In this paper we present an FFT hardware accelerator based on a butterfly (BUT) structure implemented in Rapid Single-Flux-Quantum (RSFQ) superconducting computing. Our design uses a data representation that combines Race Logic (RL) with pulse streams in order to perform arithmetic operations and generate twiddle factors efficiently. Given today’s stringent area limitations for RSFQ technology, our design aims to maximize area efficiency. Our design shows 2 to 18× higher throughput per area, measured as performance per number of Josephson junctions. Moreover, we demonstrate 20-70% area savings compared to binary RSFQ FFT implementations for 2 to 64 N-points.
In this paper we present an FFT hardware accelerator based on a butterfly (BUT) structure implemented in Rapid Single-Flux-Quantum (RSFQ) superconducting computing. Our design uses a data representation that combines Race Logic (RL) with pulse streams in order to perform arithmetic operations and generate twiddle factors efficiently. Given today’s stringent area limitations for RSFQ technology, our design aims to maximize area efficiency. Our design shows 2 to 18× higher throughput per area, measured as performance per number of Josephson junctions. Moreover, we demonstrate 20-70% area savings compared to binary RSFQ FFT implementations for 2 to 64 N-points.
Superconducting technology is a prime candidate for the future of computing. However, current superconducting prototypes are limited to small-scale examples due to stringent area constraints and complex architectures inspired from voltage-level encoding in CMOS; this is at odds with the ps-wide Single Quantum Flux (SFQ) pulses used in superconductors to carry information. In this work, we propose a wave-pipelined Unary SFQ (U-SFQ) architecture that leverages the advantages of two data representations: pulse-streams and Race Logic (RL). We introduce novel building blocks such as multipliers, adders, and memory cells, which leverage the natural properties of SFQ pulses to mitigate area constraints. We then design and simulate three popular hardware accelerators: i) a Processing Element (PE), typically used in spatial architectures; ii) A dot-product-unit (DPU), one of the most popular accelerators in artificial neural networks and digital signal processing (DSP); and iii) A Finite Impulse Response (FIR) filter, a popular and computationally demanding DSP accelerator. The proposed U-SFQ building blocks require up to 200× fewer JJs compared to their SFQ binary counterparts, exposing an area-delay trade-off. This work mitigates the stringent area constraints of superconducting technology.
In this article, 8-bit bit-slice butterfly processing units (BPUs) are proposed for 64-point rapid single-flux-quantum (RSFQ) fast Fourier transform processors. The BPUs are based on radix-2, mixed-radix, and split-radix algorithms, respectively. Unlike the previously developed bit-serial RSFQ BPUs, the proposed bit-slice BPUs continuously process 64-point data divided into eight slices of eight points each in order to reduce the hardware cost. The BPUs use synchronous concurrent-flow clocking and they can be extended to any n2-point processing.
We have designed a Decimation-in-Time (DIT) radix 2 butterfly integrated circuit. This circuit will be used to implement the 32-point Fast Fourier Transform (FFT) in a parallel data flow architecture. The radix 2 butterfly circuit uses serial RSFQ math and consists of four single bit-wide serial multipliers and eight carry-save serial adders. The circuit with 16-bit word-length employs only 3400 junctions, occupies an area of 3.8/spl times/2.0 mm/sup 2/, and dissipates less than 1.1 mW power. The multiplier is implemented using the unique RSFQ bit-clock-pipelined schema. We have successfully tested a library of serial multiply-add elements: the 8-bit multiplier at 6.3 GHz and adders with dc bias margin /spl plusmn/20%. Finally, we have demonstrated full operation of the radix 2 butterfly chip with 5-bit word length.>
The Fast Fourier Transform (FFT) is extensively used in image processing, wireless communication, and other applications. Some applications that involve very complicated, real-time FFT processing require specialized hardware for performing high-speed FFT processing. We have been developing high-speed FFT processors based on single flux quantum (SFQ) circuit technology. In this study, we developed a butterfly processing element for FFT processors that uses SFQ circuits. The butterfly processing element consists of complex number adders, subtractors, and multipliers. The circuit structure was modified compared to that of previous SFQ FFT processors to reduce latency. Several buffer circuits were inserted in the multipliers to compensate for timing jitter accumulation and discrepancies due to signal propagation delay. We designed and implemented a four-bit bit-serial butterfly processing element that contains 5763 Josephson junctions using the ISTEC Nb 2.5-kA/cm2standard 2 process and the CONNECT cell library. Correct operation of the butterfly processing unit was experimentally confirmed at a clock frequency of 25 GHz.
This research explores the use of superconductor electronics (SCE) for accelerating fully homomorphic encryption (FHE), focusing on the Number-Theoretic Transform (NTT), a key computational bottleneck in FHE schemes. We present SCE-NTT, a dedicated hardware accelerator based on superconductive single flux quantum (SFQ) logic and memory, targeting high performance and energy efficiency beyond the limits of conventional CMOS. To address SFQ constraints such as limited dense RAM and restricted fanin/fanout, we propose a deeply pipelined NTT-128 architecture using shift register memory (SRM). Designed for N=128 32-bit coefficients, NTT-128 comprises log2(N)=7 processing elements (PEs), each featuring a butterfly unit (BU), dual coefficient memories operating in ping-pong mode via FIFO-based SRM queues, and twiddle factor buffers. The BU integrates a Shoup modular multiplier optimized for a small area, leveraging precomputed twiddle factors. A new RSFQ cell library with over 50 parameterized cells, including compound logic units, was developed for implementation. Functional and timing correctness were validated using JoSIM analog simulations and Verilog models. A multiphase clocking scheme was employed to enhance robustness and reduce path-balancing overhead, improving circuit reliability. Fabricated results show the NTT-128 unit achieves 531 million NTT/sec at 34 GHz, over 100x faster than state-of-the-art CMOS equivalents. We also project that the architecture can scale to larger sizes, such as a 2^14-point NTT in approximately 482 ns. Key-switch throughput is estimated at 1.63 million operations/sec, significantly exceeding existing hardware. These results demonstrate the strong potential of SCE-based accelerators for scalable, energy-efficient secure computation in the post-quantum era, with further gains anticipated through advances in fabrication.
We have been working on the development of a high-speed fast Fourier transform (FFT) processor using single-flux-quantum (SFQ) logic circuits. In our previous studies, we designed and demonstrated a 4-bit butterfly processor, a data-shuffling circuit, and a twiddle factor ROM for 4-bit 8-point FFT using the AIST 10 kA/cm2Nb advanced process 2 at maximum frequencies of 51.6, 59.5, and 51.5, respectively. In this study, to complete the FFT processor design, we designed and demonstrated residual component circuits called a rounding circuit and a data buffer at a target frequency of 50 GHz. We also designed and experimentally confirmed the operation of an SFQ-based single-chip FFT processor integrating all the component circuits.