Single Flux Quantum (SFQ) digital logic offers a promising path to energy-efficient, high-performance computing, but faces significant scalability challenges–particularly due to the area overhead associated with gate-level path balancing and the pipelining of splitter trees. Prior efforts to reduce this overhead often unnecessarily compromise throughput, diminishing SFQ’s key performance advantage. To mitigate this, we propose a timing-aware optimization framework that unifies and enhances both traditional full path balancing (FPB) and multi-phase clocking approaches. Inspired by timing-driven EDA strategies in CMOS, our approach explicitly models gate delays and jointly optimizes clock phase assignments, pipelining, and splitter tree construction, minimizing area and latency overhead while achieving a given performance target. On benchmark circuits, our timing-aware 2-phase clocking achieves up to 30% area and 29% latency reductions over FPB at a 27ps clock period. Compared to prior multi-phase methods operating at 42ps, we achieve 22% lower area and 23% lower latency. At a tighter 21ps performance target, our timing-aware single-phase clocking improves area and latency by 28% and 7%, respectively. All optimizations are implemented using scalable, polynomial-time algorithms.

Rapid single-flux quantum (RSFQ) is one of the most advanced superconductive electronics technologies. SFQ systems operate at tens of gigahertz with up to three orders of magnitude smaller power as compared to CMOS. In conventional SFQ systems, most gates require clock signal. Each gate should have the fanins with equal logic depth, necessitating insertion of path-balancing (PB) DFFs, incurring prohibitive area penalty.Multiphase clocking is the effective method for reducing the path-balancing overhead at the cost of reduced throughput. However, existing tools are not directly applicable for technology mapping of multiphase systems. To overcome this limitation, in this work, we propose a technology mapping tool for multiphase systems. Our contribution is threefold. First, we formulate a phase assignment as a Constraint Programming with Satisfiability (CP-SAT) problem, to determine the phase of each element within the network. Second, we formulate the path balancing problem as a CP-SAT to optimize the number of DFFs within an asynchronous datapath. Finally, we integrate these methods into a technology mapping flow to convert a logic network into a multiphase SFQ circuit. In our case studies, by using seven phases, the size of the circuit (expressed as the number of Josephson junctions) is reduced, on average, by 59.94 % as compared to the dual (fast-slow) clocking method, while outperforming the state-of-the-art single-phase SFQ mapping tools.

Rapid single-flux quantum (RSFQ) is one of the most advanced cryogenic superconductive electronics technologies. With orders of magnitude smaller power dissipation, RSFQ is an attractive technology for cloud computing, aerospace electronics, and high-speed interfacing with quantum computing systems. Technological challenges however greatly complicate the realization of VLSI-complexity RSFQ systems. For example, gate-level pipelining in SFQ systems incurs a significant area overhead due to the need for path balancing. This issue is particularly detrimental to SFQ systems due to the limited layout density of RSFQ systems.

Superconducting electronics provide us with cryogenic digital circuits that can rival established technologies in performance and energy consumption. Today, the lack of tools for the design of large-scale integrated superconducting circuits is a major obstacle to their deployment. Few research institutions and companies have contributed to making such tools available. This review focuses on methods, algorithms, and open-source design tools for logic synthesis of superconducting circuits in two major families: single-flux quantum (SFQ) circuits and adiabatic quantum flux parametron (AQFP).

Rapid single-flux quantum (RSFQ), a leading cryogenic superconductive electronics (SCE) technology, offers extremely low power dissipation and high speed. However, implementing RSFQ systems at VLSI complexity faces challenges, such as substantial area overhead from gate-level pipelining and path balancing, exacerbated by RSFQ's limited layout density. T1 flip-flop (T1-FF) is an RSFQ logic cell operating as a pulse counter. Using T1-FF the full adder function can be realized with only 40% of the area required by the conventional realization. This cell however imposes complex constraints on input signal timing, complicating its use. Multiphase clocking has been recently proposed to alleviate gate-level pipelining overhead. The fanin signals can be efficiently controlled using multiphase clocking. We present the novel two-stage SFQ technology mapping methodology supporting the T1-FF. Compatible parts of the SFQ network are first replaced by the efficient T1-FFs. Multiphase retiming is next applied to assign clock phases to each logic gate and insert DFFs to satisfy the input timing. Using our flow, the area of the SFQ networks is reduced, on average, by 6% with up to 25% reduction in optimizing the 128-bit adder.

In traditional power delivery networks, the on-chip supply voltage is provided by board-level converters. Due to the significant distance between the converter and the load, variations in the load current are not effectively managed, producing a significant voltage drop at the point-of-load. To mitigate this issue, modern high-performance systems utilize on-chip voltage regulators. Due to the close proximity to the load, these regulators can quickly respond to fluctuations in the input voltage or load current, providing superior power quality. Integrated voltage regulators however require significant area, limiting the number of on-chip regulators. An algorithm for distributing on-chip voltage regulators is presented in this article. The algorithm is accelerated using the acrlong IMT, enabling the analysis of arbitrarily sized power grids. The power quality is maximized with a limited number of regulators. Practical scenarios are supported, such as limited current capacity and restricted placement. Several orders of magnitude speedup in the placement process is demonstrated while achieving up to 88% reduction in the maximum voltage drop.

Superconductive electronics is a promising candidate for supplementing or replacing existing CMOS VLSI systems. Rapid single-flux quantum (RSFQ) is one of the most advanced superconductive technologies operating at tens of gigahertz while reducing the operating power by up to three orders of magnitude as compared to conventional semiconductor systems. Achieving VLSI complexity of RSFQ integrated systems, however remains an elusive task due to fundamental differences between RSFQ and CMOS technologies. Most RSFQ logic gates, such as NOT and XOR are sequential in nature. Compared to CMOS, the number of logical pipeline stages is prohibitively large, greatly complicating the design of complex systems. Furthermore, additional circuitry, such as splitters and path balancing flip flops, constitute a major overhead. In this paper, a gate compounding technique is presented to maximize the functionality achievable within a single clock cycle. The logic gates are decomposed into primitives that can be efficiently combined to evaluate complex expressions in a single clock cycle. Structures generated by gate compounding are not sensitive to signal arrival time, simplifying the system design process. The expressive power of SFQ logic is increased, allowing any two-input truth table to be implemented within a single clock cycle. A 4-bit carry lookahead adder (CLA) is implemented using compound gates, demonstrating smaller area, pipeline depth, and clock tree size.

Rapid single-flux quantum (RSFQ) is one of the most advanced superconducting technologies with the potential to supplement or replace conventional VLSI systems. However, scaling RSFQ systems up to VLSI complexity is challenging due to fundamental differences between RSFQ and CMOS technologies. Due to the pulse-based nature of the technology, RSFQ systems require gate-level pipelining. Moreover, logic gates have an extremely limited driving capacity. Path balancing and clock distribution constitute a major overhead, often doubling the size of circuits. Gate compounding is a novel technique that substantially enriches the functionality realizable within a single clock cycle. However, standard logic synthesis tools do not support its specific synchronization constraints. In this paper, we build first a database of minimum-area compound gates covering all the Boolean functions up to 4 variables and all possible input arrival patterns. Then, we propose a technology mapping method for RSFQ circuits that exploits compound gates using the database as a cell library. We evaluate our framework over the EPFL and ISCAS benchmark circuits. Our results show, on average, a 33% lower logic depth with 24% smaller area, as compared to the state of the art.

Heterogeneous computing exploits several disparate technologies within a single system. The different components of a heterogeneous system are often placed within separate temperature zones. Selecting an appropriate operating temperature strongly affects the dissipated power, cooling power (heat load), system performance, and ambient temperature. To this date, no multitemperature design methodology exists. To overcome this limitation, a framework for thermal optimization of heterogeneous computing systems is presented in this article. The effects of operating temperature on delay and power consumption are characterized based on a graph representation of the system. In addition, thermal interactions among the components within a system are considered to accurately evaluate the total power consumption and heat load. In a practical case study, the target temperature of each component within a quantum computing system is determined to minimize the total power under target performance constraints.

Superconductive rapid single-flux quantum (RSFQ) is an emerging cryogenic technology, promising a significant boost in performance and ultralow power consumption. The operating frequency achieved by RSFQ digital integrated circuits is several orders of magnitude greater than traditional CMOS circuits. The fundamental difference of RSFQ circuits, however, renders traditional clocking techniques appropriate for CMOS unsuitable for RSFQ technology. Most RSFQ logic gates, such as AND and OR, are sequential in nature. The number of pipeline stages is therefore significantly greater in RSFQ as compared to CMOS, complicating the clock distribution network design process. This issue is further exacerbated with the need for splitters to achieve a fanout greater than one and the need for transmission lines rather than ordinary metallic wires as in CMOS. In this work, QuCTS—single-flux Quantum (SFQ) Clock Tree Synthesis—is presented. QuCTS utilizes a two-stage framework for synthesizing clock networks. In the clock skew scheduling stage, the clock signal arrival time of each gate is chosen to maximize the robustness of the circuit to timing variations. In the clock tree synthesis stage, the layout of the clock distribution network is generated based on a novel delay equilibration technique. QuCTS is the first clock tree synthesis tool for RSFQ circuits utilizing useful clock skew. The synthesized network satisfies the clock arrival time requirements while minimizing the associated overhead, such as the interconnect length and number of delay elements. The tool is validated on a set of benchmark circuits. In a prototypical case study, a clock tree is generated for the AMD2901 with 1049 clock sinks in 53 min while satisfying the clock arrival time.

The board-level power network design process is governed by system-level parameters, such as the number of layers and the ball grid array (BGA) pattern. These parameters influence the characteristics of the resulting system, such as power, speed, and cost. Evaluating the impact of these parameters is however challenging. To estimate the reduction in impedance if, for example, additional BGA balls are dedicated to the power delivery system, adjustments to the board layout, and an additional impedance extraction process are required. These processes are poorly automated, requiring significant time and labor. Automating power network exploration and prototyping can greatly enhance the board-level power delivery design process by increasing the number of possible design options. With power network exploration and prototyping, the effects of the system parameters on the electrical characteristics can be better understood, providing valuable insight into the early stages of the design process. SPROUT—an automated algorithm for prototyping printed circuit board (PCB) power networks—is presented here. This tool includes the first fully automated algorithm for board-level power network layout synthesis. Two board-level industrial power networks are synthesized using SPROUT. The impedance of the resulting layouts exhibits good agreement with manual PCB layouts while significantly reducing the design time. The tool is used to explore area/impedance tradeoffs in a three-rail system, providing useful data to enhance the PCB design process.

The board-level power network design process is governed by system-level parameters such as the number of layers and the ball grid array (BGA) pattern. These parameters influence the characteristics of the resulting system, such as power, speed, and cost. Evaluating the impact of these parameters is, however, challenging. To estimate the reduction in impedance if, for example, additional BGA balls are dedicated to the power delivery system, adjustments to the board layout and an additional impedance extraction process are required. These processes are poorly automated, requiring significant time and labor. Automating power network exploration and prototyping can greatly enhance the power delivery design process by increasing the number of possible design options. With power network exploration and prototyping, the effects of the system parameters on the electrical characteristics can be better understood, providing valuable insight into the early design stages. SPROUT - an automated algorithm for prototyping printed circuit board (PCB) power networks - is presented here. This tool includes the first fully automated algorithm for board-level power network layout synthesis. Two board-level industrial power networks are synthesized using SPROUT where a ball grid array is connected with a power management IC and decoupling capacitors across four voltage domains. The impedance of the resulting layouts is in good agreement with manual PCB layouts while requiring 95% less design time.

Unlike the routing of on-chip power delivery networks which is a highly automated process, the routing of board-level power nets is usually performed manually. The process is complicated by geometric and electrical constraints that impose restrictions on the routing process. An automated board-level power routing algorithm is presented here which provides efficient generation and refinement of power network geometries at the layout level. In a case study, a routing path connecting a power management integrated circuit to a ball grid array is routed using the automated tool, producing a low impedance network while complying with metal resource and geometric constraints.

The conventional power network design process requires iterative modifications to the existing power network to eliminate hot spots and to converge to target impedance parameters. At later stages in the IC design process, this procedure may require significant time and human resources due to the limited flexibility to accommodate necessary changes. Power delivery exploration during early stages of the design process may bring considerable savings to the system development effort. The number of iterations may be greatly reduced by choosing the initial parameters sufficiently close to the optimum. This paper presents a power delivery exploration framework based on constrained global optimization. The power network parameters are estimated at early stages of the development process, while considering both electrical and nonelectrical factors, such as area and cost. A Laplace transform-based circuit simulator is described that is well suited for optimization purposes due to the high computational efficiency when a large number of iterations is required. The proposed framework has been applied to the distribution of voltage domains in a large scale complex integrated system, while minimizing the cost of the decoupling capacitor placement. The optimal number of voltage rails are determined, demonstrating an approximately 40% lower on-chip area than alternative solutions.

Over the past decades, aggressive voltage scaling combined with increased power demands has placed stringent requirements on on-chip power quality. Unwanted voltage fluctuations and droops may cause a variety of issues, ranging from glitch power to device malfunction. If revealed at the later stages of the design process, mitigation techniques may become unbearably costly in both time and money. A framework for exploratory power delivery optimization is described to enhance the power delivery network during early stages of the design process in accordance with design specifications. The power delivery design process is converted into a constrained minimization problem, consisting of design metrics combined into objective and constraint functions. The framework supports the optimization of the power network characteristics while considering external, non-electrical design specifications, such as cost and area, providing a comprehensive network analysis capability. In one case study, a 15% reduction in decoupling capacitor placement along with a 38.6% reduction in power consumption is achieved while satisfying performance and power quality constraints.