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International Symposium on Quality Electronic Design (ISQED)

An Area Efficient Superconducting Unary CNN Accelerator

Patricia Gonzalez-Guerrero, Kylie Huch, Nirmalendu Patra, Thom Popovici, George Michelogiannakis

Published Apr 5, 2023• 3 citations
Publisher

Abstract

In superconducting circuits, information is carried by ps-wide, µV-tall, Single Flux Quanta (SFQ) pulses. These circuits can operate at frequencies of hundreds of GHz with orders of magnitude lower switching energy than complementary-metal-oxide-semiconductors (CMOS). However, under the stringent area constraints of modern superconductor technologies, fully-fledged, CMOS-inspired superconducting architectures cannot be fabricated at large scales. Unary SFQ (U-SFQ) is an alternative computing paradigm that addresses these area constraints. In U-SFQ, information is mapped to a combination of streams of SFQ pulses and in the temporal domain. In this work, we propose a U-SFQ Convolutional Neural Network (CNN) hardware accelerator capable of comparable peak performance with state-of-the-art superconducting binary (B-SFQ) approaches in 32× less area. CNNs can operate with 5 to 8 bits of resolution with no significant degradation in classification accuracy. The proposed CNN accelerator effortlessly supports this variable resolution and, for less than 7 bits, yields 5×-63× better performance than CMOS and 15×-173× better area efficiency than B-SFQ.

DOI
10.1109/isqed57927.2023.10129299

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In superconducting circuits, information is carried by ps-wide, µV-tall, Single Flux Quanta (SFQ) pulses. These circuits can operate at frequencies of hundreds of GHz with orders of magnitude lower switching energy than complementary-metal-oxide-semiconductors (CMOS). However, under the stringent area constraints of modern superconductor technologies, fully-fledged, CMOS-inspired superconducting architectures cannot be fabricated at large scales. Unary SFQ (U-SFQ) is an alternative computing paradigm that addresses these area constraints. In U-SFQ, information is mapped to a combination of streams of SFQ pulses and in the temporal domain. In this work, we propose a U-SFQ Convolutional Neural Network (CNN) hardware accelerator capable of comparable peak performance with state-of-the-art superconducting binary (B-SFQ) approaches in 32× less area. CNNs can operate with 5 to 8 bits of resolution with no significant degradation in classification accuracy. The proposed CNN accelerator effortlessly supports this variable resolution and, for less than 7 bits, yields 5×-63× better performance than CMOS and 15×-173× better area efficiency than B-SFQ.
Most popular superconducting circuits operate on information carried by ps-wide, μV-tall, single flux quantum (SFQ) pulses. These circuits can operate at frequencies of hundreds of GHz with orders of magnitude lower switching energy than complementary-metal-oxide-semiconductors (CMOS). However, under the stringent area constraints of modern superconductor technologies, fully-fledged, CMOS-inspired superconducting architectures cannot be fabricated at large scales. Unary SFQ (U-SFQ) is an alternative computing paradigm that can address these area constraints. In U-SFQ, information is mapped to a combination of streams of SFQ pulses and in the temporal domain. In this work, we extend U-SFQ to introduce novel building blocks such as a multiplier and an accumulator. These blocks reduce area and power consumption by 2 ×\times× and 4 ×\times× compared with previously proposed U-SFQ building blocks and yield at least 97% area savings compared with binary approaches. Using these multiplier and adder, we propose a U-SFQ Convolutional Neural Network (CNN) hardware accelerator capable of comparable peak performance with state-of-the-art superconducting binary approach (B-SFQ) in 32 ×\times× less area. CNNs can operate with 5–8 bits of resolution with no significant degradation in classification accuracy. For 5 bits of resolution, our proposed accelerator yields 5 ×\times× to 63 ×\times× better performance than CMOS and 15 ×\times× to 173 ×\times× better area efficiency than B-SFQ.
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.
Abstract Single-flux-quantum (SFQ) circuits are promising candidates for post-Moore integrated circuits owing to their ultra-high-speed operation and low power consumption. However, limitations in current superconducting fabrication processes pose significant challenges to achieving area-efficient SFQ-based microprocessors, particularly in the design of compact arithmetic logic units (ALUs). Unary computing enables arithmetic operations using extremely simple logic, but typically suffers from long computation latency. This paper focuses on unary computing for superconducting circuits that exploits the complementary characteristics of SFQ logic and unary computing. The ultra-high-speed nature of SFQ circuits compensates for the inherent latency of unary computation, while unary computing enables an ultra-low hardware cost by substantially reducing circuit complexity. Based on this concept, we introduce a unary computing methodology tailored for SFQ circuits and design a superconducting unary ALU with ultra-low hardware cost. The proposed ALU requires only 183 Josephson junctions (JJs), achieving approximately 88.2% reduction in JJ count and 80.4% reduction in area compared with a conventional bit-serial SFQ ALU. The proposed design, including binary-to-unary and unary-to-binary converters, was fabricated using a 10 kA cm −2 Nb four-layer superconducting circuit fabrication process and experimentally verified to operate correctly at approximately 72 GHz. The total power consumption at this frequency is approximately 58.9 µ W. This work quantitatively demonstrates the effectiveness of combining unary computing with SFQ circuits for ultra-low-cost processing systems and provides superconducting circuits as a new design option for alternative computation paradigms, such as unary computing.
Abstract With the increasing processor performance requirements of convolutional neural networks, we believe that research on superconducting neural networks based on single flux quantum (SFQ) circuits holds significant potential. However, the typical multiply and accumulate operations used in neural networks often lead to a significant increase in circuit area due to the limitations of the integration density of the current SFQ circuit fabrication process. In this work, we propose a binary neural processing element (PE) that utilizes time-domain signal expression. Time-domain signals express multi-bit binary data in time information, which reduces the number of data lines to decrease the circuit area. In the proposed binary neural PE, multiplication is achieved through exclusive-NOR gates and addition is realized by controlling the delay of time-domain signals. We designed and simulated a 3 × 3 convolution circuit using 10 Nb layer process with a critical current density of 10 kA cm−2. Compared to the convolution circuit implemented using conventional SFQ logic, the proposed circuit reduces the number of Josephson junctions by approximately 56% and decreases the area by about 60%.
Due to their high-speed operation and low power consumption, single flux quantum (SFQ) circuits are promising technologies for integrated circuits. However, current superconducting fabrication limitations impose strict area constraints, challenging the construction of large-scale systems. Unary computing (UC) encodes numerical values by concentrating all “1”s at the beginning of a bit sequence. This approach enables arithmetic operations with fewer logic gates, thereby improving the area efficiency. In this study, we propose a novel high-capacity D flip-flop (HC-DFF) cell for UC-based SFQ circuits that achieves high-density data registration while preserving UC encoding. The HC-DFF employs a cascaded storage loop structure in which each loop sequentially stores one flux quantum, avoiding the margin deterioration associated with storing multiple flux quanta in a single loop. Simulation shows that the proposed HC-DFF achieves a bias margin of –20.8% to +32.7% and supports read/write operations above 100 GHz. We fabricated the HC-DFF using a 10 kA/cm² Nb four-layer superconducting process and verified its operation through low-speed measurements. The HC-DFF offers enhanced scalability and stability while reducing the number of required Josephson junctions by 83.3% per bit compared to conventional DFF-based shift registers for saving UC signals. For short unary sequences of less than 31 bits, it retains an advantage over storing binary data with equivalent precision using conventional DFF-based shift registers.
The sorting network is crucial in fields like communication switching, data mining, image processing, neural networks, and others, where the bitonic sorting network (BSN) is an efficient comparison sorting method. It uses the compare-and-swap (CAS) units to compare two input data and decide whether to swap them. The single flux quantum (SFQ) circuits are well known for their high-speed operation and low power consumption, but they are less effective at performing numerical comparisons in CAS units. To address this issue, the unary coding (UC) method, an entropy encoding method that represents the natural number n with n ones followed by zeros, is introduced to implement a smaller SFQ-based BSN. The UC requires only AND and OR gates for CAS unit implementation. Consequently, the 8-input 32-bit UC BSN is two orders of magnitude smaller than the conventional SFQ binary coding BSN with the same precision and achieves approximately 3.3 times better energy efficiency. Additionally, compared to the CMOS-based UC BSN circuit, the energy efficiency improves by 5.8 times, even considering the cooling cost (×400). We also implemented a 4-input BSN circuit, using the 1.0 μm 10-layer Nb SFQ circuit fabrication process, and verified its operation at low speed.