Modeling Paired Cooper Pair Tunneling in Noise-Protected Circuits

Recently, a superconducting quantum circuit element implementing an effective cos(2ϕ) has been introduced to realize protection via Cooper-pair parity. The architecture, consisting of a π flux-biased symmetric ring of Josephson junctions and superinductors, has an analytical correspondence to an ideal cos(2ϕ) element via an Aharonov-Bohm-like interference of odd numbers of tunneling Cooper pairs. However, a general parameter mapping between a real and an ideal implementation of a cos(2ϕ) element remains an open question. In this work, the inductively-shunted cos(2ϕ) element – also known as the Kinetic Inductance coTunneling Element (KITE) – is mapped to an ideal model using both semiclassical and quantum mechanical simulations. Experimental support for this mapping is also demonstrated. Better understanding real-world cos(2ϕ) elements will prove invaluable for their use in larger noise-protected circuits, such as the recently demonstrated gridium qubit.