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

Extremely Energy-Efficient Integrated Circuits Using Adiabatic Superconductor Logic

尚輝 竹内

Published Mar 26, 2014• 1 citation
OpenAlex

Abstract

Complementary metal-oxide-semiconductor (CMOS) circuit technology has sustainedthe exponential growth of computing power for more than 20 years. However, it hasbeen estimated that the power consumption of a next-generation supercomputer willexceed the power supplied from a single power plant. This indicates the need to dramaticallyimprove the energy efficiency of logic devices to achieve future high-endcomputers.As an extremely energy-efficient logic, we proposed and have been investigatingadiabatic quantum-flux-parametron (AQFP) devices. Due to adiabatic switching operations,its bit energy (energy dissipation per bit) can go below Ic 0, where Ic is acritical current of a Josephson junction and 0 is a single-flux-quantum (SFQ). Ic 0corresponds to the energy dissipated at every 2 phase transition in conventional nonadiabaticsuperconductor logics.We have two objectives in this study. One is to reveal physical energy bounds oncomputation through investigation of the energy efficiency of AQFP logic. The otheris to develop fundamental circuits necessary for energy-efficient computing systemsusing AQFP logic.First, we numerically and experimentally demonstrated the sub-Ic 0 bit-energyoperations of AQFP gates to show that AQFP gates operate in adiabatic modes. Weinvestigated the dependence of energy dissipation and operation margins on circuitparameters. After optimizing the parameters, we calculated the bit energy and the biterror rate at 4.2 K to verify the sub-Ic 0 bit-energy operations at a finite temperature.Additionally, we measured the bit energy of an AQFP gate using a superconductorresonator-based method.Secondly, we numerically demonstrated the sub-kBT bit-energy operations, wherekB is the Boltzmann constant and T is temperature, to show that AQFP gates can operatebeyond thermodynamic energy bounds. We investigated the dependence of energydissipation on operation frequencies and damping conditions of Josephson junctions.By using underdamped junctions, we confirmed the sub-kBT bit-energy operationsat a finite temperature thorough circuit simulation. This result indicates that thereis no minimum energy dissipation required for the operations of AQFP gates unlessthe entropy of the system decreases, which corresponds to the Landauer’s argument on the minimum energy dissipation for computation. Also, we discussed quantummechanicalenergy bounds and experimentally demonstrated AQFP gates with underdampedjunctions.Additionally, we investigated reversible computing using AQFP logic with underdampedjunctions, in order to deal with an important but unresolved question: “Isreversible computing achievable by using practical devices?” We built a purely reversiblegate by using AQFP gates, which we designated as the reversible quantumflux-parametron (RQFP) gate. We calculated its energy dissipation and confirmed thatthere is no minimum energy dissipation for reversible logic operations using RQFPgates. To the best of our knowledge, these are the first calculation results that show nominimum energy dissipation in reversible computing that use practical circuit structures.Moreover, our experimental results have demonstrated the logical and physicalreversibility of the RQFP gate. We believe that this is the first demonstration thatshows both logical and physical reversibility using practical devices.Finally, we proposed a novel energy-efficient latch for AQFP logic, which we designatedas the quantum-flux-latch (QFL). Latches are necessary circuitries in largecomputing systems but had been missing in AQFP logic. We discussed its energyefficiency through simulation and experimentally demonstrated correct operations ofthe QFL and a 1-bit shift register using QFLs. Also, we proposed high-speed test circuitsusing QFLs and experimentally demonstrated logic operations of AQFP circuitsat high speed.We strongly believe that our results showed the extremely high energy efficiency ofAQFP logic. These results will move the AQFP logic to practical usage as extremelyenergy-efficient integrated circuits.

Related papers

Simulation of sub-kBT bit-energy operation of adiabatic quantum-flux-parametron logic with low bit-error-rate

Naoki Takeuchi, Yuki Yamanashi, Nobuyuki Yoshikawa

Adiabatic quantum-flux-parametron (AQFP) logic can achieve high energy-efficiency. The bit energy and bit-error-rate (BER) of AQFP gates with under-damped Josephson junctions were simulated. The results indicate that the bit energy reaches 12 yJ, which is only 20% of the thermal energy at 4.2 K, using unshunted 50-μA junctions and excitation currents with a rise/fall time of 2000 ps. Although the bit energy is extremely small, the bias margin, where the BER is less than 10−23, is approximately ±22%. These results indicate there is no minimum energy limitation for the operation of AQFP gates unless the entropy of the system decreases.

Applied Physics Letters•Aug 5, 2013•47 citations

Reversibility and energy dissipation in adiabatic superconductor logic

Naoki Takeuchi, Yuki Yamanashi, Nobuyuki Yoshikawa

Reversible computing is considered to be a key technology to achieve an extremely high energy efficiency in future computers. In this study, we investigated the relationship between reversibility and energy dissipation in adiabatic superconductor logic. We analyzed the evolution of phase differences of Josephson junctions in the reversible quantum-flux-parametron (RQFP) gate and confirmed that the phase differences can change time reversibly, which indicates that the RQFP gate is physically, as well as logically, reversible. We calculated energy dissipation required for the RQFP gate to perform a logic operation and numerically demonstrated that the energy dissipation can fall below the thermal limit, or the Landauer bound, by lowering operation frequencies. We also investigated the 1-bit-erasure gate as a logically irreversible gate and the quasi-RQFP gate as a physically irreversible gate. We calculated the energy dissipation of these irreversible gates and showed that the energy dissipation of these gate is dominated by non-adiabatic state changes, which are induced by unwanted interactions between gates due to logical or physical irreversibility. Our results show that, in reversible computing using adiabatic superconductor logic, logical and physical reversibility are required to achieve energy dissipation smaller than the Landauer bound without non-adiabatic processes caused by gate interactions.

Scientific Reports•Feb 28, 2017•31 citations

Simulation and Experimental Demonstration of Logic Circuits Using an Ultra-Low-Power Adiabatic Quantum-Flux-Parametron

Koji Inoue, Naoki Takeuchi, Kei Ehara +2 more

We have been investigating an ultra-low-power adiabatic quantum-flux-parametron (AQFP) logic, the energy dissipation of which can be decreased by changing its potential energy slowly or adiabatically. In the present study, we designed basic AQFP logic gates and an AQFP 1-bit full adder, and examined their operations through simulations and experiments. The AQFP 1-bit full adder is composed of 46 Josephson junctions, which is approximately one-quarter the number of junctions of a full adder using conventional rapid single-flux-quantum logic. The measurement results indicated that the AQFP 1-bit full adder has a wide current bias margin of as large as ±27.8%.

IEEE Transactions on Applied Superconductivity•Dec 24, 2012•39 citations

An adiabatic superconductor 8-bit adder with 24kBT energy dissipation per junction

Naoki Takeuchi, Taiki Yamae, Christopher Lawrence Ayala +2 more

Adiabatic quantum-flux-parametron (AQFP) logic is an energy-efficient superconductor logic family. In this paper, we conducted the high-frequency operation and energy measurement of an AQFP circuit with more than 1000 Josephson junctions in the experiment. We designed an 8-bit carry look-ahead adder (CLA) using AQFP gates and fabricated it using an advanced fabrication technology, the AIST 10 kA/cm2 Nb high-speed standard process. The correct operation of the 8-bit CLA was demonstrated at a 1-GHz clock frequency for a critical carry propagation test vector. The energy dissipation of the 8-bit CLA was measured by observing the power of excitation current. Our results showed that the energy dissipation per operation of the 8-bit CLA can be estimated to be approximately 1.5 aJ, or 24kBT per junction, where kB is the Boltzmann constant and T is the operating temperature.

Applied Physics Letters•Jan 28, 2019•66 citations

Margin and Energy Dissipation of Adiabatic Quantum-Flux-Parametron Logic at Finite Temperature

Naoki Takeuchi, Kei Ehara, Koji Inoue +2 more

We optimized the circuit parameters of a low-power adiabatic quantum-flux-parametron (AQFP) gate in terms of both bit energy and bias margin and confirmed that the bit energy of the optimized gate with a rise time of 200 ps can be decreased to 6% ofIcΦ0, whereIcis the critical current of the Josephson junctions and Φ0is the single flux quantum. In addition, we investigated the effect of thermal noise on the operation of the optimized AQFP gate. The bias margins and bit error rate of the AQFP gate were examined at finite temperature through circuit simulations, in which the thermal noise was taken into account using the Monte Carlo method. The bias margin of the AQFP gate with bias margins of ±26% at zero temperature shrunk to ±19.4% at 4.2 K, but is still large enough for circuit applications.

IEEE Transactions on Applied Superconductivity•Dec 6, 2012•67 citations

Measurement of low bit-error-rates of adiabatic quantum-flux-parametron logic using a superconductor voltage driver

Naoki Takeuchi, Hideo Suzuki, Nobuyuki Yoshikawa

Adiabatic quantum-flux-parametron (AQFP) is an energy-efficient superconductor logic. The advantage of AQFP is that the switching energy can be reduced by lowering operation frequencies or by increasing the quality factors of Josephson junctions, while keeping the energy barrier height much larger than thermal energy. In other words, both low energy dissipation and low bit error rates (BERs) can be achieved. In this paper, we report the first measurement results of the low BERs of AQFP logic. We used a superconductor voltage driver with a stack of dc superconducting-quantum-interference-devices to amplify the logic signals of AQFP gates into mV-range voltage signals for the BER measurement. Our measurement results showed 3.3 dB and 2.6 dB operation margins, in which BERs were less than 10−20, for 1 Gbps and 2 Gbps data rates, respectively. While the observed BERs were very low, the estimated switching energy for the 1-Gbps operation was only 2 zJ or 30kBT, where kB is the Boltzmann's constant and T is the temperature. Unlike conventional non-adiabatic logic, BERs are not directly associated with switching energy in AQFP.

Applied Physics Letters•May 15, 2017•27 citations
Complementary metal-oxide-semiconductor (CMOS) circuit technology has sustainedthe exponential growth of computing power for more than 20 years. However, it hasbeen estimated that the power consumption of a next-generation supercomputer willexceed the power supplied from a single power plant. This indicates the need to dramaticallyimprove the energy efficiency of logic devices to achieve future high-endcomputers.As an extremely energy-efficient logic, we proposed and have been investigatingadiabatic quantum-flux-parametron (AQFP) devices. Due to adiabatic switching operations,its bit energy (energy dissipation per bit) can go below Ic 0, where Ic is acritical current of a Josephson junction and 0 is a single-flux-quantum (SFQ). Ic 0corresponds to the energy dissipated at every 2 phase transition in conventional nonadiabaticsuperconductor logics.We have two objectives in this study. One is to reveal physical energy bounds oncomputation through investigation of the energy efficiency of AQFP logic. The otheris to develop fundamental circuits necessary for energy-efficient computing systemsusing AQFP logic.First, we numerically and experimentally demonstrated the sub-Ic 0 bit-energyoperations of AQFP gates to show that AQFP gates operate in adiabatic modes. Weinvestigated the dependence of energy dissipation and operation margins on circuitparameters. After optimizing the parameters, we calculated the bit energy and the biterror rate at 4.2 K to verify the sub-Ic 0 bit-energy operations at a finite temperature.Additionally, we measured the bit energy of an AQFP gate using a superconductorresonator-based method.Secondly, we numerically demonstrated the sub-kBT bit-energy operations, wherekB is the Boltzmann constant and T is temperature, to show that AQFP gates can operatebeyond thermodynamic energy bounds. We investigated the dependence of energydissipation on operation frequencies and damping conditions of Josephson junctions.By using underdamped junctions, we confirmed the sub-kBT bit-energy operationsat a finite temperature thorough circuit simulation. This result indicates that thereis no minimum energy dissipation required for the operations of AQFP gates unlessthe entropy of the system decreases, which corresponds to the Landauer’s argument on the minimum energy dissipation for computation. Also, we discussed quantummechanicalenergy bounds and experimentally demonstrated AQFP gates with underdampedjunctions.Additionally, we investigated reversible computing using AQFP logic with underdampedjunctions, in order to deal with an important but unresolved question: “Isreversible computing achievable by using practical devices?” We built a purely reversiblegate by using AQFP gates, which we designated as the reversible quantumflux-parametron (RQFP) gate. We calculated its energy dissipation and confirmed thatthere is no minimum energy dissipation for reversible logic operations using RQFPgates. To the best of our knowledge, these are the first calculation results that show nominimum energy dissipation in reversible computing that use practical circuit structures.Moreover, our experimental results have demonstrated the logical and physicalreversibility of the RQFP gate. We believe that this is the first demonstration thatshows both logical and physical reversibility using practical devices.Finally, we proposed a novel energy-efficient latch for AQFP logic, which we designatedas the quantum-flux-latch (QFL). Latches are necessary circuitries in largecomputing systems but had been missing in AQFP logic. We discussed its energyefficiency through simulation and experimentally demonstrated correct operations ofthe QFL and a 1-bit shift register using QFLs. Also, we proposed high-speed test circuitsusing QFLs and experimentally demonstrated logic operations of AQFP circuitsat high speed.We strongly believe that our results showed the extremely high energy efficiency ofAQFP logic. These results will move the AQFP logic to practical usage as extremelyenergy-efficient integrated circuits.
Adiabatic quantum-flux-parametron (AQFP) logic can achieve high energy-efficiency. The bit energy and bit-error-rate (BER) of AQFP gates with under-damped Josephson junctions were simulated. The results indicate that the bit energy reaches 12 yJ, which is only 20% of the thermal energy at 4.2 K, using unshunted 50-μA junctions and excitation currents with a rise/fall time of 2000 ps. Although the bit energy is extremely small, the bias margin, where the BER is less than 10−23, is approximately ±22%. These results indicate there is no minimum energy limitation for the operation of AQFP gates unless the entropy of the system decreases.
Reversible computing is considered to be a key technology to achieve an extremely high energy efficiency in future computers. In this study, we investigated the relationship between reversibility and energy dissipation in adiabatic superconductor logic. We analyzed the evolution of phase differences of Josephson junctions in the reversible quantum-flux-parametron (RQFP) gate and confirmed that the phase differences can change time reversibly, which indicates that the RQFP gate is physically, as well as logically, reversible. We calculated energy dissipation required for the RQFP gate to perform a logic operation and numerically demonstrated that the energy dissipation can fall below the thermal limit, or the Landauer bound, by lowering operation frequencies. We also investigated the 1-bit-erasure gate as a logically irreversible gate and the quasi-RQFP gate as a physically irreversible gate. We calculated the energy dissipation of these irreversible gates and showed that the energy dissipation of these gate is dominated by non-adiabatic state changes, which are induced by unwanted interactions between gates due to logical or physical irreversibility. Our results show that, in reversible computing using adiabatic superconductor logic, logical and physical reversibility are required to achieve energy dissipation smaller than the Landauer bound without non-adiabatic processes caused by gate interactions.
We have been investigating an ultra-low-power adiabatic quantum-flux-parametron (AQFP) logic, the energy dissipation of which can be decreased by changing its potential energy slowly or adiabatically. In the present study, we designed basic AQFP logic gates and an AQFP 1-bit full adder, and examined their operations through simulations and experiments. The AQFP 1-bit full adder is composed of 46 Josephson junctions, which is approximately one-quarter the number of junctions of a full adder using conventional rapid single-flux-quantum logic. The measurement results indicated that the AQFP 1-bit full adder has a wide current bias margin of as large as ±27.8%.
Adiabatic quantum-flux-parametron (AQFP) logic is an energy-efficient superconductor logic family. In this paper, we conducted the high-frequency operation and energy measurement of an AQFP circuit with more than 1000 Josephson junctions in the experiment. We designed an 8-bit carry look-ahead adder (CLA) using AQFP gates and fabricated it using an advanced fabrication technology, the AIST 10 kA/cm2 Nb high-speed standard process. The correct operation of the 8-bit CLA was demonstrated at a 1-GHz clock frequency for a critical carry propagation test vector. The energy dissipation of the 8-bit CLA was measured by observing the power of excitation current. Our results showed that the energy dissipation per operation of the 8-bit CLA can be estimated to be approximately 1.5 aJ, or 24kBT per junction, where kB is the Boltzmann constant and T is the operating temperature.
We optimized the circuit parameters of a low-power adiabatic quantum-flux-parametron (AQFP) gate in terms of both bit energy and bias margin and confirmed that the bit energy of the optimized gate with a rise time of 200 ps can be decreased to 6% ofIcΦ0, whereIcis the critical current of the Josephson junctions and Φ0is the single flux quantum. In addition, we investigated the effect of thermal noise on the operation of the optimized AQFP gate. The bias margins and bit error rate of the AQFP gate were examined at finite temperature through circuit simulations, in which the thermal noise was taken into account using the Monte Carlo method. The bias margin of the AQFP gate with bias margins of ±26% at zero temperature shrunk to ±19.4% at 4.2 K, but is still large enough for circuit applications.
Adiabatic quantum-flux-parametron (AQFP) is an energy-efficient superconductor logic. The advantage of AQFP is that the switching energy can be reduced by lowering operation frequencies or by increasing the quality factors of Josephson junctions, while keeping the energy barrier height much larger than thermal energy. In other words, both low energy dissipation and low bit error rates (BERs) can be achieved. In this paper, we report the first measurement results of the low BERs of AQFP logic. We used a superconductor voltage driver with a stack of dc superconducting-quantum-interference-devices to amplify the logic signals of AQFP gates into mV-range voltage signals for the BER measurement. Our measurement results showed 3.3 dB and 2.6 dB operation margins, in which BERs were less than 10−20, for 1 Gbps and 2 Gbps data rates, respectively. While the observed BERs were very low, the estimated switching energy for the 1-Gbps operation was only 2 zJ or 30kBT, where kB is the Boltzmann's constant and T is the temperature. Unlike conventional non-adiabatic logic, BERs are not directly associated with switching energy in AQFP.