Submitted Paper
Inserted: 17 may 2024
Last Updated: 21 may 2024
Year: 2024
Abstract:
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.
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