Following the original proposal for a 0-m qubit, Brooks, Kitaev, and Preskill presented a method for performing a protected gate on a -periodic superconducting qubit. This protected gate is achieved by adiabatically coupling a 0-T qubit to a high-inductance LC oscillator. This analysis was agnostic with regards to the actual circuit implementation of the O-T qubit. Further work showed that coupling to the LC oscillator also leads to unwanted interactions between the internal modes of the O-1 qubit. This interaction persists even in the presence of zero circuit disorder, seemingly ruining the possibility of performing a BKP-style protected gate. We propose a scheme whereby the internal degrees of freedom of the O-™ qubit can be used as the requisite ancilla mode for the protected gate proposed by BKP.
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