Superconducting integrated circuits have drawn much more attention in the past decades. The advantages of the single-flux-quantum (SFQ) logical circuits are the high operating frequency and low power consumption compared with the CMOS counterpart. In addition, Google has declared the quantum supremacy by integrating 54 Josephson-junction-based qubits, although the control and readout were through more than 100 coaxial cables. To realize a universal quantum computer in the future, one must integrate the logical circuits and quantum circuits on the same chip. Since qubits are always working at the milli-Kelvin stage and delicate to external disturbances, the bit energy and total power consumption of the logical circuits should be as small as possible. At present, the typical bit energy of SFQ circuit is ~ 10^-19 J which is roughly determined by the critical current I_c (~100 μA) of the junction and flux quantum Φ₀ (2.067´10^-15 Wb). Although the dissipated energy of adiabatic quantum-flux-parametron (AQFP) can be decreased down to sub-k_BT according to the simulation, there is a balance between the operating frequency and energy consumption.

We have proposed the half-flux-quantum (HFQ) circuits whose operating principle is based on the propagation of a half-flux-quantum between 0-π SQUIDs. The 0-π SQUID has double-well potential and a small nominal critical current I_nominal, which can be tuned by the SQUID loop inductance. As a result, the bit energy (~ I_nominalΦ₀/2₎ of HFQ circuits can be decreased easily and the operating frequency (f ~ 2V/Φ₀) can be double than SFQ circuits in theory.

In the actual circuits, we fabricated 0-0-π SQUIDs by integrating Nb/Pd₈₉Ni₁₁/Nb (SFS) junctions on the top of the AIST HSTP chip (J_c=10 kA/cm²). The π-junction with a critical current of kI_c (k>>1) was used for a non-switching phase shifter and 0-junctions act as the switching elements with critical currents of I_c. With SFQ/HFQ and HFQ/SFQ interfaces, we connected an HFQ JTL to DC/SFQ and SFQ/DC converters and measured the output waveform at 4.2 K. Meanwhile, we also developed a fabrication process of π-π-π SQUIDs, in which less superconducting layers were needed and all the junctions were fabricated with Nb/Pd₈₉Ni₁₁/Al-AlO_x/Nb (SFIS) multilayer structure. Since SFIS junction has a larger characteristic voltage than that of SFS junction, it can be used both as phase shifter and switching junction. We designed and fabricated HFQ Toggle Flip Flops (TFFs) consisting of π-π-π SQUIDs. According to the simulation, the bias margin of the HFQ TFF was about ±20%. The measurement was done with high frequency pulse trains and the output voltage measured at 4.2 K was exactly half of the input voltage (divide-by-two operation) up to 6.7 GHz, indicating the feasibility to demonstrate HFQ circuits that operating at milli-Kelvin in the future.

Acknowledgment
This work was supported by the JSPS KAKENHI, Grant Numbers JP18H05211, JP18H01498, JP19H05615 and 20K22412, and JST-CREST Program Grant Number JPMJCR20C5 and the Program for Promoting the Enhancement of Research University.

Keywords:  π-junction, SFQ, half-flux-quantum, TFF