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

Research on the Bias Network of Energy-Efficient Single Flux Quantum Circuits

Guanqun Li, Jie Ren, Yu Wu, Liliang Ying, Minghui Niu, Liyun Chen, Zhen Wang

Published May 2, 2019• 11 citations
Publisher

Abstract

Superconducting single flux quantum (SFQ) circuits have been shown to offer huge advantages that are ideal for high performance computing applications. These circuits can operate at very high frequencies (tens of GHz) but consume very low power (from nanowatts to microwatts per gate). Energy-efficient SFQ (ERSFQ) circuits, evolved from traditional rapid SFQ (RSFQ) circuits, were invented with the goal of elimination of static power dissipation. When compared with RSFQ circuits, ERSFQ circuits require a new biasing network that includes biasing Josephson junction(s), biasing inductor(s), and feeding Josephson transmission line(s). Some general suggestions on how to design the network have been offered, but a detailed analysis and optimization scenario for the network is still to be provided. In this paper, we first optimize the previously reported DC-biased two-Josephson junction per bit RSFQ shift register circuit, which can be used to provide a more robust, energy-efficient, and high memory capacity storage unit. The simulated power dissipation of 16-bit RSFQ shift register is 0.45 μW per bit when operating at 21.7 GHz. We then convert the RSFQ-based shift register into an ERSFQ structure and investigate the effects of the ERSFQ bias network on the margins of the ERSFQ circuit. Finally, we propose a more comprehensive optimization method for the ERSFQ biasing network.

DOI
10.1109/tasc.2019.2910049

Related papers

Simulation Analysis and Energy-Saving Techniques for ERSFQ Circuits

Naveen Kumar Katam, Oleg A. Mukhanov, Massoud Pedram

Energy-efficient rapid single flux quantum (ERSFQ) circuits have become a viable alternative for the implementation of superconducting circuits due to a large amount of static power consumption in RSFQ circuits. ERSFQ circuits are built upon the popular RSFQ logic circuits by replacing the power-dissipating resistor bias network with a bias network consisting of active devices. In this paper, a simulation study of ERSFQ biasing scheme is carried out by building simulation test benches for both synchronous and asynchronous ERSFQ circuits. A study is carried out to present the optimum value of biasing inductance, influence of the feeding Josephson transmission line (FJTL) and the effect of its size, the effect of the feeding clock frequency, and the effect of the circuit operating frequency. An innovative clock-choking mechanism using magnetic Josephson junctions is also proposed for the FJTL in the case of no logic circuit activity for a current-recycling circuit block, which would help in eliminating the dynamic power consumed due to the switching of bias junctions in a logic circuit. Simulation results for current recycling ERSFQ circuits are presented along with a strategy for implementing large superconducting circuits.

IEEE Transactions on Applied Superconductivity•Mar 18, 2019•23 citations

Research on expansion of E-state bias current margin in ERSFQ circuit

Yujian Ding, Bicong Weng, Xue Zhang +2 more

Abstract As a member of the superconducting integrated circuit family, energy-efficient rapid single flux quantum (ERSFQ) circuit combines low-power consumption with high frequency, showing promise for application in high-energy efficient neuromorphic computing and traditional high-performance computing. Previous studies have demonstrated that there are typically two energy dissipation states in working ERSFQ circuits: energy-efficient SFQ state (E-state) and resistive-biased SFQ state (R-state). These states occur at different biasing current ranges, and the sum of the bias margin of these two states is close to the margin of rapid single flux quantum (RSFQ) circuits of the same design. For ultra-low-power applications, the bias current margin of the R-state must be excluded, leading to a substantially narrower bias margin in ERSFQ circuits than in their RSFQ counterparts. In our previous research, we proposed the feeding pulse method to increase the bias current margin by extending the lower boundary of the E-state through the injection of feeding pulses into the feeding Josephson transmission line (FJTL). In this study, we further investigated the current distribution mechanism in ERSFQ circuits and, based on this, proposed a method of optimizing design of the FJTL to redirect excess current to the FJTL, so as to expand the upper boundary of the E-state’s bias current margin. We tested an ERSFQ 8-bit shift register of the ERSFQ by applying methods proposed in this work together with the feeding pulses method proposed before. The results demonstrated that the bias current margin of the E-state expanded from (94%, 98%) to (56%, 116%), corresponding to a 14-times increase, with both the lower and upper boundary successfully extended. Our research addresses the issue of limited current bias margin in ERSFQ circuits during actual operation, providing a more robust ERSFQ technology for future applications in neural networks and high-performance computing.

Superconductor Science and Technology•Aug 1, 2025•0 citations

Effects of Adaptive DC Biasing on Operational Margins in ERSFQ Circuits

Claudio Shawawreh, Denis Amparo, Jie Ren +7 more

Energy efficiency has become the primary parameter for the design of next-generation single flux quantum (SFQ) circuits. This, however, needs to be balanced with optimization for clock speed and bias margins. Here, we experimentally study the tradeoff between circuit activity, energy efficiency, and bias margins for zero static power dissipation ERSFQ circuits. For ERSFQ, dc power is provided by a Josephson transmission line (JTL) called a “feeding” JTL (FJTL), which acts as a voltage source. As a test case, shift registers and multiplexers were laid out and fabricated in both HYPRES's and MIT-LL's 10-kA/cm2fabrication processes and tested at low (~kHz) and high (~GHz) clock frequencies. The functional bias margins for these circuits increase significantly from +/-4% to over +/-19% when the Josephson junction count in the FJTL was increased to ~30% of total dc bias current of the circuit. Based on our findings, we discuss how to optimize ERSFQ circuits for both energy efficiency and dc bias margins.

IEEE Transactions on Applied Superconductivity•Feb 15, 2017•20 citations

xeSFQ: clockless SFQ logic with zero bias network power dissipation

Jennifer E. Volk, George Tzimpragos, Oleg A. Mukhanov

Abstract Energy-efficient rapid single flux quantum (ERSFQ) circuits suppress the dominant static power dissipation of Rapid SFQ logic by replacing bias resistors with current-limiting bias Josephson junctions (JJs) and inductors. In practice, however, these JJs introduce power dissipation in the DC bias network due to switching events required to correct data-dependent phase imbalances, with dissipation often comparable to that of dynamic power. This paper presents xeSFQ, a new SFQ logic family that integrates alternating SFQ (xSFQ) encoding with ERSFQ biasing. By enforcing a single pulse per line per logical cycle, xeSFQ maintains uniform phase across the circuit, thereby eliminating bias JJ switching during operation and achieving zero bias network power dissipation. Extensive analog simulations and logic synthesis results, from individual gates to ISCAS and EPFL benchmarks, validate this hypothesis and demonstrate the efficiency and scalability advantages of the proposed approach.

Superconductor Science and Technology•Jul 1, 2026•0 citations

Power Optimization of 50 GHz ERSFQ Circuits

Mustapha M. Habib, Timur V. Filippov, Anubhav Sahu +3 more

The Energy-efficient Rapid Single Flux Quantum (ERSFQ) logic family offers zero-static power dissipation. Any ERSFQ circuit requires a feeding Josephson transmission line (FJTL), a relatively large active transmission line, which serves as an accurate voltage source. For proper operation, the FJTL needs to be continuously pumped at a frequency that is equal to or higher than the highest clock frequency of the ERSFQ circuit. We selected an on-chip pseudo-random binary sequence (PRBS) generator as the example circuit since it naturally facilitates quantitative measurements of operating bias margins in terms of bit error rate (BER). Using external and internal flux pump sources, we performed extensive experimental studies on BER for ERSFQ PRBS generators operating at clock frequencies up to 50 GHz. We paid special attention to the over-pumping regime, where the FJTL pump frequency is higher than the PRBS clock frequency and confirmed its superiority in improving BER. At 35.56 GHz clock frequency, a group of 4 PRBS generators and 4 individual FJTLs with the bias current ratio (BCR) equal to 1, had a BER lower than 10−12and bias margins of ±25% for internal and external flux pump sources over-pumping at 6.25% above clock frequency. The maximal operational clock frequency of a single ERSFQ PRBS generator with intrinsic pump source (+6.25% over-pumping) and BER−12was 49.53 GHz. We also focused on optimization of the FJTL's size to reduce the power consumption and the area occupied by the FJTL itself. All chips were fabricated at MIT-Lincoln Laboratory using the SFQ5ee fab node. Future steps required for better understanding of ERSFQ operation are discussed.

IEEE Transactions on Applied Superconductivity•Jan 27, 2023•7 citations

18-GHz, 4.0-aJ/bit Operation of Ultra-Low-Energy Rapid Single-Flux-Quantum Shift Registers

Masamitsu Tanaka, Masato Ito, Kitayama Atsushi +2 more

We demonstrate rapid single-flux-quantum (RSFQ) circuits with reduced energy consumption by lowering the driving voltages and critical currents of Josephson junctions (JJs). At lowered voltages, the energy statically consumed by bias resistors (which is dominant in RSFQ circuits) is reduced. In addition, we show that when RSFQ circuits are driven by lowered constant voltages, the dynamic energy consumption resulting from the switching of JJs is reduced because of the suppression of the amplitudes of the signal voltage pulses, even though the switching speed becomes slower. Utilization of miniaturized JJs with smaller critical currents also leads to the reduction of static and dynamic energy consumption without decreasing the switching speed. We have designed and tested ultra-low-energy 8-bit shift registers, and verified the correctness of high-speed operations up to 18 GHz. The average energy consumption, including that at the bias resistors, was measured at 4.0 aJ/bit, which represents an energy efficiency two orders of magnitude better than that of standard RSFQ circuits.

Japanese Journal of Applied Physics•May 1, 2012•159 citations
Superconducting single flux quantum (SFQ) circuits have been shown to offer huge advantages that are ideal for high performance computing applications. These circuits can operate at very high frequencies (tens of GHz) but consume very low power (from nanowatts to microwatts per gate). Energy-efficient SFQ (ERSFQ) circuits, evolved from traditional rapid SFQ (RSFQ) circuits, were invented with the goal of elimination of static power dissipation. When compared with RSFQ circuits, ERSFQ circuits require a new biasing network that includes biasing Josephson junction(s), biasing inductor(s), and feeding Josephson transmission line(s). Some general suggestions on how to design the network have been offered, but a detailed analysis and optimization scenario for the network is still to be provided. In this paper, we first optimize the previously reported DC-biased two-Josephson junction per bit RSFQ shift register circuit, which can be used to provide a more robust, energy-efficient, and high memory capacity storage unit. The simulated power dissipation of 16-bit RSFQ shift register is 0.45 μW per bit when operating at 21.7 GHz. We then convert the RSFQ-based shift register into an ERSFQ structure and investigate the effects of the ERSFQ bias network on the margins of the ERSFQ circuit. Finally, we propose a more comprehensive optimization method for the ERSFQ biasing network.
Energy-efficient rapid single flux quantum (ERSFQ) circuits have become a viable alternative for the implementation of superconducting circuits due to a large amount of static power consumption in RSFQ circuits. ERSFQ circuits are built upon the popular RSFQ logic circuits by replacing the power-dissipating resistor bias network with a bias network consisting of active devices. In this paper, a simulation study of ERSFQ biasing scheme is carried out by building simulation test benches for both synchronous and asynchronous ERSFQ circuits. A study is carried out to present the optimum value of biasing inductance, influence of the feeding Josephson transmission line (FJTL) and the effect of its size, the effect of the feeding clock frequency, and the effect of the circuit operating frequency. An innovative clock-choking mechanism using magnetic Josephson junctions is also proposed for the FJTL in the case of no logic circuit activity for a current-recycling circuit block, which would help in eliminating the dynamic power consumed due to the switching of bias junctions in a logic circuit. Simulation results for current recycling ERSFQ circuits are presented along with a strategy for implementing large superconducting circuits.
Abstract As a member of the superconducting integrated circuit family, energy-efficient rapid single flux quantum (ERSFQ) circuit combines low-power consumption with high frequency, showing promise for application in high-energy efficient neuromorphic computing and traditional high-performance computing. Previous studies have demonstrated that there are typically two energy dissipation states in working ERSFQ circuits: energy-efficient SFQ state (E-state) and resistive-biased SFQ state (R-state). These states occur at different biasing current ranges, and the sum of the bias margin of these two states is close to the margin of rapid single flux quantum (RSFQ) circuits of the same design. For ultra-low-power applications, the bias current margin of the R-state must be excluded, leading to a substantially narrower bias margin in ERSFQ circuits than in their RSFQ counterparts. In our previous research, we proposed the feeding pulse method to increase the bias current margin by extending the lower boundary of the E-state through the injection of feeding pulses into the feeding Josephson transmission line (FJTL). In this study, we further investigated the current distribution mechanism in ERSFQ circuits and, based on this, proposed a method of optimizing design of the FJTL to redirect excess current to the FJTL, so as to expand the upper boundary of the E-state’s bias current margin. We tested an ERSFQ 8-bit shift register of the ERSFQ by applying methods proposed in this work together with the feeding pulses method proposed before. The results demonstrated that the bias current margin of the E-state expanded from (94%, 98%) to (56%, 116%), corresponding to a 14-times increase, with both the lower and upper boundary successfully extended. Our research addresses the issue of limited current bias margin in ERSFQ circuits during actual operation, providing a more robust ERSFQ technology for future applications in neural networks and high-performance computing.
Energy efficiency has become the primary parameter for the design of next-generation single flux quantum (SFQ) circuits. This, however, needs to be balanced with optimization for clock speed and bias margins. Here, we experimentally study the tradeoff between circuit activity, energy efficiency, and bias margins for zero static power dissipation ERSFQ circuits. For ERSFQ, dc power is provided by a Josephson transmission line (JTL) called a “feeding” JTL (FJTL), which acts as a voltage source. As a test case, shift registers and multiplexers were laid out and fabricated in both HYPRES's and MIT-LL's 10-kA/cm2fabrication processes and tested at low (~kHz) and high (~GHz) clock frequencies. The functional bias margins for these circuits increase significantly from +/-4% to over +/-19% when the Josephson junction count in the FJTL was increased to ~30% of total dc bias current of the circuit. Based on our findings, we discuss how to optimize ERSFQ circuits for both energy efficiency and dc bias margins.
Abstract Energy-efficient rapid single flux quantum (ERSFQ) circuits suppress the dominant static power dissipation of Rapid SFQ logic by replacing bias resistors with current-limiting bias Josephson junctions (JJs) and inductors. In practice, however, these JJs introduce power dissipation in the DC bias network due to switching events required to correct data-dependent phase imbalances, with dissipation often comparable to that of dynamic power. This paper presents xeSFQ, a new SFQ logic family that integrates alternating SFQ (xSFQ) encoding with ERSFQ biasing. By enforcing a single pulse per line per logical cycle, xeSFQ maintains uniform phase across the circuit, thereby eliminating bias JJ switching during operation and achieving zero bias network power dissipation. Extensive analog simulations and logic synthesis results, from individual gates to ISCAS and EPFL benchmarks, validate this hypothesis and demonstrate the efficiency and scalability advantages of the proposed approach.
The Energy-efficient Rapid Single Flux Quantum (ERSFQ) logic family offers zero-static power dissipation. Any ERSFQ circuit requires a feeding Josephson transmission line (FJTL), a relatively large active transmission line, which serves as an accurate voltage source. For proper operation, the FJTL needs to be continuously pumped at a frequency that is equal to or higher than the highest clock frequency of the ERSFQ circuit. We selected an on-chip pseudo-random binary sequence (PRBS) generator as the example circuit since it naturally facilitates quantitative measurements of operating bias margins in terms of bit error rate (BER). Using external and internal flux pump sources, we performed extensive experimental studies on BER for ERSFQ PRBS generators operating at clock frequencies up to 50 GHz. We paid special attention to the over-pumping regime, where the FJTL pump frequency is higher than the PRBS clock frequency and confirmed its superiority in improving BER. At 35.56 GHz clock frequency, a group of 4 PRBS generators and 4 individual FJTLs with the bias current ratio (BCR) equal to 1, had a BER lower than 10−12and bias margins of ±25% for internal and external flux pump sources over-pumping at 6.25% above clock frequency. The maximal operational clock frequency of a single ERSFQ PRBS generator with intrinsic pump source (+6.25% over-pumping) and BER−12was 49.53 GHz. We also focused on optimization of the FJTL's size to reduce the power consumption and the area occupied by the FJTL itself. All chips were fabricated at MIT-Lincoln Laboratory using the SFQ5ee fab node. Future steps required for better understanding of ERSFQ operation are discussed.
We demonstrate rapid single-flux-quantum (RSFQ) circuits with reduced energy consumption by lowering the driving voltages and critical currents of Josephson junctions (JJs). At lowered voltages, the energy statically consumed by bias resistors (which is dominant in RSFQ circuits) is reduced. In addition, we show that when RSFQ circuits are driven by lowered constant voltages, the dynamic energy consumption resulting from the switching of JJs is reduced because of the suppression of the amplitudes of the signal voltage pulses, even though the switching speed becomes slower. Utilization of miniaturized JJs with smaller critical currents also leads to the reduction of static and dynamic energy consumption without decreasing the switching speed. We have designed and tested ultra-low-energy 8-bit shift registers, and verified the correctness of high-speed operations up to 18 GHz. The average energy consumption, including that at the bias resistors, was measured at 4.0 aJ/bit, which represents an energy efficiency two orders of magnitude better than that of standard RSFQ circuits.