
modified by ruffini on 21 May 2024


Submitted Paper

Inserted: 17 may 2024
Last Updated: 21 may 2024

Year: 2024


In this paper we introduce a simple variational model describing the ground state of a superconducting charge qubit. The model gives rise to a shape optimization problem that aims at maximizing the number of qubit states at a given gating voltage. We show that for small values of the charge optimal shapes exist and are $C^{2,\alpha}$-nearly spherical sets. In contrast, for large values of the charge the optimal shape does not exist, with the energy favoring disjoint collections of sets.