Schematic picture of the proposed 2JJ flux qubit with a SQUID configuration (a) and its circuit diagram (b). The loop carrying supercurrent is pierced by an externally applied magnetic flux (towards the viewer). The individual SIS Josephson junctions are characterized by coupling energies , , critical currents , , and capacitances , which do not differ significantly. The loop inductance is small enough that the 2JJ SQUID has only two metastable flux states. The parameter (see below).
Potential in temperature units for the 1JJ qubit with (1) and for the 2JJ qubit with the parameter pairs (2) and (0.8, 1.276) (3) at external magnetic flux . The geometric ring inductance is for both qubits; the potential barrier heights in curves 1–3 are equal, .
Integral phase-current relation for 2JJ qubit at various : 0.9 (1), 0.8 (2), 0.5 (3) (a); the functions (1), (2) for the 2JJ qubit at . The straight line (3) corresponds to the definition of . The values of and (the latter being -independent) correspond to (b).
The function for the 2JJ qubit at (1), ScS qubit (2), and 1JJ qubit (3); the points on the numerical curves corresponding to equal height of the potential barrier for all the qubits are indicated by arrows (a); The function for the 2JJ qubit and various : 0.9 (1), 0.85 (2), 0.8 (3) and the “level line” of equal heights of the potential barriers at varying (4) (b). The numerically obtained results are represented by hollow circles, and the analytical results are plotted by solid lines in (a) and (b). The dashed lines show the lowest boundary at which the level height becomes equal to the potential barrier height . For 1JJ and ScS qubits, the capacitance of the corresponding (SIS and ScS) junctions is , while for the 2JJ qubit the capacitance of the larger SIS junction is . The geometric inductance of the ring is , and the parameter for all the qubits. For the 2JJ flux qubit the parameter at .
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