Electronic capacitance in tunnel junctions for protected charge-parity qubits*

The prospects of implementing the charge-parity topologically protected qubit rely on the hybridization of states resulting from concatenated cos(2φ) elements known as plaquettes, implemented with dc SQUIDs with non-negligible inductances. The required junction parameters for optimal protection with these plaquettes fall outside the range of standard transmon junctions, where both the large Josephson and charging energy required can push the plasma frequency close to the superconductor gap frequency. As a result, a renormalization occurs in the form of an extra electronic capacitance that acts to push down the effective plasma frequency. This electronic capacitance contributes to the overall junction capacitance and poses a significant obstacle in creating junctions for new charge-parity qubits with optimal protection. This talk will describe measurements of electronic capacitance in small tunnel junctions and strategies for mitigating this in future charge-parity topologically protected devices.