Bound states in the continuum in a heavy 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 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 state supporting a continuum of modes. In the case without noise, we find BIC decay times that can be much larger than seconds T1≫s when the fluxonium is coupled to superconducting waveguide, while typical device frequencies are in the order of GHz. We have also analyzed the noise in a realistic situation, arguing that the most dangerous noise source is the well-known 1/f flux noise. Even in its presence, we show that decay times could reach the range of T1∼10ms.