Chaotic Fluctuations in a Universal Set of Transmon Qubit Gates

Transmon qubits arise from the quantization of nonlinear resonators, systems that are prone to the buildup of strong, possibly chaotic, fluctuations. Such instabilities will likely affect fast gate operations which involve the transient population of higher excited states outside the computational subspace. Here, we extend the statistical analysis from the spectrum of the generator to that of dynamics itself and show that the instantaneous eigenphases of the time evolution operator, in particular of their curvatures, allows for identifying the subspace most affected by instabilities. Our analysis shows that fast entangling gates, operating at speeds close to the so-called quantum speed limit, contain transient regimes where the dynamics indeed becomes partially chaotic for just two transmons. Surprisingly, this does not reflect in gate reliability, rather, slower operations lead to relatively enhanced errors.