Adiabatic timescale of the qubit approximation for flux qubits

Flux qubit design is a task of choosing the best fabrication and control parameters for some desired protocol of quantum annealing. Conventionally it is done through experiments, circuit simulation and non-rigorous noise estimates. Our long-term goal is to develop a simplified rigorous theoretical model where the task of qubit design can be defined and leads to a non-trivial optimum for the fabrication and control parameters. To that end, we study circuit models for a variety of flux qubits in the large barrier regime, where the problem is analytically tractable. This still allows one to do a full anneal starting with a superposition of the ground states of each well, and in fact modern capacitively shunted flux qubit (CSFQ) experiments choose the schedule in this way. We compute an adiabatic timescale of the qubit approximation, characterizing the leakage to the non-qubit states. We find that this leakage leads to a “freezeout” of the coherent tunneling close to the end of the anneal even in the closed system setting.