Adiabatic Quantum-flux-parametron Logic Research Articles

Adiabatic quantum-flux-parametron boosters for long interconnection and large fanouts

Adiabatic quantum flux parametron (AQFP) is energy-efficient superconducting logic that operates with zero static energy consumption and extremely small dynamic energy consumption thanks to the adiabatic switching of the logic gates. One drawback in AQFP logic circuits is the wire length and fan-out limitations because of the low driving ability of the logic gates, which results in a large circuit area and significant latency. In the present study, we propose AQFP boosters with high driving ability. Two types of AQFP boosters are proposed: one is composed of a parallel connection of AQFP buffers, and the other uses multistage buffers driven by one excitation clock. We evaluated the maximum wire length of the proposed boosters by circuit simulations, including thermal noises, and found that the maximum wire length is 3.9 mm for fan-out one and 1 mm for fan-out four. We implemented the boosters and demonstrated their correct operations at low-speed tests. We also demonstrated a 5-to-31 decoder using the proposed boosters. It was shown that the circuit area, latency, and energy consumption were improved by about 30% compared to the design without the boosters.

A Full-Custom Design Flow and a Top-Down RTL-to-GDS Flow for Adiabatic Quantum-Flux-Parametron Logic Using a Commercial EDA Design Suite

The adiabatic quantum-flux-parametron (AQFP) circuit is a superconductor digital logic family with extremely low power consumption. It consumes five orders less power than the state-of-the-art CMOS circuits and three orders of magnitude less power than RSFQ circuits, another competing digital superconductor technology. The computing resources required by society are increasing every year, and the AQFP circuit is a strong candidate for the next generation of computers. In previous research, a 4-bit MANA microprocessor and a 16-bit Kogge-Stone adder using AQFP logic were designed and demonstrated. These circuits were designed almost by hand, and the development environment needs to be improved to implement AQFP circuits for practical applications. So, we used Synopsys EDA tools typically used for CMOS design to create a full-custom design flow for logic cell design and a top-down flow to design combinational logic circuits automatically. We integrated a circuit design editor with simulation and verification tools for the full-custom design flow. For the top-down flow, we created an environment that automatically performs logic synthesis, path balancing, cell placement, and signal and excitation routing. 1024-bit adders with more than two million Josephson junctions (JJs) have been successfully designed.

An Adiabatic Quantum-Flux-Parametron 8-bit Ripple Carry Adder Using Delay-Line Clocking

Adiabatic quantum-flux-parametron (AQFP) logic is a superconductor logic family that can operate with low switching energy due to adiabatic switching. In a previous study, we proposed a low-latency clocking scheme called delay-line clocking, in which the latency for each logic operation is determined by the propagation delay of the excitation current. We demonstrated several AQFP logic gates with delay-line clocking and demonstrated a phase skipping operation, in which some of the AQFP buffers for phase synchronization are removed to reduce the junction count and energy dissipation. In the present study, we design and demonstrate an AQFP 8-bit ripple carry adder with delay-line clocking to show that delay-line clocking and the phase skipping operation are applicable to large-scale AQFP circuits. The latency of this adder is 960 ps, which is 40% of that for a conventional design. Moreover, due to the phase skipping operation, the junction count is reduced to approximately 70% of that for the conventional design. We find that this adder can operate at up to 4 GHz. The above results indicate that large-scale AQFP circuits can operate with low latency and low junction count by using delay-line clocking and a phase skipping operation.

Sigmoid function generator using stochastic adiabatic superconductor logic

Stochastic-computing-based artificial neural networks (SC-ANNs) can be used to perform hardware- and energy-efficient neuromorphic computing. We have been developing SC-ANNs using an energy-efficient superconductor logic family, namely, adiabatic quantum-flux-parametron (AQFP) logic. AQFP logic is suitable as a building block for SC-ANNs since it can perform stochastic operations with extremely small energy dissipation. In this Letter, we propose and demonstrate a sigmoid function generator (SFG) for AQFP SC-ANNs, which we refer to as the AQFP SFG. An SFG is an important circuit in neural networks that generates outputs from the sum of weighted inputs in accordance with the sigmoid function. The AQFP SFG performs the sigmoid function using a finite state machine based on an AQFP buffer coupled to a flux storage loop. We experimentally demonstrate that the AQFP SFG generates output signals from stochastic bitstreams in accordance with the sigmoid function and that the characteristics of the sigmoid function can be controlled by a bias current. Furthermore, we show that the AQFP SFG operates with small power dissipation due to its simple structure.

Scalable flux controllers using adiabatic superconductor logic for quantum processors

Quantum processors have the potential to accelerate specific computing tasks but are difficult to scale up due to engineering limitations, such as the number of available cables and cooling power for dilution refrigerators for quantum bits (qubits). Hence, it is very important to develop scalable, energy-efficient interface circuits that can control many qubits via a few control lines inside a dilution refrigerator. One of the most important interface circuits is the flux controller (FC), which generates arbitrary dc flux bias to adjust the characteristics of component devices such as qubits. In this paper, we propose and demonstrate FCs using an energy-efficient superconductor logic family, adiabatic quantum-flux-parametron (AQFP) logic. We develop two types of FCs: the AQFP FC and the AQFP/single-flux-quantum (AQFP/SFQ) FC. Both FCs require only a few control lines and have extremely small power dissipation, thus exhibiting high scalability. Furthermore, the AQFP/SFQ FC can control flux bias using ballistic SFQ transmission, which is crucial for integration with qubits. As a proof of concept, we demonstrate AQFP and AQFP/SFQ FCs at 4.2 K, fabricated by the AIST high-speed standard process. Our results indicate that AQFP logic is highly suitable for use as qubit interface circuits for very large-scale quantum processors, especially from the viewpoint of the control line count, power dissipation, and amount of supply currents.

Transmission Line Effects of Long Gate-to-Gate Interconnections in Adiabatic Quantum-Flux-Parametron Logic Circuits

Adiabatic quantum-flux-parametron (AQFP) logic is an energy-efficient superconductor logic family that utilizes adiabatic switching of logic gates. At present, a pure inductance is used to model a gate-to-gate interconnection in AQFP logic circuits. However, it is necessary to consider the transmission line effects when the interconnection length becomes long to take into account the propagation delay. This study investigated the transmission line effects of a long gate-to-gate interconnection in AQFP logic circuits. We observed reflection effects in a long transmission line between AQFP gates. These effects induced errors when the interconnection length exceeded several hundred micrometers. We adopted a damping resistance to stabilize the reflection effect to realize an error-free long gate-to-gate interconnection. The circuit simulations confirmed that a damping resistance connected in parallel to the transmission line effectively stabilizes the reflection effect, enabling an interconnection length that is longer than 1 mm. We fabricated AQFP buffer chains that included a long transmission line with and without a parallel damping resistance, and measured their bit error rates. The results showed that the parallel damping resistance effectively improves the bit error rate at high frequencies.

Adiabatic Quantum-Flux-Parametron: A Tutorial Review

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.

A High-Speed Interface Based on a Josephson Latching Driver for Adiabatic Quantum-Flux-Parametron 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 1 GHz and 4 GHz, respectively.

A 16-Bit Parallel Prefix Carry Look-Ahead Kogge-Stone Adder Implemented in Adiabatic Quantum-Flux-Parametron Logic

Extremely energy-efficient logic devices are required for future low-power high-performance computing systems. Superconductor electronic technology has a number of energy-efficient logic families. Among them is the adiabatic quantum-flux-parametron (AQFP) logic family, which adiabatically switches the quantum-flux-parametron (QFP) circuit when it is excited by an AC power-clock. When compared to state-of-the-art CMOS technology, AQFP logic circuits have the advantage of relatively fast clock rates (5 GHz to 10 GHz) and 5 - 6 orders of magnitude reduction in energy before cooling overhead. We have been developing extremely energy-efficient computing processor components using the AQFP. The adder is the most basic computational unit and is important in the development of a processor. In this work, we designed and measured a 16-bit parallel prefix carry look-ahead Kogge-Stone adder (KSA). We fabricated the circuit using the AIST 10 kA/cm2 High-speed STandard Process (HSTP). Due to a malfunction in the measurement system, we were not able to confirm the complete operation of the circuit at the low frequency of 100 kHz in liquid He, but we confirmed that the outputs that we did observe are correct for two types of tests: (1) critical tests and (2) 110 random input tests in total. The operation margin of the circuit is wide, and we did not observe any calculation errors during measurement.

Low-Latency Adiabatic Quantum-Flux-Parametron Circuit Integrated With a Hybrid Serializer/Deserializer

Adiabatic quantum-flux-parametron (AQFP) logic is an ultra-low-power superconductor logic family. AQFP logic gates are powered and clocked by dedicated clocking schemes using ac excitation currents to implement an energy-efficient switching process, adiabatic switching. We have proposed a low-latency clocking scheme, delay-line clocking, and demonstrated basic AQFP logic gates. In order to test more complex circuits, a serializer/deserializer (SerDes) should be incorporated into the AQFP circuit under test, since the number of input/output (I/O) cables is limited by equipment. Therefore, in the present study we propose and develop a novel SerDes for testing delay-line-clocked AQFP circuits by combining AQFP and rapid single-flux-quantum (RSFQ) logic families, which we refer to as the AQFP/RSFQ hybrid SerDes. The hybrid SerDes comprises RSFQ shift registers to facilitate the data storage during serial-to-parallel and parallel-to-serial conversion. Furthermore, all the component circuits in the hybrid SerDes are clocked by the identical excitation current to synchronize the AQFP and RSFQ parts. We fabricate and demonstrate a delay-line-clocked AQFP circuit (8-to-3 encoder, which is the largest delay-line-clocked circuit ever designed) integrated with the hybrid SerDes at 4.2 K up to 4.5 GHz. Our measurement results indicate that the hybrid SerDes enables the testing of delay-line-clocked AQFP circuits with only a few I/O cables and is thus a powerful tool for the development of very large-scale integration AQFP circuits.

Adiabatic quantum-flux-parametron with delay-line clocking: logic gate demonstration and phase skipping operation

Adiabatic quantum-flux-parametron (AQFP) logic is an energy-efficient superconductor logic family. The latency of AQFP circuits is relatively long compared to that of other superconductor logic families and thus such circuits require low-latency clocking schemes. In a previous study, we proposed a low-latency clocking scheme called delay-line clocking, in which the latency for each logic operation is determined by the propagation delay of the excitation current, and demonstrated a simple AQFP buffer chain that adopts delay-line clocking. However, it is unclear whether more complex AQFP circuits can adopt delay-line clocking. In the present study, we demonstrate AQFP logic gates (AND and XOR gates) that use delay-line clocking as a step towards implementing large-scale AQFP circuits with delay-line clocking. AND and XOR gates with a latency of approximately 20 ps per gate are shown to operate at up to 5 and 4 GHz, respectively, in experiments. We also demonstrate that delay-line clocking enables phase skipping operation, in which some of the AQFP buffers for phase synchronization are removed to reduce the junction count and energy dissipation. The results indicate that delay-line clocking can enable low-latency, low-energy, large-scale AQFP circuits.

A Compact Interface Between Adiabatic Quantum-Flux-Parametron and Rapid Single-Flux-Quantum Circuits

Each superconductor logic family has distinct features and advantages. For instance, adiabatic quantum-flux-parametron (AQFP) circuits operate with very high energy efficiency, and rapid single-flux-quantum (RSFQ) circuits operate at very high clock frequencies. To build a hybrid system that combines the above advantages, we propose a compact interface between AQFP and RSFQ circuits that converts current signals in AQFP logic into flux signals in RSFQ logic using a non-adiabatic quantum-flux-parametron gate. Compared to a previously proposed AQFP/RSFQ interface, the proposed interface has far fewer Josephson junctions (4 vs. 11). We optimize the circuit parameters of the AQFP/RSFQ interface and demonstrate the interface at low speed as proof of concept. Furthermore, we demonstrate data propagation between AQFP circuits along a long passive transmission line via the AQFP/RSFQ interface at low speed to show that the AQFP/RSFQ interface can alleviate the interconnect length limit in AQFP circuits.

An Adiabatic Superconductor Comparator With 46 nA Sensitivity

Adiabatic quantum-flux-parametron (AQFP) circuits can operate with extremely small energy dissipation (∼1 zJ per junction at 5 GHz) and high sensitivity (∼1 μA) owing to adiabatic switching. Thus, AQFP logic is suitable to use as readout interfaces for cryogenic detectors, such as superconducting nanowire single-photon detectors (SSPDs). In order to extend the application of AQFP logic to various detectors, it is crucial to achieve even better sensitivity because some detectors, such as WSi SSPDs and transition edge sensors (TESs), require sub-μA sensitivity. In the present study, we propose a high-sensitivity AQFP comparator with a current transformer (CT), which increases the equivalent input current and thereby improves the sensitivity. Numerical simulation shows that the proposed comparator achieves a sensitivity approximately six times better than that of a conventional AQFP comparator. Furthermore, we demonstrate a sensitivity of 46 nA at 4.2 K for a sampling frequency of 500 Hz in the experiment.

MANA: A Monolithic Adiabatic iNtegration Architecture Microprocessor Using 1.4-zJ/op Unshunted Superconductor Josephson Junction Devices

We conducted the first successful demonstration of an adiabatic microprocessor based on unshunted Josephson junction (JJ) devices manufactured using a Nb/AlO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> /Nb superconductor IC fabrication process. It is a hybrid of RISC and dataflow architectures operating on 4-b data words. We demonstrate register file R/W access, ALU execution, hardware stalling, and program branching performed at 100 kHz under the cryogenic temperature of 4.2 K. We also successfully demonstrated a high-speed breakout chip of the microprocessor execution units up to 2.5 GHz. We use a logic primitive called the adiabatic quantum-flux-parametron (AQFP), which has a switching energy of 1.4 zJ per JJ when driven by a four-phase 5-GHz sinusoidal ac-clock at 4.2 K. These demonstrations show that AQFP logic is capable of both processing and memory operations and that we have a path toward practical adiabatic computing operating at high-clock rates while dissipating very little energy.

Binary Counters Using Adiabatic Quantum-Flux-Parametron Logic

Adiabatic quantum-flux-parametron (AQFP) logic is an energy-efficient superconductor logic family. In this article, we design binary counters, namely an up counter, a down counter, and an up/down counter, based on AQFP logic. These binary counters are T-flip-flop-based and count logic 1s in the input signal that is synchronized with excitation currents, which clock the counters. The internal state of a T flip-flop changes when the internal state of the previous T flip-flop changes from logic 1 to 0 and from logic 0 to 1 for the count-up and count-down operations, respectively. Each internal state of a T flip-flop is read out serially by a buffer chain coupled to the T flip-flops. We fabricate 4-bit up, down, and up/down counters using the AIST 10 kA/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> Nb high-speed standard process and demonstrate their correct operation at low frequency. This is the first demonstration of binary counters based on AQFP logic.

Scalable readout interface for superconducting nanowire single-photon detectors using AQFP and RSFQ logic families.

We propose a scalable readout interface for superconducting nanowire single-photon detector (SSPD) arrays, which we call the AQFP/RSFQ interface. This interface is composed of adiabatic quantum-flux-parametron (AQFP) and rapid single-flux-quantum (RSFQ) logic families. The AQFP part reads out the spatial information of an SSPD array via a single cable, and the RSFQ part reads out the temporal information via a single cable. The hybrid interface has high temporal resolution owing to low timing jitter in the operation of the RSFQ part. In addition, the hybrid interface achieves high circuit scalability because of low supply current in the operation of the AQFP part. Therefore, the hybrid interface is suitable for handling many-pixel SSPD arrays. We demonstrate a four-pixel SSPD array using the hybrid interface as proof of concept. The measurement results show that the hybrid interface can read out all of the pixels with a low error rate and low timing jitter.

Low-latency power-dividing clocking scheme for adiabatic quantum-flux-parametron logic

Adiabatic quantum-flux-parametron (AQFP) logic is a highly energy-efficient superconductor logic family. Traditionally, AQFP circuits have relied on the four-phase clocking scheme, which uses a pair of ac current sources with a 90° phase difference. The operation of each logic gate thus takes a quarter clock cycle, leading to a relatively long latency for some applications. In this Letter, we propose a low-latency clocking scheme for AQFP logic based on microwave power dividers (PDs). The whole circuit is powered by a single excitation current, which is equally split for each logic stage by a serial-type PD. As a result, the latency between adjacent logic stages is determined by the transmission line length (propagation delay) inside the PD, which can be much shorter than a quarter clock cycle. Note that the low-latency performance is independent of the horizontal length of the AQFP circuit, and thus, the proposed clocking scheme is applicable to large-scale designs where a large number of gates are horizontally placed in a single stage. For validation, several numerical simulations are conducted and a six-stage AQFP test circuit is demonstrated using the proposed power-dividing clocking scheme (with a designed latency of 20 ps per gate) at a temperature of 4.2 K.

A compact AQFP logic cell design using an 8-metal layer superconductor process

Adiabatic quantum-flux-parametron (AQFP) is an adiabatic logic based on the quantum-flux-parametron. It has extremely low switching energy, as well as high signal gain and high robustness. In this work, we present the development of an AQFP cell library using the MIT LL 100 μA μm−2 superconductor electronics fabrication process, SFQ5ee. Four types of basic sub-cells, i.e. buffer, inverter, constant, and branch, are designed as the building blocks for combinational AQFP logic cells. Taking advantage of the 8 metal layers, we place the dc superconducting quantum interference device (SQUID) part of a buffer above the ground plane and the signal transformer part below the ground plane to mitigate unwanted couplings. In addition, by vertically overlapping the signal transformer and the dc SQUID, the dimension of a buffer is reduced to 15 μm × 20 μm, which is only 30% of that of the conventional design. More complex AQFP logic cells, such as the majority gate, AND gate, and OR gate, are designed by arraying the sub-cells together. Correct operations and wide excitation current margins are confirmed for the established AQFP logic cells by both simulation and experiments.

Design and Demonstration of an Adiabatic-Quantum-Flux-Parametron Field-Programmable Gate Array Using Josephson-CMOS Hybrid Memories

Adiabatic quantum-flux-parametron (AQFP) logic is a promising technology for future energy-efficient high-performance information processing systems. Its static power is zero because of ac flux bias, and its dynamic power is considerably reduced, thanks to the adiabatic switching of the junctions. The lack of high-density memories in the AQFP logic, however, makes it challenging to realize large-scale information processing systems with the use of pure AQFP circuits. We have been developing a Josephson-CMOS hybrid memory to overcome the memory bottleneck in AQFP digital systems. By utilizing the high sensitivity of the AQFP gate, the output current from CMOS memories can be significantly decreased resulting in the reduction of the power consumption. In this article, we designed and fabricated a low-power area-efficient AQFP-CMOS hybrid field-programmable gate array (FPGA), where a CMOS memory is utilized as a rewritable read-only memory to control the AQFP circuits. The AQFP circuit for the AQFP-CMOS hybrid FPGA is composed of logic blocks, switch blocks, and connection blocks, which are clocked by four-phase excitation currents. The AQFP-CMOS hybrid FPGA is fabricated by using the AIST 10 kA/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> Nb high-speed standard process and the Rohm 0.18 μm CMOS process. The area and power consumption of the two-by-two AQFP logic-cell system are estimated to be approximately 6.56 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and 12.4 nW at 5 GHz operations, respectively. The power consumption of the CMOS memory was estimated to be 1.02 μW assuming the CMOS source voltage of 3 mV. We demonstrated the operation of the AQFP-CMOS hybrid FPGA at low speed by combining the AQFP logic and the CMOS memory.

Systematic method to evaluate energy dissipation in adiabatic quantum-flux-parametron logic

Adiabatic quantum-flux-parametron (AQFP) logic is an energy-efficient superconductor logic. It operates with zero static power dissipation and very low dynamic power dissipation owing to adiabatic switching. In previous numerical studies, we have evaluated the energy dissipation of basic AQFP logic gates and demonstrated sub-kBT switching energy, where kB is Boltzmann's constant and T is the temperature, by integrating the product of the excitation current and voltage associated with the gates over time. However, this method is not applicable to complex logic gates, especially those in which the number of inputs is different from the number of outputs. In this study, we establish a systematic method to evaluate the energy dissipation of general AQFP logic gates. In the proposed method, the energy dissipation is calculated by subtracting the energy dissipation of the peripheral circuits from that of the entire circuit. In this way, the energy change due to the interaction between gates, which makes it difficult to evaluate the energy dissipation, can be deducted. We evaluate the energy dissipation of a majority gate using this method.