Superconducting Digital Logic Families Using Quantum Phase-slip Junctions

Abstract

Superconducting electronics based computing is being actively pursued as an alternative to CMOS-based computing for high performance computing due to their inherent advantages such as low-power and high switching speed. These circuits are predominantly based on Josephson junctions. In this work, superconducting digital electronic circuits based on a device called quantum phase-slip junction are explored. Quantum phase-slip junctions are dual to Josephson junctions based on charge-flux duality of Maxwell's equations. Therefore, incorporating these devices into superconducting computers could lead to certain advantages that may overcome some of the challenges currently faced by Josephson junction based circuits, as explained in later chapters in this document.

Three different superconducting logic circuit families are introduced using quantum phase-slip junctions and Josephson junctions, namely charge-based logic family, complementary quantum logic family and adiabatic quantum charge parametron logic family, with different advantages and challenges for each of the circuit families. The various circuits comprising these logic families have been demonstrated using circuit simulations in a program called WRSPICE. For this purpose, a SPICE model has been developed for quantum phase-slip junctions that can be loaded into WRSPICE.

Charge-based logic family using quantum-phase-slip junctions is inspired from single-flux quantum family based on Josephson junctions. The presence or absence of a single charge pulse (i.e. a current pulse of a constant area equal to $2e$ where $e$ is the charge of an electron, generated by switching a quantum phase-slip junction) constitutes the logical bit $1$ and $0$ respectively. Several circuits in this logic family are exact dual versions of single-flux quantum family, while several additional circuits are designed that are exclusive to charge-based logic family. It is comprised of logic gates such as AND, OR, XOR, NAND, NOR etc., and various data manipulation circuits such as buffer circuits, fan-out circuits and merger circuits.

Complementary quantum logic family combines the charge-based logic with quantum phase-slip junctions and flux-based logic with Josephson junctions. Therefore, it consists of circuits that convert flux to charge and vice-versa. Additionally, a control circuit has been designed that has a gate input to turn the output signal ON or OFF. Logic and fan-out circuits have been demonstrated using circuit simulations that comprise of basic principles introduced in flux-charge conversion circuits and control circuit.

Adiabatic quantum charge parametron family is a variation of charge-based logic family that when operated in a certain mode of operation allows switching from logical bit $1$ to $0$ and vice-versa while dissipating energy less than the thermal energy at that temperature. Therefore, these circuits are compatible with reversible computing. The switching energy calculations that correspond to the circuit parameters and its operating conditions required for adiabatic switching (i.e. when switching energy is below the thermal energy $K_BT$) are shown. Universal logic gates such as the Majority gate has been designed and demonstrated in simulation. Several examples that use Majority gate to achieve logic operations such as AND, OR, XOR etc. are shown.

Theoretical calculations were performed based on existing physics models for quantum phase-slip junctions to extract the physical design parameters of the devices based on required circuit parameters according to simulation. Using the same calculations, materials suitable for these devices were estimated that provide highest probability of exhibiting quantum phase-slips. Additionally, the operating temperature of the circuit families introduced for several materials of interest are obtained from these calculations. The switching speeds versus power dissipation for varying device parameters are calculated and compared to existing superconducting technologies using Josephson junctions.

The work presented in this dissertation is intended to generate interest in a new field of digital logic circuits using quantum phase-slip junctions, the devices that were not previously explored for use in classical computing systems. The new circuit families introduced exhibit several potential advantages over the existing circuits in terms of higher energy efficiency, faster switching speed as well as ease of operation that may lead to a possibility of higher integration density.