Abstract Reversible logic circuits can perform logic operations in a thermodynamically reversible manner, or without energy dissipation. The reversible quantum-flux-parametron (RQFP) is a reversible logic gate using adiabatic superconductor logic. In the present study, we design and demonstrate a reversible full adder (RFA) using RQFP gates in order to demonstrate that RQFP gates can be used as building blocks to design reversible logic circuits. An analysis of the time evolution of the phase differences across the Josephson junctions in the RFA showed that its logic state can change quasi-statically during a logic operation. Calculation of the energy dissipation of the RFA showed that it decreases in proportion to the operating frequency. These numerical calculation results ensure that the RFA is thermodynamically and logically reversible. In addition, we experimentally demonstrated correct operation of the RFA for all input data combinations. These results reveal that logic circuits designed using RQFP gates can perform reversible computing, i.e. RQFP gates can be used as building blocks of reversible logic circuits.
Abstract Reversible logic circuits can perform logic operations in a thermodynamically reversible manner, or without energy dissipation. The reversible quantum-flux-parametron (RQFP) is a reversible logic gate using adiabatic superconductor logic. In the present study, we design and demonstrate a reversible full adder (RFA) using RQFP gates in order to demonstrate that RQFP gates can be used as building blocks to design reversible logic circuits. An analysis of the time evolution of the phase differences across the Josephson junctions in the RFA showed that its logic state can change quasi-statically during a logic operation. Calculation of the energy dissipation of the RFA showed that it decreases in proportion to the operating frequency. These numerical calculation results ensure that the RFA is thermodynamically and logically reversible. In addition, we experimentally demonstrated correct operation of the RFA for all input data combinations. These results reveal that logic circuits designed using RQFP gates can perform reversible computing, i.e. RQFP gates can be used as building blocks of reversible logic circuits.
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.
Reversible computing, deriving its inspiration from Landauer's principle, has captured significant interest as a promising technology for logic operations without energy dissipation. The reversible quantum-flux-parametron (RQFP) stands as the first practical reversible logic gate using adiabatic superconducting devices, whose logical and physical reversibility has been experimentally demonstrated. However, due to its unique logic function and structure, the design of RQFP logic circuits is a highly challenging task. At present, there are no automated design tools available for RQFP logic. Therefore, this paper proposes the first exact logic synthesis algorithm for RQFP logic. It formulates the synthesis problem as the Boolean satisfiability problem and subsequently constructs and calls upon the incremental propositional logic model iteratively for optimal synthesis with the least number of gates and garbage outputs. Experimental results on the reversible logic benchmark from RevLib demonstrate the effectiveness of the proposed algorithm.
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%.
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.
Reversible computing has gained increasing attention as a prospective solution for energy dissipation, particularly in quantum computing. As the first practical reversible logic gate using adiabatic superconducting devices, the reversible quantum-flux-parametron (RQFP) has been experimentally demonstrated in logical and physical reversibility. However, the circuit design of RQFP logic poses enormous challenges due to its distinctive logic function and structure. Furthermore, the circuit scale severely restricts the applicability of the existing exact logic synthesis method for RQFP logic. Therefore, this paper proposes RCGP, an automatic synthesis framework based on efficient Cartesian genetic programming, to generate large RQFP logic circuits. RCGP considers the characteristics of RQFP logic circuits to minimize the number of gates and garbage outputs. Meanwhile, RCGP combines circuit simulation with formal verification to assess the functional equivalence between the parent and its offspring. Experimental results on reversible logic benchmarks demonstrate the effectiveness of RCGP.
Abstract Adiabatic quantum-flux-parametron (AQFP) logic is an energy-efficient superconductor logic with zero static power and very small dynamic power due to adiabatic switching operations. In order to build large-scale digital circuits, we built AQFP logic cells using superconductor magnetic shields, which are necessary in order to avoid unwanted magnetic couplings between the cells and excitation currents. In preliminary experimental tests, we confirmed that the unwanted coupling became negligibly small thanks to the superconductor shields. As a demonstration, we designed a four-to-one multiplexor and a 16-junction full adder using the shielded logic cells. In both circuits, we confirmed correct logic operations with wide operation margins of excitation currents. These results indicate that large-scale AQFP digital circuits can be realized using the shielded logic cells.