The geometric properties of a lattice can have profound consequences on its band spectrum. For example, symmetry constraints and geometric frustration can give rise to topologicially nontrivial and dispersionless bands, respectively. Line-graph lattices are a perfect example of both of these features: Their lowest energy bands are perfectly flat, and here we develop a formalism to connect some of their geometric properties with the presence or absence of fragile topology in their flat bands. This theoretical work will enable experimental studies of fragile topology in several types of line-graph lattices, most naturally suited to superconducting circuits.
We use the quasienergy structure emerging in a periodically driven fluxonium superconducting circuit to encode quantum information with dynamically induced flux-insensitive sweet spots. The framework of Floquet theory provides an intuitive description of these high-coherence working points located away from the half-flux symmetry point of the undriven qubit. This approach offers flexibility in choosing the flux bias point and the energy of the logical qubit states as shown in Huang et al.[arXiv:2004.12458 (2020)]. We characterize the response of the system to noise in the modulation amplitude and dc flux bias, and experimentally demonstrate an optimal working point that is simultaneously insensitive against fluctuations in both. We observe a 40-fold enhancement of the qubit coherence times measured with Ramsey-type interferometry at the dynamical sweet spot compared with static operation at the same bias point.
Protecting superconducting qubits from low-frequency noise is essential for advancing superconducting quan- tum computation. We here introduce a protocol for engineering dynamical sweet spots which reduce the sus- ceptibility of a qubit to low-frequency noise. Based on the application of periodic drives, the location of the dynamical sweet spots can be obtained analytically in the framework of Floquet theory. In particular, for the example of fluxonium biased slightly away from half a flux quantum, we predict an enhancement of pure- dephasing by three orders of magnitude. Employing the Floquet eigenstates as the computational basis, we show that high-fidelity single-qubit gates can be implemented while maintaining dynamical sweet-spot opera- tion. We further confirm that qubit readout can be performed by adiabatically mapping the Floquet states back to the static qubit states, and subsequently applying standard measurement techniques. Our work provides an in- tuitive tool to encode quantum information in robust, time-dependent states, and may be extended to alternative architectures for quantum information processing.