The gradiometer flux qubit without an external flux bias

We analyse the potential of the gradiometer flux qubit (GFQ), which should be insensitive to flux noise because of the nature of the gradiometer structure. However, to enjoy the benefit of such a design, we must be careful in choosing the initial condition. In the fluxoid quantization condition the flux integer n, which is set to zero in the usual single-loop flux qubit analysis, plays an important role in the GFQ potential. We found that it is impossible to construct a double-well potential if we choose the wrong initial condition. For a qubit application, n must be a small odd integer and the best choice would be n = 1. We also provide a precise and efficient numerical method for calculating the energy spectrum of the arbitrary GFQ potential; this will become useful in designing the circuitry parameters. The state control and read-out schemes are also optimized to a situation where a minimum requirement for using electronics is possible, which reduces noise from instruments directly.