Abstract Body

Superconductor integrated circuits are becoming increasingly vital in advanced technological applications. As these circuits scale up, ensuring their reliable operation becomes critical despite inherent parameter variations. Therefore, designing circuits with robust tolerance to these deviations is essential, and this is where automated optimization tools play a crucial role.

There are various optimization tools for single flux quantum (SFQ) circuits, which take a long optimization time due to old simulation tools, programming languages, and optimization algorithms. These optimization tools have also been developed for the traditional SFQ circuits. In recent years, superconductor circuits have been proposed that do not use switching of junctions or 2π phase change [1], [2], which is different from the conventional SFQ circuits. Conventional optimization tools cannot be used directly on these circuits.

In this study, we present MarginX, a novel, simple, and rapid circuit parameter optimization tool designed for superconductor circuits composed of various types of Josephson junctions (JJs). MarginX was originally developed for extracting circuit parameter margins of SFQ circuits with normal (0-) and π-shifted JJs [3]. We have now enhanced MarginX to include circuit parameter optimization. By utilizing the time dependence of the JJ phase to determine correct operation, MarginX is applicable to both DC- and AC-biased superconductor circuits.

We optimized several SFQ logic gates and compared the optimization results and calculation time with other optimization tools. The calculation time required for the SFQ logic gate is less than 3% of that of the other optimization tools in most cases. We demonstrated the margin expansion of the half flux quantum circuit composed of both normal (0-) and π-shifted Josephson junctions. We also demonstrated optimization of adiabatic quantum flux parametron buffer [1] as an example of an AC- biased superconductor circuit. We believe MarginX is a valuable tool for designing various types of superconducting circuits.

References

[1] N. Takeuchi, D. Ozawa, Y. Yamanashi, and N. Yoshikawa, “An adiabatic quantum flux parametron as an ultra-low-power logic device,” Supercond. Sci. Technol., vol. 26, no. 3, p. 035010, Mar. 2013.

[2] T. Kamiya, M. Tanaka, K. Sano, and A. Fujimaki, “Energy/Space- Efficient Rapid Single-Flux-Quantum Circuits by Using π-Shifted Josephson Junctions,” IEICE Trans. Electron., vol. E101-C, no. 5, pp. 385–390, May 2018.

[3] Y. Yamanashi, S. Nakaishi, and N. Yoshikawa, “Simulation of the Margins in Single Flux Quantum Circuits Containing π-Shifted Josephson Junctions,” IEEE Trans. Appl. Supercond., vol. 29, no. 5, p. 1301805, Aug. 2019.

Acknowledgment

This work was supported by JSPS KAKENHI Grant Number JP22H01542 and JP24H00311. The authors thank Sotaro Nakaishi for developing the initial version of MarginX.

Figure 1. The optimization flowchart of MarginX. In one iteration, Ν (default value is 100) netlists with all circuit parameters randomly varied are created and the yield is calculated. The new circuit parameters are updated to the average of the parameters of the successfully operating circuit in every iteration. m is the sum of the successfully operating circuits. The default value of iteration n = 500.

Keywords: superconductor integrated circuits, margin, optimization, center of gravity method