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

High-Capacity DFF Cells for Unary Computing Using Single-Flux Quantum Circuits

Zeyu Han, Nobuyuki Yoshikawa, Yuki Yamanashi

Published Aug 25, 2025• 1 citation
Publisher

Abstract

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.

DOI
10.1109/tasc.2025.3602472

Related papers

A superconducting unary arithmetic logic unit with ultra-low hardware cost

Zeyu Han, Nobuyuki Yoshikawa, Yuki Yamanashi

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.

Superconductor Science and Technology•Jun 5, 2026•0 citations

100 GHz Demonstrations Based on the Single-Flux-Quantum Cell Library for the 10 kA/cm2 Nb Multi-Layer Process

Yuki Yamanashi, Toshiki Kainuma, Nobuyuki Yoshikawa +7 more

A single flux quantum (SFQ) logic cell library has been developed for the 10kA/cm2 Nb multi-layer fabrication process to efficiently design large-scale SFQ digital circuits. In the new cell library, the critical current density of Josephson junctions is increased from 2.5kA/cm2 to 10kA/cm2 compared to our conventional cell library, and the McCumber-Stwart parameter of each Josephson junction is increased to 2 in order to increase the circuit operation speed. More than 300 cells have been designed, including fundamental logic cells and wiring cells for passive interconnects. We have measured all cells and confirmed they stably operate with wide operating margins. On-chip high-speed test of the toggle flip-flop (TFF) cell has been performed by measuring the input and output voltages. The TFF cell at the input frequency of up to 400GHz was confirmed to operate correctly. Also, several fundamental digital circuits, a 4-bit concurrent-flow shift register and a bit-serial adder have been designed using the new cell library, and the correct operations of the circuits have been demonstrated at high clock frequencies of more than 100GHz.

IEICE Transactions on Electronics•Jan 1, 2010•94 citations

HiPerRF: A Dual-Bit Dense Storage SFQ Register File

Haipeng Zha, Naveen Kumar Katam, Massoud Pedram +1 more

Single Flux Quantum (SFQ) superconducting technology provides significant power and performance benefits in the era of diminishing CMOS scaling. Recent advances in design tools and fabrication facilities have brought SFQ based computing to the forefront. One challenge faced by SFQ technology is to have a compact and robust on-chip memory, which can be used for implementing register files and cache memory. While dense memories are being investigated through the development of three-terminal devices such as Nanocryotrons, in this work, we build on a novel memory cell built using traditional Josephson junctions (JJs). In particular, we design a high capacity register file, called HiPerRF, that builds on a High Capacity Destructive ReadOut (HC-DRO) cell in SFQ technology. HC-DRO design can store up to three fluxon pulses, thereby providing the equivalent of 2-bit storage in a single cell. However, these cells provide only destructive readout capability, namely each value can be read only once. However, CPU register file contents are read multiple times in any program, and hence a destructive readout complicates register file design. HiPerRF provides the non-destructive property using a loopback write mechanism, thereby preserving the higher density of HC-DRO cells without compromising the multi-read demands of a register file. HiPerRF reduces the JJ count of the register file design, after accounting for all the peripheral access circuitry costs, by 56.1% and reduces the static power by 46.2%. Furthermore, HiPerRF reduces the JJ count by 16.3% even when considering an entire in-order RISC-V CPU core.

IEEE International Symposium on High-Performance Computer Architecture (HPCA)•Apr 1, 2022•12 citations

A Finite State Automaton for the Tsetlin Machine Using High-Capacity Resettable D Flip-Flop Cells

Zeyu Han, Nobuyuki Yoshikawa, Yuki Yamanashi

Single Flux Quantum (SFQ) circuits provide ultrafast operation and low power consumption, making them attractive candidates for machine learning accelerators. The Tsetlin Machine (TM) is a low-complexity and highly interpretable architecture, organized as a voting system of propositional clauses. In the TM, an ensemble of finite-state automata (FSAs), called Tsetlin automata, independently decides whether to include or exclude specific literals. The chosen literals are assembled into propositional clauses that collectively form the voting system, while each FSA updates its state based on rewards or penalties determined by the prediction outcome. However, existing FSA designs for TM based on SFQ circuits still suffer from either a narrow margin or excessive circuit area. To achieve compact and stable state transitions using SFQ circuits, we designed High-Capacity Resettable D Flip-Flop (HC-RDFF) cells by cascading storage loops. The proposed FSA was implemented using two HC-RDFFs to store the include and exclude states, respectively. The FSA with 16 states requires only 395 Josephson junctions with a static power of approximately 128 μW, exhibiting a bias margin of −21% to +25% at low speed and a maximum operating frequency of 20 GHz in simulation. We fabricated the HC-RDFF and the FSA using a 10 kA/cm² Nb four-layer superconducting process and verified their correct operation through low-speed measurements. The number of FSA states can be increased simply by extending the cascaded storage loops in the HC-RDFFs. We expect the proposed FSA to be suitable for constructing stable TM systems based on SFQ circuits with reduced hardware costs.

IEEE Transactions on Applied Superconductivity•Jan 27, 2026•0 citations

Superconducting Shuttle-Flux Shift Register for Race Logic and Its Applications

Meriam Gay Bautista, Patricia Gonzalez-Guerrero, Darren Lyles +1 more

This paper presents a superconducting, magnetically-coupled, shuttle-flux shift register (SF-SR) that stores single flux quantum (SFQ) pulses. This shift register has a DC bias operating margin of ±34% at 10 GHz, with a power dissipation of$3.6~\mu W$and 38% fewer Josephson junctions (JJs) when scaled up to multiple stages compared to a data flip-flop (DFF) based shift register. The clock input is inductively coupled and is independent from the data input. We then present three applications for our SF-SR. In the first application, we add two non-destructive readout (NDRO) cells to construct a buffer that temporarily stores the temporal information of a series of race logic (RL) pulses. The second application is a pseudo-random number generator based on a linear function shift register (LFSR). The third application is N parallel SF-SRs that can act similar to a deserializer or instead can emulate a single SF-SR of N times higher clock frequency. These three applications motivate deep shift registers with many shifting intervals, which our SF-SR can implement with fewer JJs and lower power consumption compared to DFF-based shift registers.

IEEE Transactions on Circuits and Systems I Regular Papers•Oct 10, 2022•6 citations

Multi Fluxon Storage and its Implications for Microprocessor Design

Naveen Kumar Katam, Haipeng Zha, Massoud Pedram +1 more

Abstract One of the main challenges for single flux quantum (SFQ) technology to successfully implement a microprocessor is to have a compact and robust on-chip memory that can be used for register files and cache memory. In this context, we designed high capacity destructive readout (HC-DRO) cells. The design is based on our insight that each cell can store more than one SFQ pulse with the same area footprint of a regular DRO cell. In our current design, we demonstrate a single HC-DRO cell that can store up to three SFQ pulses thereby enabling us to store the equivalent of two bits of memory in a single cell. We have designed a register file (RF) architecture for a microprocessor and used the HC-DRO cells to reduce the Josephson junction count required for its implementation. The RF architecture presented in this work can also be used for implementing cache memories. We also demonstrate the benefits of doubling the storage density with HC-DRO cells by designing a 2-bit branch predictor circuit block for a 5-stage pipeline microprocessor that dramatically improves the cycles per instruction metric of an SFQ based microprocessor. All the design details are presented in the paper by verifying the design concepts through JSIM simulations and Verilog simulations.

Journal of Physics Conference Series•Jun 1, 2020•11 citations
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.
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.
A single flux quantum (SFQ) logic cell library has been developed for the 10kA/cm2 Nb multi-layer fabrication process to efficiently design large-scale SFQ digital circuits. In the new cell library, the critical current density of Josephson junctions is increased from 2.5kA/cm2 to 10kA/cm2 compared to our conventional cell library, and the McCumber-Stwart parameter of each Josephson junction is increased to 2 in order to increase the circuit operation speed. More than 300 cells have been designed, including fundamental logic cells and wiring cells for passive interconnects. We have measured all cells and confirmed they stably operate with wide operating margins. On-chip high-speed test of the toggle flip-flop (TFF) cell has been performed by measuring the input and output voltages. The TFF cell at the input frequency of up to 400GHz was confirmed to operate correctly. Also, several fundamental digital circuits, a 4-bit concurrent-flow shift register and a bit-serial adder have been designed using the new cell library, and the correct operations of the circuits have been demonstrated at high clock frequencies of more than 100GHz.
Single Flux Quantum (SFQ) superconducting technology provides significant power and performance benefits in the era of diminishing CMOS scaling. Recent advances in design tools and fabrication facilities have brought SFQ based computing to the forefront. One challenge faced by SFQ technology is to have a compact and robust on-chip memory, which can be used for implementing register files and cache memory. While dense memories are being investigated through the development of three-terminal devices such as Nanocryotrons, in this work, we build on a novel memory cell built using traditional Josephson junctions (JJs). In particular, we design a high capacity register file, called HiPerRF, that builds on a High Capacity Destructive ReadOut (HC-DRO) cell in SFQ technology. HC-DRO design can store up to three fluxon pulses, thereby providing the equivalent of 2-bit storage in a single cell. However, these cells provide only destructive readout capability, namely each value can be read only once. However, CPU register file contents are read multiple times in any program, and hence a destructive readout complicates register file design. HiPerRF provides the non-destructive property using a loopback write mechanism, thereby preserving the higher density of HC-DRO cells without compromising the multi-read demands of a register file. HiPerRF reduces the JJ count of the register file design, after accounting for all the peripheral access circuitry costs, by 56.1% and reduces the static power by 46.2%. Furthermore, HiPerRF reduces the JJ count by 16.3% even when considering an entire in-order RISC-V CPU core.
Single Flux Quantum (SFQ) circuits provide ultrafast operation and low power consumption, making them attractive candidates for machine learning accelerators. The Tsetlin Machine (TM) is a low-complexity and highly interpretable architecture, organized as a voting system of propositional clauses. In the TM, an ensemble of finite-state automata (FSAs), called Tsetlin automata, independently decides whether to include or exclude specific literals. The chosen literals are assembled into propositional clauses that collectively form the voting system, while each FSA updates its state based on rewards or penalties determined by the prediction outcome. However, existing FSA designs for TM based on SFQ circuits still suffer from either a narrow margin or excessive circuit area. To achieve compact and stable state transitions using SFQ circuits, we designed High-Capacity Resettable D Flip-Flop (HC-RDFF) cells by cascading storage loops. The proposed FSA was implemented using two HC-RDFFs to store the include and exclude states, respectively. The FSA with 16 states requires only 395 Josephson junctions with a static power of approximately 128 μW, exhibiting a bias margin of −21% to +25% at low speed and a maximum operating frequency of 20 GHz in simulation. We fabricated the HC-RDFF and the FSA using a 10 kA/cm² Nb four-layer superconducting process and verified their correct operation through low-speed measurements. The number of FSA states can be increased simply by extending the cascaded storage loops in the HC-RDFFs. We expect the proposed FSA to be suitable for constructing stable TM systems based on SFQ circuits with reduced hardware costs.
This paper presents a superconducting, magnetically-coupled, shuttle-flux shift register (SF-SR) that stores single flux quantum (SFQ) pulses. This shift register has a DC bias operating margin of ±34% at 10 GHz, with a power dissipation of3.6 μW3.6~\mu W3.6 μWand 38% fewer Josephson junctions (JJs) when scaled up to multiple stages compared to a data flip-flop (DFF) based shift register. The clock input is inductively coupled and is independent from the data input. We then present three applications for our SF-SR. In the first application, we add two non-destructive readout (NDRO) cells to construct a buffer that temporarily stores the temporal information of a series of race logic (RL) pulses. The second application is a pseudo-random number generator based on a linear function shift register (LFSR). The third application is N parallel SF-SRs that can act similar to a deserializer or instead can emulate a single SF-SR of N times higher clock frequency. These three applications motivate deep shift registers with many shifting intervals, which our SF-SR can implement with fewer JJs and lower power consumption compared to DFF-based shift registers.
Abstract One of the main challenges for single flux quantum (SFQ) technology to successfully implement a microprocessor is to have a compact and robust on-chip memory that can be used for register files and cache memory. In this context, we designed high capacity destructive readout (HC-DRO) cells. The design is based on our insight that each cell can store more than one SFQ pulse with the same area footprint of a regular DRO cell. In our current design, we demonstrate a single HC-DRO cell that can store up to three SFQ pulses thereby enabling us to store the equivalent of two bits of memory in a single cell. We have designed a register file (RF) architecture for a microprocessor and used the HC-DRO cells to reduce the Josephson junction count required for its implementation. The RF architecture presented in this work can also be used for implementing cache memories. We also demonstrate the benefits of doubling the storage density with HC-DRO cells by designing a 2-bit branch predictor circuit block for a 5-stage pipeline microprocessor that dramatically improves the cycles per instruction metric of an SFQ based microprocessor. All the design details are presented in the paper by verifying the design concepts through JSIM simulations and Verilog simulations.