Superconducting circuit with charge-parity protection: Theory

Superconducting qubits that encode quantum information over multiple local degrees of freedom should exhibit improved coherence times (protected qubits). However, the limitation of current fabrication techniques hinders their experimental realization. We propose an experimentally accessible prototype of a protected qubit. It resembles a transmon qubit, with its Josephson junction replaced by an element that exclusively permits tunneling of pairs of Cooper pairs. This renders the lowest two energy eigenstates nearly degenerate, owing to the conservation of Cooper pair number parity. Here, the operator that maps one ground state to the other can only be expressed as a linear combination of local degrees of freedom, providing a primitive form of protection. Numerical simulations of the energy spectrum, wavefunctions, and coherence times validate this analysis.