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IEEE Transactions on Applied Superconductivity

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

Naoki Takeuchi, Kei Ehara, Koji Inoue, Yuki Yamanashi, Nobuyuki Yoshikawa

Published Dec 6, 2012• 67 citations
Publisher

Abstract

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.

DOI
10.1109/tasc.2012.2232336

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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) 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.
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%.
Ultra-low-power adiabatic quantum flux parametron (QFP) logic is investigated since it has the potential to reduce the bit energy per operation to the order of the thermal energy. In this approach, nonhysteretic QFPs are operated slowly to prevent nonadiabatic energy dissipation occurring during switching events. The designed adiabatic QFP gate is estimated to have a dynamic energy dissipation of 12% of I c Φ 0 for a rise/fall time of 1000 ps. It can be further reduced by reducing circuit inductances. Three stages of adiabatic QFP NOT gates were fabricated using a Nb Josephson integrated circuit process and their correct operation was confirmed.
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 devices can operate under extremely low bit energy approaching the thermal limit by varying their potential energy adiabatically using ac bias currents. We have proposed an on-chip ac power source, which is composed of a Josephson relaxation oscillator and a superconductingLCresonator in order to drive AQFP circuits at 5 GHz or higher frequencies. We herein experimentally confirmed the correct switching operation of an AQFP gate at 4.94 GHz using the proposed on-chip ac power source. Furthermore, we confirmed that the ac power source can drive approximately 800 AQFP gates.
Adiabatic quantum flux parametron (AQFP) is a very energy-efficient superconductor logic. In AQFP logic, dynamic energy dissipation can be drastically reduced due to adiabatic switching operations using ac excitation currents. In the present study, we evaluated circuit yields using a large-scale AQFP circuit composed of as many as 10,000 AQFP gates with approximately 20,000 Josephson junctions. We measured eleven chips from four wafers and obtained circuit yields of 48% for 1,000-gate circuits and 22% for 10,000-gate circuits, respectively. In all the circuits, which worked correctly, the margins of excitation currents were as wide as approximately ±20%.