Abstract Body

A traveling-wave parametric amplifier (TWPA) is utilized to increase the readout fidelity of superconducting qubits. More than 2,000 junctions are implemented in TWPAs, which adopt Josephson junctions (JJs) as a part of transmission lines, for increasing the amplification [1]. Since the size variation in fabricated JJs affects the amplification characteristics, it has been recognized as a challenge to improve the manufacturing yield of TWPA across a wafer. Our aim is to increase the manufacturing yield of TWPA where the amplification in wide frequency region is stabilized. A sample is fabricated by the superconducting multi-layer process [2], which has a precise controllability of JJ fabrication with uniformity across the wafer. Deviation of the characteristics (L, I_c, etc.) in the sample is evaluated at 4.2 K. We study co-optimization of design and fabrication in TWPA by clarifying impact of JJ size variation on amplification characteristics through both simulation and experiment.

TWPA is composed of repeated unit cells where a phase matching is adopted in every three cycles as similarly in Ref [1]. The circuit parameters are designed to increase the manufacturing yield by taking into account the alignment margin, with particular focus on the JJs and via interconnections between superconducting multi-layers. To reduce the size variation of JJs, the junction size is set to 2 um square. An oxidation condition for forming JJs is controlled so that a critical current (I_c) is 4 uA. Figure 1(a) shows the simulation results of the amplification characteristics for the input signal. The blue line shows the amplification calculated using commonly available JosephsonCircuit [3]. The orange line is the result of the simulation using JoSIM [4], which implements the circuit of TWPA. Since JoSIM performs time-domain analysis, the input, idler, and pump signals can be obtained simultaneously, which allows for verification of the phase matching (delta-k = 0). The results calculated by JoSIM are converted to frequency-domain characteristics by the fast Fourier transform. In the 3-5 GHz region and at the edge of the stop-band, quantitative agreement between the two calculations is observed. In the 5-7.5 GHz region, the average value of JoSIM corresponds to the JosephsonCircuit characteristics. Oscillations are observed in the results of JoSIM. This may be due to the difference in criteria for the convergence conditions between the two simulations; JosephsonCircuit sometimes outputs anomalous characteristics when the convergence conditions are not met in the iteration. We will investigate the cause of the oscillation by both simulation and experiment. Note that our simulation adopts the standard deviation as a parameter in order to clarify impact of fabrication variation (Dev.). The results at Dev. of 1-2% are shown in Fig. 1(b). The margin-aware design ensures that the amplification characteristics are maintained even at Dev. of 2 %. No amplification characteristics were observed at Dev. of 10 %.

To establish the TWPA process, a test chip is fabricated and the value of Dev. is experimentally investigated. (Fig. 1(c)). In the presentation, we will show the controllability of the junction variation across the wafer by experiment. The amplification characteristics of TWPA with the Dev. evaluated from experiment and the method of co-optimization will be discussed.

References

[1] C. Macklin et al., Science 350 (2015) 307.
[2] M. Hidaka et al.: “Fabrication process of superconducting flux qubits for quantum annealing,” Proceedings in 14th Superconducting SFQ VLSI Workshop and 3rd Workshop on Quantum and Classical Cryogenic Devices, Circuits and Systems (2021).
[3] https://github.com/kpobrien/JosephsonCircuits.jl
[4] J. Delport et al., IEEE Trans. Appl. Supercond., 29 (2019) 1300905.

Figure 1 (a) The simulation results of the amplification characteristics in TWPA. (b) The gain analysis at 6 GHz using JoSIM with size variation of JJs. (c) Test chip design.