Charge-Related SQUID and Tunable Phase-Slip Flux Qubit

A phase-slip flux qubit, exactly dual to a charge qubit, is composed of a superconducting loop interrupted by a phase-slip junction. We propose a tunable phase-slip flux qubit by replacing the phase-slip junction with a charge-related superconducting quantum interference device (SQUID) consisting of two phase-slip junctions connected in series with a superconducting island. This charge-SQUID acts as an effective phase-slip junction controlled by the applied gate voltage and can be used to tune the energy-level splitting of the qubit. In addition, we show that a large inductance inserted in the loop can reduce the inductance energy and consequently suppress the dominating flux noise of the phase-slip flux qubit. This enhanced phase-slip flux qubit is exactly dual to a transmon qubit.