Engineering robust logical qubits from Bose-Einstein condensates in circuit QED

Increasing the fault tolerance of qubits is a major challenge towards the practical application of quantum algorithms. With the possibility to cheaply fabricate and couple superconducting (SC) qubits on NISQ devices, new possibilities emerge to compose logical qubits out of several SC elements. We propose a setup for a logical qubit built from SC qubits flux-coupled to a microwave cavity mode. Our design is based on a recently discovered stabilizing mechanism in the Bose-Hubbard wheel in the strongly interacting regime, and exploits the extreme robustness of a Z₂ symmetry-protected Bose-Einstein condensate phase. We investigate the impact of practically unavoidable perturbations in form of disorder potentially perturbing the flux-coupling between SC qubits and the cavity. We show that even in the presence of typical fabrication uncertainties, the gap of the logical qubits is extreme robust. Upon a further introduction of an additional SC qubit serving as a probe site, we demonstrate that the proposed logical qubit can be read out reliably.