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 C2,α-nearly spherical sets. In contrast, we prove that balls are not minimizers for large values of the charge and conjecture that optimal shapes do not exist, with the energy favoring disjoint collections of sets.
@article{arxiv.2405.10569,
title = {An optimal design problem for a charge qubit},
author = {Dario Mazzoleni and Cyrill B. Muratov and Berardo Ruffini},
journal= {arXiv preprint arXiv:2405.10569},
year = {2025}
}