Protected gates for superconducting qubits via their internal modes

Protected superconducting qubits such as the zero-pi qubit promise to substantially reduce physical error rates through a multi-mode encoding. However, this protection comes at the cost of increased difficulty to perform single and two-qubit gates. Brooks, Kitaev and Preskill introduced a method to perform protected gates by coupling a zero-pi qubit to a high-impedance resonator [1]. Here, we propose to utilize the internal modes of the zero-pi qubit in place of this ancillary resonator. We present multi-mode numerical simulations to compare using either of two internal modes to perform a protected or unprotected gate, as well as assess the impact of the finite dynamical range of a SQUID used to control the interaction. In particular, our results reveal that a protected gate is possible even when this interaction strength does not vanish, alleviating one of the main experimental challenges in the original proposal.

[1] P. Brooks, A. Kitaev, and J. Preskill, Protected gates for superconducting qubits, Phys. Rev. A 87, 052306 (2013).