Chaotic fluctuations in a universal set of transmon qubit gates.
Abstract.
Transmon qubits arise from the quantization of nonlinear resonators, systems that are prone
to the buildup of strong, possibly even chaotic, fluctuations. One may wonder to what extent
fast gate operations, which involve the transient population of states outside the computational
subspace, can be affected by such instabilities. We here consider the eigenphases and -states
of the time evolution operators describing a universal gate set, and analyze them by methodology
otherwise applied in the context of many-body physics. Specifically, we discuss their spectral
statistic, the distribution of time dependent level curvatures, and state occupations in- and
outside the computational subspace. We observe 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. We find that for these gates even small variations of Hamiltonian
or control parameters lead to large gate errors and speculate on the consequences for the
practical implementation of quantum control.