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Journal of Experimental and Theoretical Physics Letters

Phase Logic Based on π Josephson Junctions

A. A. Maksimovskaya, Vsevolod I. Ruzhickiy, N. V. Klenov, Sergey V. Bakurskiy, M. Yu. Kupriyanov, Igor I. Soloviev

Published Jun 1, 2022• 14 citations
Publisher

Abstract

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.

DOI
10.1134/s0021364022600884

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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.
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.
Superconducting digital computing systems, primarily involving Josephson junctions are actively being pursued as high performance and low energy dissipating alternatives to CMOS-based technologies for petascale and exascale computers, although several challenges still exist in overcoming barriers to practically implement these technologies. In this paper, we present an alternative superconducting logic structure: quantized charge-based logic circuits using quantum phase-slip junctions, which have been identified as dual devices to Josephson junctions. Basic principles of logic implementation using quantum phase-slips are presented in simulations with the help of a SPICE model that has been developed for the quantum phase-slip structures. Circuit elements that form the building blocks for complex logic circuit design are introduced. Two different logic gate designs: or gate and xor gate are presented to demonstrate the usage of the building blocks introduced.
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.
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.
Magnetic flux quantization in superconductors allows the implementation of fast and energy-efficient digital superconducting circuits. However, information representation in magnetic flux severely limits the functional density and is a long-standing problem. Here, we introduce the concept of superconducting digital circuits that do not utilize magnetic flux and have no inductors. We argue that neither the use of geometric nor kinetic inductance is promising for the scaling down of superconducting circuits. The key idea of our approach is the utilization of bistable Josephson junctions, allowing the representation of information through the Josephson energy. Since the proposed circuits are composed only of Josephson junctions, they can be called all-Josephson junction (all-JJ) circuits. We present a methodology for the design of circuits consisting of conventional and bistable junctions. We analyze the principles of the circuit's functioning, ranging from simple logic cells to an 8-bit parallel adder. The utilization of bistable junctions in the all-JJ circuits is promising for the simplification of schematics and a decrease of the JJ count, leading to space efficiency.
Abstract Superconductor Electronics (SCE) is a fast and power-efficient technology with great potential for overcoming conventional CMOS electronics’ scaling limits. Nevertheless, the primary challenge confronting SCE today is its integration level, which lags several orders of magnitude behind CMOS circuits. In this study, we have innovated and simulated a novel logic family grounded in the principles of phase shifts occurring in 0 and π Josephson junctions. The fast phase logic (FPL) eliminates the need for large inductor loops and shunt resistances by combining the half-flux and phase logic. Therefore, the Josephson junction (JJ) area only limits the integration density. The cells designed with this paradigm are fast, and the clock-to-Q delay for logic cells is about 4ps. While maintaining over 50% parameter margins for wiring cells. This logic is power efficient and can increase the integration by at least 100×in the SCE chips.