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IEEE Transactions on Applied Superconductivity

Asynchronous Single Flux Quantum Logic Gates Using Self-Clocking

Yuki Yamanashi, Taisei Fujisawa, Zongyuan Li, Nobuyuki Yoshikawa

Published Feb 10, 2023• 7 citations
Publisher

Abstract

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.

DOI
10.1109/tasc.2023.3244148

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IEEE Transactions on Applied Superconductivity•Mar 4, 2020•39 citations
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.
We propose an asynchronous OR gate based on the self-clocking method in single flux quantum (SFQ) circuits, which achieves output delay characteristics insensitive to input patterns. In a conventional self-clocking asynchronous OR gate, an imbalance in the number of SFQ pulses used for internal clock generation when generating an output pulse causes a significant input-pattern dependence in output delay. The proposed OR gate removes this imbalance by combining a self-clocking exclusive-OR gate and a self-clocking AND gate. We designed and evaluated the proposed OR gate assuming the use of the 10 kA/cm2 Nb fabrication process. At the standard bias voltage of 2.5 mV, the proposed OR gate exhibited no output delay difference among input patterns. The proposed OR gate has a more complex structure, leading to increased power consumption and gate area. In addition, 2N-input asynchronous OR circuits constructed using the proposed OR gate maintained stable operation as the number of logic stages increased, which could not be achieved using the conventional OR gate. By suppressing the output delay difference, the proposed OR gate enables stable operation of cascaded asynchronous OR structures with many logic stages.
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.
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%.
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.
We propose an algorithm of digit-serial adders using single-flux-quantum (SFQ) circuits. The proposed digit-serial adder adapts the carry look-ahead (CLA) adder architecture to generate carry signals, which are generated from the digit-serial data and fed back internally to the following digit-serial data to increase the throughput of the calculation. We have designed and implemented a 4-bit digit-serial adder using the SRL 2.5kA/cm2 niobium standard process to demonstrate its high-speed operation. The total number of Josephson junctions is 2316. We have successfully tested full operations of the 4-bit digit-serial adder with a bias margin of ± 15% at 25GHz. Its maximum operation frequency was 30GHz.
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.