Optimization of Half-Flux-Quantum Circuits Composed of π-Shift and Conventional Josephson Junctions

We report optimization of half-flux-quantum (HFQ) circuits composed of SQUIDs containing conventional Josephson junctions and π-shift magnetic Josephson junctions. The SQUID can act as a Josephson junction with an extremely small critical current and be easily switched by a weak driving force with the assistance of the circulating current that is induced due to the π-shift and quantization conditions. It leads to a drastic reduction of both static and dynamic power consumption. However, the parameter margins of the HFQ circuits obtained so far is narrow compared with conventional single-flux-quantum circuits. Since HFQ circuits use many circuit elements and require the two junctions in the SQUID to switch alternately and symmetrically, circuit parameter optimization is much more difficult. In this study, we developed an optimization tool for HFQ circuits, including operation judgment and margin calculation. We improved the critical margin of the HFQ Josephson transmission line to 39%. We also optimized the HFQ splitter, confluence buffer, and D flip-flop. We discuss design guidelines for HFQ circuits based on our systematic exploration of the optimized circuit parameter sets. We suggest that the optimized loop inductances are around 0.5 and 1.5 of Φ ₀ /2 for data transmission and storage, respectively.