Bound states in the continuum in a fluxonium qutrit

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 fluxonium-relevant operators into the qutrit subspace, as this long-lived configuration corresponds to the second excited fluxonium level. This state becomes a bound state in the continuum (BIC) when the coupling occurs to an extended system supporting a continuum of modes. In the case without noise, we find BIC lifetimes T1 that can be much larger than seconds when the fluxonium is coupled to a superconducting waveguide, while typical device frequencies are on the order of gigahertz. We have performed a detailed study of the different sources of decoherence in a realistic experiment, finding that upwards transitions caused by a finite temperature in the waveguide and decay induced by 1/f flux noise are the most dangerous ones. Even in their presence, BIC decay times could reach the range of T1 ti 10-1 ms, while preparation times are of the order of 102 ns.