Bound states in the continuum in a fluxonium qutrit

The heavy fluxonium at zero external flux has a long-lived state when coupled capacitively to any other system. We analyze it by projecting all the relevant operators into qutrit subspace, as this configuration corresponds second excited level. This becomes bound-state in continuum (BIC) coupling occurs an extended system supporting of modes. In case without noise, we find BIC lifetimes that can be much larger than seconds $T_1\gg {\rm s}$ is superconducting waveguide, while typical device frequencies are order ${\rm GHz}$. have performed detailed study different sources decoherence realistic experiment, obtaining upward transitions caused finite temperature waveguide and decay induced $1/f$-flux noise most dangerous ones. Even their presence, BICs times could reach range ${T_1\sim \rm 10^{-1} ms},$ preparation $10^{2}$ns.