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Journal of Communications Technology and Electronics

π Junctions in Adiabatic Superconductor Logic Cells

Igor I. Soloviev, G. S. Khismatullin, N. V. Klenov, Andrey E. Schegolev

Published Dec 1, 2022• 5 citations
Publisher

Abstract

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.

DOI
10.1134/s106422692212021x

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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.
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.
Superconductor/ferromagnet/superconductor Josephson junctions across which the phases of superconducting order parameters are shifted by π in the ground state are called π Josephson junctions (π-JJs). Recently, several groups have established the fabrication technology of π-JJs so that superconductor logic families exploit π-JJs to improve circuit performance. In this paper, we investigate the advantages of π-JJs in adiabatic quantum-flux-parametron (AQFP) logic, which is an adiabatic superconductor logic based on the quantum-flux-parametron. First, we show that AQFP logic with π-JJs (π-AQFP) can operate using only π-JJs and can be powered and clocked in the same way as the conventional AQFP logic. Then, we show that π-AQFP logic can realize inverters without using signal transformers, which generally occupy a large area in AQFP gates and are difficult to miniaturize. We demonstrate π-AQFP inverters using numerical simulation to establish that π-AQFP logic operates adiabatically and robustly. Our results show that π-JJs can be easily incorporated into AQFP logic and enhance the circuit density of AQFP logic.
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.
We have found that the size of some rapid single-flux quantum (RSFQ) logic cells based on conventional 0-type Josephson junctions can be significantly reduced by using a π-type junction as a phase shifter in passive (nonswitching) mode. In comparison with the recently suggested active (switching) π-junctions mode, the passive mode offers much greater operation margins for their critical current Icπ. This gives π-junctions a chance to be implemented in RSFQ designs in the near future. As an example, we have simulated the operation of a toggle flip flop with zero-geometrical inductance of the fluxon storage loop. Simulations show that the parametric inductance of the π-junction and its normal resistance Rn form a low-pass filter, which sets the low limit for π-junctions IcπRn product, but offers a wide range of variations of the other parameters. The possible reduction of RSFQ cell size by using π-junctions opens the way to scale superconducting logic circuits down to the submicron dimensions.
We present a concept of an advanced rapid single-flux-quantum (RSFQ) logic circuit family using the combination of 0-shifted and π-shifted Josephson junctions. A π-shift in the current-phase relationship can be obtained in several types of Josephson junctions, such as Josephson junctions containing a ferromagnet barrier layer, depending on its thickness and temperature. We use a superconducting quantum interference devices composed of a pair of 0- and π-shifted Josephson junctions (0-π SQUIDs) as a basic circuit element. Unlike the conventional RSFQ logic, bistability is obtained by spontaneous circular currents without using a large superconductor loop, and the state can be flipped by smaller driving currents. These features lead to energy- and/or space-efficient logic gates. In this paper, we show several example circuits where we represent signals by flips of the states of a 0-π SQUID. We obtained successful operation of the circuits from numerical simulation.
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.