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.