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

arXiv:1902.07836 · IEEE Transactions on Applied Superconductivity

ERSFQ 8-bit Parallel Binary Shifter for Energy-Efficient Superconducting CPU

Alex F. Kirichenko, Michael Y. Kamkar, Jason Walter, Igor V. Vernik

Published Mar 18, 2019• 7 citations
arXivHTMLPDF

Abstract

We have designed and tested a parallel 8-bit ERSFQ binary shifter that is one of the essential circuits in the design of the energy-efficient superconducting CPU. The binary shifter performs a bidirectional SHIFT instruction of an 8-bit argument. It consists of a bidirectional triple-port shift register controlled by two (left and right) shift pulse generators asynchronously generating a set number of shift pulses. At first clock cycle, an 8-bit word is loaded into the binary shifter and a 3-bit shift argument is loaded into the desired shift-pulse generator. Next, the generator produces the required number of shift SFQ pulses (from 0 to 7) asynchronously, with a repetition rate set by the internal generator delay of ~ 30 ps. These SFQ pulses are applied to the left (positive) or the right (negative) input of the binary shifter. Finally, after the shift operation is completed, the resulting 8-bit word goes to the parallel output. The complete 8-bit ERSFQ binary shifter, consisting of 820 Josephson junctions, was simulated and optimized using PSCAN2. It was fabricated in MIT Lincoln Lab's 10-kA/cm2SFQ5ee fabrication process with a high-kinetic inductance layer. We have successfully tested the binary shifter at both the LSB-to-MSB and MSB-to-LSB propagation regimes for all eight shift arguments. A single shift operation on a single input word demonstrated operational margins of ±16% of the dc bias current. The correct functionality of the 8-bit ERSFQ binary shifter with the large, exhaustive data pattern was observed within ±10% margins of the dc bias current. In this paper, we describe the design and present the test results for the ERSFQ 8-bit parallel binary shifter.

DOI
10.1109/tasc.2019.2904490

Related papers

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

Guanqun Li, Jie Ren, Yu Wu +4 more

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.

IEEE Transactions on Applied Superconductivity•May 2, 2019•11 citations

ERSFQ 8-Bit Parallel Adders as a Process Benchmark

Alex F. Kirichenko, I. V. Vernik, John A. Vivalda +2 more

We have designed and demonstrated two versions of an ERSFQ 8-bit parallel adder. ERSFQ is a resistor-free approach to dc biasing of Single Flux Quantum circuits that dissipates orders of magnitude less power than a traditional RSFQ logic while operating and has zero dissipation in inactive mode. The adders were designed for and fabricated with various fabrication processes, including HYPRES's 1.0-μm 4-layer 4.5 kA/cm2process, HYPRES's 0.25-μm 4-layer 4.5 kA/cm2process, HYPRES's 0.25-μm 6-layer 4.5 kA/cm2planarized process, and MIT Lincoln Lab's 0.25-μm 4-layer 10 kA/cm2process. These circuits serve as a good LSI fabrication process benchmark. We describe design and report on test results of all versions of the adder.

IEEE Transactions on Applied Superconductivity•Nov 20, 2014•37 citations

ERSFQ 8-Bit Parallel Arithmetic Logic Unit

Alex F. Kirichenko, Igor V. Vernik, Michael Y. Kamkar +4 more

We have designed and tested a parallel 8-bit ERSFQ arithmetic logic unit (ALU). The ALU design employs wave-pipelined instruction execution and features modular bit-slice architecture that is easily extendable to any number of bits and adaptable to current recycling. A carry signal synchronized with an asynchronous instruction propagation provides the wave-pipeline operation of the ALU. The ALU instruction set consists of 14 arithmetical and logical instructions. It has been designed and simulated for operation up to a 10 GHz clock rate at the 10-kA/cm2fabrication process. The ALU is embedded into a shift-register-based high-frequency testbed with on-chip clock generator to allow for comprehensive high frequency testing for all possible operands. The 8-bit ERSFQ ALU, comprising 6840 Josephson junctions, has been fabricated with MIT Lincoln Lab's 10-kA/cm2SFQ5ee fabrication process featuring eight Nb wiring layers and a high-kinetic inductance layer needed for ERSFQ technology. We evaluated the bias margins for all instructions and various operands at both low and high frequency clock. At low frequency, clock and all instruction propagation through ALU were observed with bias margins of +/-11% and +/-9%, respectively. Also at low speed, the ALU exhibited correct functionality for all arithmetical and logical instructions with +/-6% bias margins. We tested the 8-bit ALU for all instructions up to 2.8 GHz clock frequency.

arXiv:1902.09500•IEEE Transactions on Applied Superconductivity•Mar 18, 2019•47 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

Experimental Investigation of ERSFQ Circuit for Parallel Multibit Data Transmission

Timur V. Filippov, Denis Amparo, Michael Y. Kamkar +4 more

We present test results for parallel data communication ERSFQ circuits with clock recovery. We experimentally study on-chip and chip-to-chip parallel data communication circuits with 4-, 8- and 16-bit word lengths. The largest circuit is a 16-bit chip-to-chip communication test circuit embedded into a testbed with clock distributed over a combination of active and passive transmission lines with transmitter/receiver pairs, and is comprised of 3464 Josephson junctions in total. All ERSFQ circuits are fabricated using MITLL 10-kA/cm2SFQ5ee process. For the chip-to-chip communication experiment, a multi-chip module (MCM) is assembled using Hypres' MCM flip-chip bonding process which connected the MIT-LL-made flip-chip to the Hypres-made MCM carrier using 220 signal bumps with 50 um pitch. We experimentally confirmed correct functionality of 4-, 8- and 16-bit circuits and measured their current bias margins. For the 16- bit chip-to-chip communication circuit mounted to a MCM, we measured ±12% dc bias margins similar to the margins measured for the on-chip version of the same circuit. The MCM circuit is also evaluated at high clock speed generated by an external source, while the data words are changed at low speed. The correct functionality is observed without significant reduction in the bias margins using average-voltage test approach.

IEEE International Superconductive Electronics Conference (ISEC)•Jun 1, 2017•11 citations

Fast RSFQ and ERSFQ Parallel Counters

M. Celik, Timur V. Filippov, Anubhav Sahu +4 more

Historically one of the most challenging high-speed RSFQ circuits to implement has been a parallel counter that sums a set of unweighted inputs and produces a binary-weighted word at the same clock rate. A 7-to-3 parallel counter that sums 7 inputs has been designed and tested at clock frequencies up to 50 GHz using its own dedicated testbed. Yielded in both 10- and 20-kA/cm2 current densities using MIT Lincoln Laboratory's foundry, this 7-to-3 summing circuit has become a digital circuit benchmark. Most recently, a version with 15 parallel inputs producing a 4-bit output was designed using two flavors of 8-to-4 summing circuits. The first (8-to-4a), based on the 7-to-3 parallel counter, sums 8 unweighted inputs whereas the second (8-to-4b) sums two 4-bit binary-weighted words by pairwise summing of bits of equal weights from two 8-to-4a blocks. Design considerations for scaling this circuit will be discussed together with the circuit performance and yield.

IEEE International Superconductive Electronics Conference (ISEC)•Jul 1, 2019•2 citations
We have designed and tested a parallel 8-bit ERSFQ binary shifter that is one of the essential circuits in the design of the energy-efficient superconducting CPU. The binary shifter performs a bidirectional SHIFT instruction of an 8-bit argument. It consists of a bidirectional triple-port shift register controlled by two (left and right) shift pulse generators asynchronously generating a set number of shift pulses. At first clock cycle, an 8-bit word is loaded into the binary shifter and a 3-bit shift argument is loaded into the desired shift-pulse generator. Next, the generator produces the required number of shift SFQ pulses (from 0 to 7) asynchronously, with a repetition rate set by the internal generator delay of ~ 30 ps. These SFQ pulses are applied to the left (positive) or the right (negative) input of the binary shifter. Finally, after the shift operation is completed, the resulting 8-bit word goes to the parallel output. The complete 8-bit ERSFQ binary shifter, consisting of 820 Josephson junctions, was simulated and optimized using PSCAN2. It was fabricated in MIT Lincoln Lab's 10-kA/cm2SFQ5ee fabrication process with a high-kinetic inductance layer. We have successfully tested the binary shifter at both the LSB-to-MSB and MSB-to-LSB propagation regimes for all eight shift arguments. A single shift operation on a single input word demonstrated operational margins of ±16% of the dc bias current. The correct functionality of the 8-bit ERSFQ binary shifter with the large, exhaustive data pattern was observed within ±10% margins of the dc bias current. In this paper, we describe the design and present the test results for the ERSFQ 8-bit parallel binary shifter.
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.
We have designed and demonstrated two versions of an ERSFQ 8-bit parallel adder. ERSFQ is a resistor-free approach to dc biasing of Single Flux Quantum circuits that dissipates orders of magnitude less power than a traditional RSFQ logic while operating and has zero dissipation in inactive mode. The adders were designed for and fabricated with various fabrication processes, including HYPRES's 1.0-μm 4-layer 4.5 kA/cm2process, HYPRES's 0.25-μm 4-layer 4.5 kA/cm2process, HYPRES's 0.25-μm 6-layer 4.5 kA/cm2planarized process, and MIT Lincoln Lab's 0.25-μm 4-layer 10 kA/cm2process. These circuits serve as a good LSI fabrication process benchmark. We describe design and report on test results of all versions of the adder.
We have designed and tested a parallel 8-bit ERSFQ arithmetic logic unit (ALU). The ALU design employs wave-pipelined instruction execution and features modular bit-slice architecture that is easily extendable to any number of bits and adaptable to current recycling. A carry signal synchronized with an asynchronous instruction propagation provides the wave-pipeline operation of the ALU. The ALU instruction set consists of 14 arithmetical and logical instructions. It has been designed and simulated for operation up to a 10 GHz clock rate at the 10-kA/cm2fabrication process. The ALU is embedded into a shift-register-based high-frequency testbed with on-chip clock generator to allow for comprehensive high frequency testing for all possible operands. The 8-bit ERSFQ ALU, comprising 6840 Josephson junctions, has been fabricated with MIT Lincoln Lab's 10-kA/cm2SFQ5ee fabrication process featuring eight Nb wiring layers and a high-kinetic inductance layer needed for ERSFQ technology. We evaluated the bias margins for all instructions and various operands at both low and high frequency clock. At low frequency, clock and all instruction propagation through ALU were observed with bias margins of +/-11% and +/-9%, respectively. Also at low speed, the ALU exhibited correct functionality for all arithmetical and logical instructions with +/-6% bias margins. We tested the 8-bit ALU for all instructions up to 2.8 GHz clock frequency.
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.
We present test results for parallel data communication ERSFQ circuits with clock recovery. We experimentally study on-chip and chip-to-chip parallel data communication circuits with 4-, 8- and 16-bit word lengths. The largest circuit is a 16-bit chip-to-chip communication test circuit embedded into a testbed with clock distributed over a combination of active and passive transmission lines with transmitter/receiver pairs, and is comprised of 3464 Josephson junctions in total. All ERSFQ circuits are fabricated using MITLL 10-kA/cm2SFQ5ee process. For the chip-to-chip communication experiment, a multi-chip module (MCM) is assembled using Hypres' MCM flip-chip bonding process which connected the MIT-LL-made flip-chip to the Hypres-made MCM carrier using 220 signal bumps with 50 um pitch. We experimentally confirmed correct functionality of 4-, 8- and 16-bit circuits and measured their current bias margins. For the 16- bit chip-to-chip communication circuit mounted to a MCM, we measured ±12% dc bias margins similar to the margins measured for the on-chip version of the same circuit. The MCM circuit is also evaluated at high clock speed generated by an external source, while the data words are changed at low speed. The correct functionality is observed without significant reduction in the bias margins using average-voltage test approach.
Historically one of the most challenging high-speed RSFQ circuits to implement has been a parallel counter that sums a set of unweighted inputs and produces a binary-weighted word at the same clock rate. A 7-to-3 parallel counter that sums 7 inputs has been designed and tested at clock frequencies up to 50 GHz using its own dedicated testbed. Yielded in both 10- and 20-kA/cm2 current densities using MIT Lincoln Laboratory's foundry, this 7-to-3 summing circuit has become a digital circuit benchmark. Most recently, a version with 15 parallel inputs producing a 4-bit output was designed using two flavors of 8-to-4 summing circuits. The first (8-to-4a), based on the 7-to-3 parallel counter, sums 8 unweighted inputs whereas the second (8-to-4b) sums two 4-bit binary-weighted words by pairwise summing of bits of equal weights from two 8-to-4a blocks. Design considerations for scaling this circuit will be discussed together with the circuit performance and yield.