The adiabatic quantum-flux-parametron (AQFP) is an energy-efficient superconductor logic element based on the quantum flux parametron. AQFP circuits can operate with energy dissipation near the thermodynamic and quantum limits by maximizing the energy efficiency of adiabatic switching. We have established the design methodology for AQFP logic and developed various energy-efficient systems using AQFP logic, such as a low-power microprocessor, reversible computer, single-photon image sensor, and stochastic electronics. We have thus demonstrated the feasibility of the wide application of AQFP logic in future information and communications technology. In this paper, we present a tutorial review on AQFP logic to provide insights into AQFP circuit technology as an introduction to this research field. We describe the historical background, operating principle, design methodology, and recent progress of AQFP logic.

The adiabatic quantum flux parametron (AQFP) is an energy-efficient, high-speed superconducting logic device. To observe the tiny output currents from the AQFP in experiments, high-speed voltage drivers are indispensable. In the present study, we develop a compact voltage driver for AQFP logic based on a Josephson latching driver (JLD), which has been used as a high-speed driver for rapid single-flux-quantum (RSFQ) logic. In the JLD-based voltage driver, the signal currents of AQFP gates are converted into gap-voltage-level signals via an AQFP/RSFQ interface and a four-junction logic gate. Furthermore, this voltage driver includes only 15 Josephson junctions, which is much fewer than in the case for the previously designed driver based on dc superconducting quantum interference devices (60 junctions). In measurement, we successfully operate the JLD-based voltage driver up to 4 GHz. We also evaluate the bit error rate (BER) of the driver and find that the BER is 7.92×10-10 and 2.67×10-3 at 1GHz and 4GHz, respectively.

The adiabatic quantum-flux-parametron (AQFP) is an energy-efficient superconductor logic device. In a previous study, we proposed a low-latency clocking scheme called delay-line clocking, and several low-latency AQFP logic gates have been demonstrated. In delay-line clocking, the latency between adjacent excitation phases is determined by the propagation delay of excitation currents, and thus the rising time of excitation currents should be sufficiently small; otherwise, an AQFP gate can switch before the previous gate is fully excited. This means that delay-line clocking needs high clock frequencies, because typical excitation currents are sinusoidal and the rising time depends on the frequency. However, AQFP circuits need to be tested in a wide frequency range experimentally. Hence, in the present study, we investigate AQFP circuits adopting delay-line clocking with square excitation currents to apply delay-line clocking in a low frequency range. Square excitation currents have shorter rising time than sinusoidal excitation currents and thus enable low frequency operation. We demonstrate an AQFP buffer chain with delay-line clocking using square excitation currents, in which the latency is approximately 20ps per gate, and confirm that the operating margin for the buffer chain is kept sufficiently wide at clock frequencies below 1GHz, whereas in the sinusoidal case the operating margin shrinks below 500MHz. These results indicate that AQFP circuits adopting delay-line clocking can operate in a low frequency range by using square excitation currents.

We have been studying a superconducting quantum-computing system where superconducting qubits are controlled and read out by rapid single-flux- quantum (RSFQ) circuits. In this study, we designed and fabricated an RSFQ microwave chopper, which turns on and off an externally applied microwave to control qubit states with the time resolution of sub-nanosecond. The chopper is implemented in a microwave module and mounted in a dilution refrigerator. We tested the microwave chopper at 4.2 K. The amplitude of the output microwave was approximately 100 µV which is much larger than that of previously designed chopper. We also confirmed that the irradiation time can be controlled by RSFQ control circuits.

We have been investigating reversible quantum-flux-parametron (RQFP), which is a reversible logic gate using adiabatic quantum-flux-parametron (AQFP), toward realizing superconductor reversible computing. In this paper, we review the recent progress of RQFP. Followed by a brief explanation on AQFP, we first review the difference between irreversible logic gates and RQFP in light of time evolution and energy dissipation, based on our previous studies. Numerical calculation results reveal that the logic state of RQFP can be changed quasi-statically and adiabatically, or thermodynamically reversibly, and that the energy dissipation required for RQFP to perform a logic operation can be arbitrarily reduced. Lastly, we show recent experimental results of an RQFP cell, which was newly designed for the latest cell library. We observed the wide operation margins of more than 4.7dB with respect to excitation currents.

We have studied ultra-low-power superconductor circuits using adiabatic quantum flux parametron (AQFP) logic. Latches, which store logic data in logic circuits, are indispensable logic elements in the realization of AQFP computing systems. Among them, feedback latches, which hold data by using a feedback loop, have advantages in terms of their wide operation margins and high stability. Their drawbacks are their large junction counts and long latency. In this paper, we propose a majority gate-based feedback latch for AQFP logic with a reduced number of junctions. We designed and fabricated the proposed AQFP latches using a standard National Institute of Advanced Industrial Science and Technology (AIST) process. The measurement results showed that the feedback latches operate with wide operation margins that are comparable with circuit simulation results.

We describe a calculation tool and modeling methods to find self and mutual inductance and current distribution in superconductive multilayer circuit layouts. Accuracy of the numerical solver is discussed and compared with experimental measurements. Effects of modeling parameter selection on calculation results are shown, and we make conclusions on the selection of modeling parameters for fast but sufficiently accurate calculations when calibration methods are used. Circuit theory for the calculation of branch impedances from the output of the numerical solver is discussed, and compensation for solution difficulties is shown through example. We elaborate on the construction of extraction models for superconductive integrated circuits, with and without resistive branches. We also propose a method to calculate current distribution in a multilayer circuit with multiple bias current feed points. Finally, detailed examples are shown where the effects of stacked vias, bias pillars, coupling, ground connection stacks and ground return currents in circuit layouts for the AIST advanced process (ADP2) and standard process (STP2) are analyzed. We show that multilayer inductance and current distribution extraction in such circuits provides much more information than merely branch inductance, and can be used to improve layouts; for example through reduced coupling between conductors.

We developed a Nb 4-layer process for fabricating superconducting integrated circuits that involves using caldera planarization to increase the flexibility and reliability of the fabrication process. We call this process the planarized high-speed standard process (PHSTP). Planarization enables us to flexibly adjust most of the Nb and SiO2 film thicknesses; we can select reduced film thicknesses to obtain larger mutual coupling depending on the application. It also reduces the risk of intra-layer shorts due to etching residues at the step-edge regions. We describe the detailed process flows of the planarization for the Josephson junction layer and the evaluation of devices fabricated with PHSTP. The results indicated no short defects or degradation in junction characteristics and good agreement between designed and measured inductances and resistances. We also developed single-flux-quantum (SFQ) and adiabatic quantum-flux-parametron (AQFP) logic cell libraries and tested circuits fabricated with PHSTP. We found that the designed circuits operated correctly. The SFQ shift-registers fabricated using PHSTP showed a high yield. Numerical simulation results indicate that the AQFP gates with increased mutual coupling by the planarized layer structure increase the maximum interconnect length between gates.