Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Transactions on Applied Superconductivity

Rapid Single-Flux-Quantum Logic Circuits Using Clockless Gates

Takahiro Kawaguchi, Kazuyoshi Takagi, Naofumi Takagi

Published Mar 26, 2021• 20 citations
Publisher

Abstract

An architecture of rapid single-flux-quantum logic circuits using clockless gates is proposed. Compared with a circuit composed of only clocked gates, a circuit using clockless gates includes fewer clocked gates, and therefore, a smaller clock distribution network. A circuit in the proposed architecture is constructed from pipeline stages. Each pipeline stage consists of a column of clocked gates and a succeeding block of clockless gates. The function of a pipeline register of a stage is implemented by the latching function of the clocked gates in the column. The combinational logic of a stage is implemented by the logic function of the clocked gates in the column and that of the clockless gates in the block. We designed a two-stage-pipelined 4-bit carry-lookahead-adder using clockless gates as a design example of the proposed architecture. It had reductions of the count of clocked gates and the area by 33 and 13%, respectively, compared with that composed of only clocked gates. The 4-bit adder in the proposed architecture was fabricated and demonstrated with the maximum clock frequency of 21.4 GHz and the bias margin of ±16%.

DOI
10.1109/tasc.2021.3068960

Related papers

Asynchronous Single Flux Quantum Logic Gates Using Self-Clocking

Yuki Yamanashi, Taisei Fujisawa, Zongyuan Li +1 more

We propose an asynchronous single flux quantum (SFQ) logic gate composed of a conventional clocked logic gate and an input signal merger that generates a self-clock for the clocked logic gate. By using this self-clocking, we can design any 0-preserving logic gate, including exclusive OR (XOR). The proposed asynchronous SFQ logic gates have adjustable allowable input skew by varying the delay between the merger and internal clock input for the clocked logic gate. We design and evaluate the asynchronous AND, OR, and XOR gates that have an allowable input skew of approximately 8 ps assuming the use of the 10 kA/cm2Nb fabrication process using the proposed design method. We experimentally confirm the correct operation of the asynchronous SFQ XOR gate. We design a completely asynchronous 4-bit-input carry-lookahead adder (CLA) using the designed asynchronous gates. We found that the circuit area and number of Josephson junctions required to design a 4-bit-input CLA can be reduced by > 50% compared to that of the synchronous concurrent-flow 4-bit-input CLA without deterioration of the throughput.

IEEE Transactions on Applied Superconductivity•Feb 10, 2023•7 citations

Compound Logic Gates for Pipeline Depth Minimization in Single Flux Quantum Integrated Systems

Rassul Bairamkulov, Giovanni De Micheli

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.

ACM Great Lakes Symposium on VLSI (GLSVLSI)•May 31, 2023•6 citations

Asynchronous Dynamic Single-Flux Quantum Majority Gates

Gleb Krylov, Eby G. Friedman

Among the major issues in modern large-scale rapid single-flux quantum (RSFQ) circuits are the complexity of the clock network, tight timing tolerances, poor applicability of existing CMOS-based design algorithms, and extremely deep pipelines, which reduce the effective clock frequency. In this article, asynchronous dynamic single-flux quantum majority gates are proposed to solve some of these problems. The proposed logic gates exhibit high bias margins and do not require significant area or a large number of Josephson junctions as compared to existing RSFQ logic gates. These gates exhibit a tradeoff among the input skew tolerance, clock frequency, and bias margins. Asynchronous logic gates greatly reduce the complexity of the clock network in large-scale RSFQ circuits, thereby alleviating certain timing issues and reducing the required bias currents. Furthermore, asynchronous logic allows existing design algorithms to utilize CMOS approaches for synthesis, verification, and testability. The adoption of majority logic in complex RSFQ circuits also reduces the pipeline depth, enabling higher clock speeds in very large scale integration RSFQ circuits.

IEEE Transactions on Applied Superconductivity•Mar 4, 2020•39 citations

Simulation and optimization of binary full-adder cells in rapid single flux quantum logic

S.S. Martinet, Mark F. Bocko

The authors consider the design of a binary carry full-adder cell using the logic gates and buffers belonging to the rapid single-flux-quantum (RSFQ) logic family. They have taken advantage of the unique properties of RSFQ pulse logic to realize two designs: one using two logic gates and a toggle flip-flop in two stages of logic, the other using two logic gates in one stage of logic. They have determined the parameter margins of the two full-adder cells and optimized them to obtain critical margins approaching +or-30%. Simulations of the full-adder cells have revealed critical delays and maximum clock frequencies of 58 ps and 17 GHz and 33 ps and 30 GHz, respectively.>

IEEE Transactions on Applied Superconductivity•Mar 1, 1993•6 citations

Case study in RSFQ design: fast pipelined parallel adder

P. Bunyk, P. Litskevitch

We present a design for parallel pipelined carry-lookahead Kogge-Stone 32and 64-bit integer adders with the traditional concurrent flow timing scheme, and the results of its gate-level logical simulation using a VHDL model, with parameters reduced from the physical-level simulation of RSFQ cells. The design uses only five different types of bit processing blocks and is easily scalable to any length of the operands. The multi-pulse logic representation together with interchanging logical polarity between pipeline stages is used to simplify the design of the blocks, which contain only two types of clocked RSFQ gates: an inverter and a D-flip-flop. Simulations show that in the absence of thermal fluctuations and random parameter spread the clock frequency of the adder implemented in the projected 0.8 /spl mu/m Nb-trilayer technology could be as high as 150 GHz. However, an approximate account of these factors shows that in order to achieve a 99% adder fabrication yield and a 10/sup -25/ adder error rate the maximal frequency should be reduced to 60 GHz for 1.5% Josephson junction spread and to 52 GHz for 3% spread. Adder latency is close to 260 ps for 32 bits and 320 ps for 64 bits. We plan to re-design the adders to increase their speed.

IEEE Transactions on Applied Superconductivity•Jun 1, 1999•40 citations

Design Method of Single Flux Quantum Logic Circuits Using Dynamically Reconfigurable Logic Gates

Shohei Nishimoto

In this study, we designed and tested dynamically reconfigurable AND/OR and NAND/NOR single flux quantum (SFQ) logic gates. The measured dc bias margins at low frequency were 99%-126% and 121%-144% for AND/OR and NAND/NOR gates, respectively. The experimentally confirmed maximum operating frequencies of the AND/OR and NAND/NOR gates were 36 and 24 GHz, respectively. We investigated a circuit design method that enables the efficient design of SFQ logic circuits by using dynamically reconfigurable SFQ logic gates. The logic circuits were designed with a small number of gates using the input data pattern dependence of the Boolean function and reconfiguring the dynamically reconfigurable SFQ logic gates. As a case study, we designed and tested a bit-serial SFQ full adder using the investigated circuit design method. Compared with the conventional bit-serial SFQ full adder, the delay of the proposed full adder was reduced by 27%, assuming a clock frequency of 20 GHz. We confirmed correct operation of the adder with a low-speed test.

The Japan Society of Applied Physics•Feb 6, 2014•0 citations
An architecture of rapid single-flux-quantum logic circuits using clockless gates is proposed. Compared with a circuit composed of only clocked gates, a circuit using clockless gates includes fewer clocked gates, and therefore, a smaller clock distribution network. A circuit in the proposed architecture is constructed from pipeline stages. Each pipeline stage consists of a column of clocked gates and a succeeding block of clockless gates. The function of a pipeline register of a stage is implemented by the latching function of the clocked gates in the column. The combinational logic of a stage is implemented by the logic function of the clocked gates in the column and that of the clockless gates in the block. We designed a two-stage-pipelined 4-bit carry-lookahead-adder using clockless gates as a design example of the proposed architecture. It had reductions of the count of clocked gates and the area by 33 and 13%, respectively, compared with that composed of only clocked gates. The 4-bit adder in the proposed architecture was fabricated and demonstrated with the maximum clock frequency of 21.4 GHz and the bias margin of ±16%.
We propose an asynchronous single flux quantum (SFQ) logic gate composed of a conventional clocked logic gate and an input signal merger that generates a self-clock for the clocked logic gate. By using this self-clocking, we can design any 0-preserving logic gate, including exclusive OR (XOR). The proposed asynchronous SFQ logic gates have adjustable allowable input skew by varying the delay between the merger and internal clock input for the clocked logic gate. We design and evaluate the asynchronous AND, OR, and XOR gates that have an allowable input skew of approximately 8 ps assuming the use of the 10 kA/cm2Nb fabrication process using the proposed design method. We experimentally confirm the correct operation of the asynchronous SFQ XOR gate. We design a completely asynchronous 4-bit-input carry-lookahead adder (CLA) using the designed asynchronous gates. We found that the circuit area and number of Josephson junctions required to design a 4-bit-input CLA can be reduced by > 50% compared to that of the synchronous concurrent-flow 4-bit-input CLA without deterioration of the throughput.
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.
Among the major issues in modern large-scale rapid single-flux quantum (RSFQ) circuits are the complexity of the clock network, tight timing tolerances, poor applicability of existing CMOS-based design algorithms, and extremely deep pipelines, which reduce the effective clock frequency. In this article, asynchronous dynamic single-flux quantum majority gates are proposed to solve some of these problems. The proposed logic gates exhibit high bias margins and do not require significant area or a large number of Josephson junctions as compared to existing RSFQ logic gates. These gates exhibit a tradeoff among the input skew tolerance, clock frequency, and bias margins. Asynchronous logic gates greatly reduce the complexity of the clock network in large-scale RSFQ circuits, thereby alleviating certain timing issues and reducing the required bias currents. Furthermore, asynchronous logic allows existing design algorithms to utilize CMOS approaches for synthesis, verification, and testability. The adoption of majority logic in complex RSFQ circuits also reduces the pipeline depth, enabling higher clock speeds in very large scale integration RSFQ circuits.
The authors consider the design of a binary carry full-adder cell using the logic gates and buffers belonging to the rapid single-flux-quantum (RSFQ) logic family. They have taken advantage of the unique properties of RSFQ pulse logic to realize two designs: one using two logic gates and a toggle flip-flop in two stages of logic, the other using two logic gates in one stage of logic. They have determined the parameter margins of the two full-adder cells and optimized them to obtain critical margins approaching +or-30%. Simulations of the full-adder cells have revealed critical delays and maximum clock frequencies of 58 ps and 17 GHz and 33 ps and 30 GHz, respectively.>
We present a design for parallel pipelined carry-lookahead Kogge-Stone 32and 64-bit integer adders with the traditional concurrent flow timing scheme, and the results of its gate-level logical simulation using a VHDL model, with parameters reduced from the physical-level simulation of RSFQ cells. The design uses only five different types of bit processing blocks and is easily scalable to any length of the operands. The multi-pulse logic representation together with interchanging logical polarity between pipeline stages is used to simplify the design of the blocks, which contain only two types of clocked RSFQ gates: an inverter and a D-flip-flop. Simulations show that in the absence of thermal fluctuations and random parameter spread the clock frequency of the adder implemented in the projected 0.8 /spl mu/m Nb-trilayer technology could be as high as 150 GHz. However, an approximate account of these factors shows that in order to achieve a 99% adder fabrication yield and a 10/sup -25/ adder error rate the maximal frequency should be reduced to 60 GHz for 1.5% Josephson junction spread and to 52 GHz for 3% spread. Adder latency is close to 260 ps for 32 bits and 320 ps for 64 bits. We plan to re-design the adders to increase their speed.
In this study, we designed and tested dynamically reconfigurable AND/OR and NAND/NOR single flux quantum (SFQ) logic gates. The measured dc bias margins at low frequency were 99%-126% and 121%-144% for AND/OR and NAND/NOR gates, respectively. The experimentally confirmed maximum operating frequencies of the AND/OR and NAND/NOR gates were 36 and 24 GHz, respectively. We investigated a circuit design method that enables the efficient design of SFQ logic circuits by using dynamically reconfigurable SFQ logic gates. The logic circuits were designed with a small number of gates using the input data pattern dependence of the Boolean function and reconfiguring the dynamically reconfigurable SFQ logic gates. As a case study, we designed and tested a bit-serial SFQ full adder using the investigated circuit design method. Compared with the conventional bit-serial SFQ full adder, the delay of the proposed full adder was reduced by 27%, assuming a clock frequency of 20 GHz. We confirmed correct operation of the adder with a low-speed test.