Non-degenerate Noise-Resilient Superconducting Qubit

We propose a superconducting qubit based on engineering of the first and second harmonics of the Josephson energy/phase relation E_J1cosφ and E_J2cos2φ. By constructing a circuit such that the energy scales of both harmonics E_J1 and E_J2 are negative, we create a periodic potential with two non-degenerate minima. The qubit is then formed from the lowest-energy states of each minimum. Bit-flip protection of the qubit arises due to the localization of each qubit state to their respective minima, while phase-flip protection can be understood by considering the circuit within the Born-Oppenheimer approximation. We discuss implementations of qubit control and readout. Finally, we estimate the qubit coherence times using numerical diagonalization of the complete circuit in conjunction with state-of-the-art noise models.