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High-Throughput Low-Latency Single-Flux-Quantum Circuits with Feedback Path

Ryota Kashima, Ikki Nagaoka, Tomoki Nakano, Masamitsu Tanaka, Taro Yamashita, Akira Fujimaki

Published Jul 30, 2021• 0 citations
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A High-Throughput Single-Flux Quantum Floating-Point Serial Divider Using the Signed-Digit Representation

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We propose a floating-point serial divider for a single-flux quantum (SFQ) logic implementation based on a hardware algorithm of division using subtract and shift operations. Fast serial calculations are performed by utilizing the signed-digit representation. The divider is implemented with a regularly aligned pipeline structure called a systolic array. The processing element of the systolic array is designed using several logic gates unique to the SFQ circuits, to reduce the number of pipeline stages. As a result, high throughput and low latency is achieved with a small circuit size. The throughput approaches the maximum throughput of serial processing. A 4-bit divider was fabricated using the 2.5-kA/cm2niobium process technology, and successful operation up to 19 GHz was demonstrated.

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Single-flux-quantum logic

T. Van Duzer

This paper reviews the several families of single-flux-quantum logic that have appeared in the literature as well as a new one designed in our Laboratory. Some of these have been evaluated in full-adder circuits and found to have approximately the same latency (time between input and output) as a voltage-state circuit. It is pointed out that the throughput of single-flux-quantum circuits can be much higher than with voltage-state circuits because of a much shorter reset time. The applications for these circuits are greatest in data-independent computation such as signal processing. The prospects and problems for these kinds of circuits are discussed both for low- and high-temperature superconductors.

•Mar 1, 1992•0 citations
We propose a floating-point serial divider for a single-flux quantum (SFQ) logic implementation based on a hardware algorithm of division using subtract and shift operations. Fast serial calculations are performed by utilizing the signed-digit representation. The divider is implemented with a regularly aligned pipeline structure called a systolic array. The processing element of the systolic array is designed using several logic gates unique to the SFQ circuits, to reduce the number of pipeline stages. As a result, high throughput and low latency is achieved with a small circuit size. The throughput approaches the maximum throughput of serial processing. A 4-bit divider was fabricated using the 2.5-kA/cm2niobium process technology, and successful operation up to 19 GHz was demonstrated.
In this article, we demonstrated a high-throughput gate-level-pipelined 8-bit multiply-accumulate (MAC) unit with a long feedback loop using low-voltage rapid single-flux quantum (LV-RSFQ) logic. The long feedback loop in the MAC unit is an obstacle for high-throughput operation because the logic gates must wait for the delayed inputs from the feedback loop. The LV-RSFQ logic makes high-frequency operation even more difficult by larger and more variable feedback delay. We design the feedback loop by using counter-flow clocking and adding many D flip-flops to divide the long feedback loop into shorter paths. The target clock frequency of the MAC unit with a feedback loop was set to 30 GHz by the experimental results of the MAC unit without a feedback loop. We model the clock frequency and its circuit overhead in a feedback loop to design the feedback loop in the MAC unit achieving 30 GHz with a minimum overhead. The test chips are fabricated using the national institute of advanced industrial science and technology (AIST) 10-kA/cm2\boldsymbol{^{2}}2Advanced Process 2. We have successfully obtained high-throughput 30-GHz operations in the LV-RSFQ MAC unit with a long feedback loop by using the model-based design. The maximum operating frequency of the MAC unit reaches 40 GHz.
This paper reviews the several families of single-flux-quantum logic that have appeared in the literature as well as a new one designed in our Laboratory. Some of these have been evaluated in full-adder circuits and found to have approximately the same latency (time between input and output) as a voltage-state circuit. It is pointed out that the throughput of single-flux-quantum circuits can be much higher than with voltage-state circuits because of a much shorter reset time. The applications for these circuits are greatest in data-independent computation such as signal processing. The prospects and problems for these kinds of circuits are discussed both for low- and high-temperature superconductors.