Resilient superconducting-element design with genetic algorithms

We present superconducting quantum circuits that exhibit atomic energy spectra and selection rules in ladder and lambda three-level configurations designed using genetic algorithms. These heuristic optimization techniques are employed to adapt the topology and parameters of a set of electrical circuits to find the suitable architecture matching the required energy levels and relevant transition matrix elements. We analyze the performance of the optimizer on one-dimensional single- and multiloop circuits to design ladder (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">Ξ</a:mi></a:math>) and lambda (<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi mathvariant="normal">Λ</d:mi></d:math>) three-level systems with specific transition matrix elements. As expected, attaining both the required energy spectrum and the needed selection rules is challenging for single-loop circuits, but they can be accurately obtained even with just two loops. Additionally, we show that our multiloop circuits are robust against random fluctuations in their circuit parameters, i.e., under eventual fabrication flaws. Developing an optimization algorithm for automated circuit quantization opens an avenue to engineering superconducting circuits with specific symmetry to be used as modules within large-scale setups. This may allow us to mitigate the well-known current errors observed in the first generation of quantum processors.