Adiabatic superconducting logic circuits can ensure the practical implementation of operations with the energy dissipation below the Landauer limit. However, applications of the existing solutions are limited because of two contradictory requirements of a high energy efficiency and a sufficiently fast response of devices. Josephson junctions with a negative critical current (π junctions) allow one to obtain a certain form of the potential energy of superconducting circuits and, as a result, a practically required degree of control of dynamic processes in the proposed reversible logic cells. The features of the current transport and balance of Josephson phases in circuits with π junctions make it possible to improve the coupling between the parts of a reversible computer by a factor more than 2. At the same time, the continuous evolution of the state is ensured at higher critical currents and higher characteristic voltages of the main Josephson junctions of adiabatic superconducting logic cells, which allows an increase in the response rate.
Adiabatic superconducting logic circuits can ensure the practical implementation of operations with the energy dissipation below the Landauer limit. However, applications of the existing solutions are limited because of two contradictory requirements of a high energy efficiency and a sufficiently fast response of devices. Josephson junctions with a negative critical current (π junctions) allow one to obtain a certain form of the potential energy of superconducting circuits and, as a result, a practically required degree of control of dynamic processes in the proposed reversible logic cells. The features of the current transport and balance of Josephson phases in circuits with π junctions make it possible to improve the coupling between the parts of a reversible computer by a factor more than 2. At the same time, the continuous evolution of the state is ensured at higher critical currents and higher characteristic voltages of the main Josephson junctions of adiabatic superconducting logic cells, which allows an increase in the response rate.
Abstract Recently, adiabatic superconducting logic has been actively used to process broadband group signals in situations in which ultralow energy dissipation is critical in computing (e.g., in coprocessors that control the operation of future quantum computers). This paper presents a general approach to the analysis of the basic principles of operation of logic circuits based on a superconducting quantum parametron; the key parameters responsible for the efficiency of the functioning of such cells are indicated. On the basis of a general approach, improved cells containing Josephson junctions with a negative critical current (π junctions) are proposed and investigated.
The transition to Josephson digital circuits with the representation of information in the form of phase jumps of the superconducting order parameter on heterostructures promises a radical increase in the degree of integration while maintaining high speed and energy efficiency. However, it is not yet possible to manufacture reproducible bistable Josephson junctions, which are necessary for the functioning of the previously proposed basic units of the phase logic. To solve this problem, the concept of phase logic based on π junctions is proposed and analyzed within the resistive model of Josephson heterostructures. The potential energy of such junctions has a single minimum, with a difference in the order parameters of the electrodes equal to π. It is demonstrated that the use of π junctions allows one to implement the entire set of logic devices necessary for the operation of digital computing devices based on phase logic.
Today's industrial digital logic gates are reaching a technological limit and meanwhile, superconducting circuits produce fundamentally different technologies for the future of digital computing. The standard logic is irreversible and yet superconducting circuits allow digital reversible logic with a much higher energy efficiency per gate operation. Previous reversible gate circuits were “adiabatic,” meaning that they used adiabatic-clocking waveforms for their operation power. However, we are studying logic starting from a ballistic model, where ftuxons enable gates using only energy from their inertia. Our ftuxons are defined in Long Josephson Junctions (LJJs) and may travel ballistically, similar to a particle with negligible damping. Once a ftuxon's energy approaches close enough to the gate, a resonance is induced at the gate and the ftuxon loses its definite topology. Gates are comprised of the (few Josephson-penetration-depth long) ends of LJJs and a connecting circuit interface. Only after the resonance does a ftuxon get formed and yield the gate result without external power: a ftuxon for bit-state 0 or an antiftuxon for bit-state 1. Through earlier analysis of the numerically discovered phenomena we find that dynamics can be described with ftuxon- and antiftuxon-like excitations at the ends of LJJs within the gate. The bit-switching action in our gates is resonant indicating fundamentally different dynamics than the classic model of adiabatic reversible circuits. Our ballistic Reversible Fluxon Logic (RFL) gates have no added damping and calculated energy efficiencies of over 97%. Thus in our dynamical process the “bit energy” is preserved. However, irreversible logic completely dissipates this at each operation (e.g., charging energy in CMOS or SFQ energy in irreversible SFQ logic). An RFL gate can achieve a fast gate operation since its resonance is only few JJ plasma periods. We also describe the CNOT in our technology. It is enabled by a couple of vital gates: A IDSN logic gate, similar to our other ballistic gates, and a Store-aNd-Launch (SNL) timing gate to ensure proper synchronization of the bits. The latter allows bit storage followed by launching of a data ftuxon using an adiabatic pulse from a clock ftuxon with lower energy than the data ftuxon for good CNOT efficiency.
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.
Low energy dissipation and ability to operate at low temperatures provide for Josephson junction circuits a niche as a support for low temperature devices. With high speed operation (Chen W. et al., 1999) capability the Josephson junction circuits make a prime candidate for applications which are difficult to engineer with existing CMOS technology. The development of Josephson junction technology took a major turn for the better with the invention of the Rapid-Single-Flux-Quantum (RSFQ) devices (Likharev K.K. et al., 1991), an improvement over voltage biased Josephson Junctions logic which were plagued with the junction switching and reset problems. The modern applications of SFQ circuits extend to a larger range of temperature operation and the applications vary from low temperature magnetic sensor, to high speed mixed signal circuits, voltage and current standards (Turner C.W. et al., 1998), and auxiliary components for quantum computing circuits. Most of the SFQ circuits are fabricated with Niobium, but Aluminum based circuits are being used for quantum gates (Nielsen M.A. et al., 2000) and qubit operations. SFQ circuits based on Magnesium di-Boride junctions are being developed for higher temperature operations (Tahara S. et al., 2004). Predominantly most of the Josephson junction circuits today are operated at around 4K. All the circuits are optimized usually for liquid helium temperatures, so the circuits operated in helium bath Dewars or cryostat's do not experience any temperature gradients or drift effects which can affect the operating margins. With the improvement in the fabrication technology and soft-wares for SFQ circuit technology, the designing complex circuits have become easier. Complex Circuits with over 20K junctions such digital synthesizer and digital RF Trans-receiver have already been demonstrated (Oleg M.A. et al., 2011). Development of circuits over 100K junctions are actively under progress. However, with enormously large circuits, power requirements also increase. Looking at the range of applications and complexity of the problems of energy minimization, we try to look at the problem in two approaches. One for large complex circuits, we try to reduce the power bias itself, or the overall load of current that is supplied
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.