We propose an architecture for bit-flip error correction of Andreev spins that is protected by Kramers’ degeneracy. Specifically, we show that a coupling network of linear inductors and Andreev spin qubits results in a static Hamiltonian composed of the stabilizers of a bit-flip code. The electrodynamics of the many-body spin states also respect these stabilizers, and we show how reflectometry off a single coupled resonator can thereby accomplish their projective measurement. We further show how circuit-mediated spin couplings enable error correction operations and a complete set of single- and two-module logical quantum gates. The concept, which we dub the “Ising molecule qubit,” is experimentally feasible and provides a path for compact noise-biased qubits.

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• Andreev bound states
• Fermions
• Mesoscopics
• Quantum circuits
• Radio frequency techniques
• Spin dynamics
• Superconductors