Exponentially robust non-Clifford gate in a driven-dissipative circuit

TL;DR

This paper introduces a topologically robust non-Clifford $\

Contribution

It presents a novel protocol for a protected non-Clifford $\

Findings

Exponential suppression of infidelity due to imperfections.

Operation timescales of microseconds for GHz resonators.

Resilience to noise and control imperfections.

Abstract

Recent work (Nathan et al, arXiv:2405.05671) proposed an architecture for a dissipatively stabilized GKP qubit, and protocols for protected Clifford gates. Here we propose a protocol for a protected non-Clifford $\sqrt{T}$ gate at the physical qubit level, based on the inclusion of a quartic flux potential generated by ancillary Josephson junctions. We show that such a gate is topologically robust with exponentially suppressed infidelity from control or device imperfections, and operates on microsecond timescales for GHz resonators. We analyze the resilience of the protocol to noise, imperfect control, and imperfect targeting of circuit parameters.