The extremely low-bit energy characteristic of the adiabatic quantum-flux-parametron (AQFP) circuit makes it a promising candidate for highly energy-efficient computing systems. However, in contrast with conventional circuit design, general logic synthesis tools can not make sure that the circuit functionality of generated AQFP circuits is correct. AQFP circuits require buffer and splitter insertion for dataflow synchronization at all clock phases of the circuit and multifan-out driving. Notably, buffers and splitters inserted take up much area and delay in AQFP circuits, also causing a significant increase in energy dissipation. To address this problem, this article analyses in detail why buffer and splitter insertion is necessary for AQFP circuits and proposes a global optimization framework for this purpose. This framework consists of three parts: 1) logic level assignment; 2) splitter tree generation; and 3) buffer insertion. An integer linear programming algorithm is proposed for the logic level assignment to estimate the globally optimal number of inserted buffers and splitters. Subsequently, a dynamic programming-based multiway search tree generation algorithm is proposed to construct an optimal splitter tree for each net of the input circuit. Moreover, three optimization strategies are proposed to further enhance the effectiveness and efficiency of our framework. Experimental results on ISCAS’85 and EPFL benchmarks demonstrate the effectiveness and efficiency of our proposed framework compared with the state-of-the-art, particularly with significant advantages on large circuits.

Reversible computing has garnered significant attention as a promising avenue for achieving energy-efficient computing systems, particularly within the realm of quantum computing. The reversible quantum-flux-parametron (RQFP) is the first practical reversible logic gate utilizing adiabatic superconducting devices, with experimental evidence supporting both its logical and physical reversibility. Each RQFP logic gate operates on alternating current (AC) power and features three input ports and three output ports. Notably, each output port is capable of implementing a majority function while driving only a single fan-out. Additionally, the three inputs to each gate must arrive in the same clock phase. These inherent characteristics present substantial challenges in the design of RQFP logic circuits. To address these challenges, this article proposes an automatic synthesis framework for RQFP logic circuit design based on efficient Cartesian genetic programming (CGP). The framework aims to minimize both the number of RQFP logic gates and the number of garbage outputs within the generated RQFP logic circuit. It incorporates the specific characteristics of the RQFP logic circuit by encoding them into the genotype of a CGP individual. It also introduces several point mutation operations to facilitate the generation of new individuals. Furthermore, the framework integrates circuit simulation with formal verification to assess the functional equivalence between the parent and its offspring. Experimental results on RevLib and reversible reciprocal circuit benchmarks demonstrate the effectiveness of our framework.

Superconducting circuits, like Adiabatic Quantum- Flux-Parametron (AQFP), offer exceptional energy efficiency but face challenges in physical design due to sophisticated spacing and timing constraints. Current design tools often neglect the importance of constraint adherence throughout the entire design flow. In this paper, we propose SuperFlow, a fully-customized RTL-to-GDS design flow tailored for AQFP devices. SuperFlow leverages a synthesis tool based on CMOS technology to transform any input RTL netlist to an AQFP-based netlist. Subsequently, we devise a novel place-and-route procedure that simultaneously con-siders wirelength, timing, and routability for AQFP circuits. The process culminates in the generation of the AQFP circuit layout, followed by a Design Rule Check (DR C) to identify and rectify any layout violations. Our experimental results demonstrate that SuperFlow achieves 12.8% wirelength improvement on average and 12.1 % better timing quality compared with previous state- of-the-art placers for AQFP circuits.

We consider the problem of safe multi-agent motion planning for drones in uncertain, cluttered workspaces. For this problem, we present a tractable motion planner that builds upon the strengths of reinforcement learning and constrained-control-based trajectory planning. First, we use single-agent reinforcement learning to learn motion plans from data that reach the target but may not be collision-free. Next, we use a convex optimization, chance constraints, and set-based methods for constrained control to ensure safety, despite the uncertainty in the workspace, agent motion, and sensing. The proposed approach can handle state and control constraints on the agents, and enforce collision avoidance among themselves and with static obstacles in the workspace with high probability. The proposed approach yields a safe, real-time implementable, multi-agent motion planner that is simpler to train than methods based solely on learning. Numerical simulations and experiments show the efficacy of the approach.

As a highly energy-efficient application of low-temperature superconductivity, the adiabatic quantum-flux-parametron (AQFP) logic circuit has characteristics of extremely low-power consumption, making it an attractive candidate for extremely energy-efficient computing systems. Since logic gates are driven by the alternating current (AC) serving as the clock signal in AQFP circuits, plenty of AQFP buffers are required to ensure that the dataflow is synchronized at all logic levels of the circuit. Meanwhile, since the currently developed AQFP logic gates can only drive a single output, splitters are required by logic gates to drive multiple fan-outs. These gates take up a significant amount of the circuit's area and delay. This paper proposes a global optimization algorithm for buffer and splitter (B/S) insertion to address the issues above. The B/S insertion is first identified as a combinational optimization problem, and a dynamic programming formulation is presented to find the global optimal solution. Due to the limitation of its impractical search space, an integer linear programming formulation is proposed to explore the global optimization of B/S insertion approximately. Experimental results on the ISCAS'85 and simple arithmetic benchmark circuits show the effectiveness of the proposed method, with an average reduction of 8.22% and 7.37% in the number of buffers and splitters inserted compared to the state-of-the-art methods from ICCAD'21 and DAC'22, respectively.

Adiabatic quantum-flux-parametron (AQFP) logic, an energy-efficient superconductor logic with no static power consumption and ultra-low switching energy, is a promising candidate for energy-efficient computing systems. Due to the native majority function in AQFP logic, which can represent more complex logic with the same cost as the AND/OR function, the design of AQFP circuits differs from AND-OR-inverter-based logic circuits. Besides, AQFP logic has the path balancing requirement and fan-out limitation, making traditional majority-based logic optimization methods not applicable. This paper proposes a global optimization method over the majority-inverter graph (MIG) to minimize the JJ number and circuit depth of AQFP circuits. MIG-based transformation methods are first illustrated to construct the feasible domain. The normalized energy-delay-product (EDP), the product of the JJ number and circuit depth of AQFP circuits, is used as the objective function. Then, Bayesian optimization is used to explore the global optimal transformation sequence applied to AQFP MIG-based logic optimization. Experimental results show that the proposed method has a significant improvement in the JJ number and circuit depth compared with the state-of-the-art.

Reversible computing, deriving its inspiration from Landauer's principle, has captured significant interest as a promising technology for logic operations without energy dissipation. The reversible quantum-flux-parametron (RQFP) stands as the first practical reversible logic gate using adiabatic superconducting devices, whose logical and physical reversibility has been experimentally demonstrated. However, due to its unique logic function and structure, the design of RQFP logic circuits is a highly challenging task. At present, there are no automated design tools available for RQFP logic. Therefore, this paper proposes the first exact logic synthesis algorithm for RQFP logic. It formulates the synthesis problem as the Boolean satisfiability problem and subsequently constructs and calls upon the incremental propositional logic model iteratively for optimal synthesis with the least number of gates and garbage outputs. Experimental results on the reversible logic benchmark from RevLib demonstrate the effectiveness of the proposed algorithm.

Addressing the pressing need for energy-efficient computing technologies, innovations such as Josephson junctions-based superconducting logic circuits, particularly the Adiabatic Quantum-Flux-Parametron (AQFP) logic, have sparked increased research interest. AQFP logic, boasting superior energy efficiency, faces unique design challenges. The current 4-phase clocking scheme results in considerable circuit latency, a problem further amplified with larger logic depth in the circuit. A novel delay-line clocking scheme proposes increasing the number of clock phases, which could significantly improve circuit latency but also risks more severe timing violations. To address this issue, this paper proposes DLPlace, the first placement framework tailored for the delay-line clocking scheme, aiming to boost the performance of AQFP circuits. DLPlace formulates timing-aware global placement as a Lagrangian problem, targeting minimizing the circuit latency, to determine the positions of all gates and the delays of delay lines by the subgradient method. A timing-aware detailed placement approach is then proposed, where DLPlace introduces a row-wise gate order rearrangement method to reduce wirelength and timing violations in AQFP circuits. Furthermore, a dynamic programming approach is employed to achieve wirelength and timing legalization, thereby addressing the unique requirements of AQFP logic. The effectiveness of DLPlace is validated through AQFP benchmark experiments, demonstrating a significant reduction in both hardware footprint and circuit latency compared to the baselines. This new framework paves the way for the further optimization of AQFP circuit performance, offering a promising solution to the physical design challenges in superconductive electronics-based computing.

Adiabatic Quantum-Flux-Parametron (AQFP) is a superconducting logic with extremely high energy efficiency. By employing the distinct polarity of current to denote logic ‘0’ and ‘1’, AQFP devices serve as excellent carriers for binary neural network (BNN) computations. Although recent research has made initial strides toward developing an AQFP-based BNN accelerator, several critical challenges remain, preventing the design from being a comprehensive solution. In this paper, we propose SupeRBNN, an AQFP-based randomized BNN acceleration framework that leverages software-hardware co-optimization to eventually make the AQFP devices a feasible solution for BNN acceleration. Specifically, we investigate the randomized behavior of the AQFP devices and analyze the impact of crossbar size on current attenuation, subsequently formulating the current amplitude into the values suitable for use in BNN computation. To tackle the accumulation problem and improve overall hardware performance, we propose a stochastic computing-based accumulation module and a clocking scheme adjustment-based circuit optimization method. To effectively train the BNN models that are compatible with the distinctive characteristics of AQFP devices, we further propose a novel randomized BNN training solution that utilizes algorithm-hardware co-optimization, enabling simultaneous optimization of hardware configurations. In addition, we propose implementing batch normalization matching and the weight rectified clamp method to further improve the overall performance. We validate our SupeRBNN framework across various datasets and network architectures, comparing it with implementations based on different technologies, including CMOS, ReRAM, and superconducting RSFQ/ERSFQ. Experimental results demonstrate that our design achieves an energy efficiency of approximately 7.8 × 104 times higher than that of the ReRAM-based BNN framework while maintaining a similar level of model accuracy. Furthermore, when compared with superconductor-based counterparts, our framework demonstrates at least two orders of magnitude higher energy efficiency.

Adiabatic Quantum-Flux-Parametron (AQFP) is a superconducting logic with extremely high energy efficiency. AQFP circuits adopt the deep pipeline structure, where the four-phase AC-power serves as both the energy supply and the clock signal and transfers the data from one clock phase to the next. However, the deep pipeline structure causes the stage delay of the data propagation is comparable to the delay of the zigzag clocking, which triggers timing violations easily. In this paper, we propose a timing-aware analytical strategy for the AQFP placement, TAAS, that immensely reduces timing violations under specific spacing constraints and wirelength constraints of AQFP. TAAS includes two main characteristics: 1) a timing-aware objective function that incorporates a four-phase timing model for the analytical global placement. 2) a unique detailed placement including the timing-aware dynamic programming technique and the time-space cell regularization. To validate the effectiveness of TAAS, various representative circuits are adopted as benchmarks. As shown in the experimental results, our strategy can increase the maximum operating frequency by up to 30% ~ 40% with a negligible wirelength increase -3.41%~1%.

We study the problem of safe multi-agent motion planning in cluttered environments. Existing multi-agent reinforcement learning-based motion planners only provide approximate safety enforcement. We propose a safe reinforcement learning algorithm that leverages single-agent reinforcement learning for target regulation and a subsequent convex optimization-based filtering that ensures the collective safety of the system. Our approach yields a safe, real-time implementable multi-agent motion planner that is simpler to train and enforces safety as hard constraints. Our approach can handle state and control constraints on the agents, and enforce collision avoidance among themselves and with static obstacles in the environment. Numerical simulations and hardware experiments show the efficacy of the approach.

Adiabatic Quantum-Flux-Parametron (AQFP) superconducting technology exhibits a high energy efficiency among superconducting electronics, however lacks effective design automation tools. In this work, we develop the first, efficient placement and routing framework for AQFP circuits considering the unique features and constraints, using MIT-LL technology as an example. Our proposed placement framework iteratively executes a fixed-order, row-wise placement algorithm, where the row-wise algorithm derives optimal solution with polynomial-time complexity. To address the maximum wirelength constraint issue in AQFP circuits, a whole row of buffers (or even more rows) is inserted. A* routing algorithm is adopted as the backbone algorithm, incorporating dynamic step size and net negotiation process to reduce the computational complexity accounting for AQFP characteristics, improving overall routability. Extensive experimental results demonstrate the effectiveness of our proposed framework.

Adiabatic Quantum-Flux-Parametron (AQFP) is a superconducting logic with very low energy dissipation. Each AQFP cell is driven by AC-power to serve as both power supply and clock signal. The clock signals trigger the data flow from one clock phase to the next clock phase, and the delay for each output in the same phase has to be equal. At the same time, the signal current attenuates as the wire becomes longer. When a wire exceeds a maximum length, the weak current causes incorrect data. Thus, rows of buffers have to be inserted as repeaters to satisfy both delay synchronization and wirelength constraint. These inserted buffers significantly increase the power consumption and also the total delay of AQFP circuits. In this paper, we propose an analytical strategy for AQFP placement (ASAP) to provide effective placement results that greatly reduce the number of additional inserted buffers. ASAP includes two main characteristics: 1) a new wire-length function for analytical global placement and 2) detailed placement including fixed-order Lagrangian relaxation and cell balancing algorithm. Experimental results show the efficiency of ASAP framework and a 53% reduction of buffers over the state-of-the-art method.

Adiabatic Quantum-Flux-Parametron (AQFP) logic is an adiabatic superconductor logic that has been proposed as alternative to CMOS logic with extremely high energy efficiency. In AQFP technology, majority-based gates have the same area as two-input AND/OR gates while offering more complex logic. Therefore, majority-based logic (MAJ) is more preferred than and-or-inverter-based logic (AOI) to implement logic functions in AQFP for higher energy efficiency. In this paper, we propose a majority gates synthesis framework for AQFP circuits that is capable of converting any AOI netlist to its corresponding MAJ netlist by mapping all feasible three-input sub- netlists to corresponding MAJ based implementations. In addition, the proposed tool can insert the optimal amount of buffers and splitters for equivalent delay as required in the AQFP technology. Experimental results suggest that the proposed method can reduce delay and area by up to 60.00% and 60.98%, respectively.

Adiabatic Quantum-Flux-Parametron (AQFP) logic is an adiabatic superconductor logic that has been proposed as alternative to CMOS logic with extremely high energy efficiency. In AQFP technology, gates are driven by AC-power, which also serves as clock signal to synchronize the outputs of all gates in the same clock phase. As a matter of fact, AQFP circuits may require huge amount of buffers and splitters to be inserted to allow inputs to any gate having equal delay. Existing buffer and splitter insertion method does not deliver optimization, which could lead to huge space and delay overhead. A better automated buffer and splitter framework is imminent for more efficient AQFP circuits design. In this paper, we propose an automated buffer and splitter insertion method that is capable of adding optimized amount of buffers and splitters to any given gate-level netlist to achieve equal delay for all gates. The proposed method achieve equal delay by inserting buffers and splitters with any library limitation on the size of splitters. Experimental results suggest that the proposed method can deliver better results compared with the existing method, with up-to 40.84% less in size and 3.13% less in delay when splitter fan-out size is limited to four.

The Adiabatic Quantum-Flux-Parametron (AQFP) superconducting technology has been recently developed, which achieves the highest energy efficiency among superconducting logic families, potentially 104--105 gain compared with state-of-the-art CMOS. In 2016, the successful fabrication and testing of AQFP-based circuits with the scale of 83,000 JJs have demonstrated the scalability and potential of implementing large-scale systems using AQFP. As a result, it will be promising for AQFP in high-performance computing and deep space applications, with Deep Neural Network (DNN) inference acceleration as an important example.

Single-flux quantum logic (SFQ) circuits, in which a flux quantum is used as an information carrier, have the possibility for opening the door to a new digital system operated at over 100-GHz clock frequency at extremely low power dissipation. The SFQ logic system is a so-called pulse logic, which is completely different from the level logic for semiconductors like CMOS, so circuit design technologies for SFQ logic circuits have to be newly developed. Recently, much progress in basic technologies for designing SFQ circuits and operating circuits at high speeds has been made. With advances in these design tools, large-scale circuits including more than several thousand junctions can be easily operated with the clock frequency of more than several tens of gigahertz. High-end routers and high-end computers are possible applications of SFQ logic circuits because of their high throughput nature and the low power dissipation of SFQ logic. In this paper, recent advances of SFQ circuit design technologies and recent developments of switches for high-end routers and microprocessors for high-end computers that are considered possible applications for SFQ logic will be described.