Abstract Body

We report numerical and experimental evaluation of the cascade connection of flux transfer circuits using π-shift Josephson junctions (π-junctions) that can be used for enhanced couplers between spins in a quantum annealer. In recent years, quantum annealers using superconductor flux qubits [1] have been actively researched and developed. The quantum annealers are expected to solve large-scale combinatorial optimization problems in a realistic time frame, such as the traveling salesperson problem and factorization problems that would take an enormous amount of time using conventional computers. The state-of-the-art quantum annealers show significant progress in integration; for example, D-Wave’s Advantage2 prototype is planned to be equipped with over 1,200 flux qubits [2]. However, the number of spins that can be connected to each other limits the flexibility in problem mapping because of signal attenuation over long-distance wiring.

To address these issues, we proposed a flux transfer circuit using π junctions (π-FTC) that allows for more efficient flux transmission [3]. The negative inductance nature of a π-junction inserted in the superconductor loops is utilized for the current enhancement. Because the current-enhancement effect is constrained by the loop inductance not to show a hysteresis characteristic, we connect multiple stages of π-FTCs to achieve longer distance wirings. We reported the numerical analysis of the current-enhancement effect of multi-stage connections using a current source [4]. This study aims to evaluate the cascade connection of π-FTCs as a coupler toward quantum annealer application.

First, we numerically simulated two spins connected by π-FTCs, including classical, thermal noise. In this study, a SQUID containing a π-junctions serves as a spin device in a quantum annealer. Our numerical simulation showed that the cascade connection of π-FTCs could contributes to enhancing the coupling currents, resulting in strong interaction of two spins. （The one stage of π-FTC connects the both spins 5% stronger, the two has 8% and the three has 4% stronger connection than conventional FTCs. Then, we fabricated test circuits using cascade connection of π-FTCs with 1, 3 and 5 stages. The π-junctions were the magnetic Josephson junctions of the Nb/Pd89Ni11/Nb structure [5], and we formed them on a chip fabricated with the AIST Nb four-layer process. The figure shows the fabricated test circuit. Because the critical current density of the conventional Josephson junctions is relatively high (10kA/cm²) in this fabrication, the junction critical current was around 50 µA, and we conducted the measurement at 4.2 K. The detailed measurement results will be given in the presentation.

References

[1] M. W. Johnson et al., “Quantum annealing with manufactured spins,” Nature, vol. 473, no. 7346, pp. 194–198, 2011.

[2] D-Wave Quantum Inc., “D-Wave Announces 1,200+ Qubit Advantage2™ Prototype in New, Lower- Noise Fabrication Stack, Demonstrating 20x Faster Time-to-Solution on Important Class of Hard Optimization Problems,” https://www.dwavesys.com/company/newsroom/press-release/ (accessed on August 20, 2024).

[3] M. Higashi, et al., “Flux transfer circuits breaking conventional limit in transfer coefficient based on a negative inductance of a π-junction”, Supercond. Sci. Technol., vol. 37, no. 4, p. 045003, 2024.

[4] H. Hori, et al., “Circuit applications of the negative inductance of a π-junction,” to be presented at Applied Superconductor Conference, 2EPo1B-07, 2024.

[5] H. Ito, et al., “Fabrication of superconductor–ferromagnet–insulator–superconductor Josephson junctions with critical current uniformity applicable to integrated circuits,” Applied Physics Express, vol. 10, no. 3, p. 033101, 2017.

Acknowledgment

This work was supported by the JSPS KAKENHI, Grant Numbers 23H05447, 22H01548 and 23K13376. The circuits were partly fabricated at Qufab, AIST.