Ground State Spin Logic

Designing and optimizing cost functions and energy landscapes is a problem encountered in many fields of science and engineering. These landscapes and cost functions can be embedded and annealed in experimentally controllable spin Hamiltonians. Using an approach based on group theory and symmetries, we examine the embedding of Boolean logic gates into the ground state subspace of such spin systems. We describe parameterized families of diagonal Hamiltonians and symmetry operations which preserve the ground state subspace encoding the truth tables of Boolean formulas. The ground state embeddings of adder circuits are used to illustrate how gates are combined and simplified using symmetry. Our work is relevant for experimental demonstrations of ground state embeddings found in both classical optimization as well as adiabatic quantum optimization.Comment: 6 pages + 3 pages appendix, 7 figures, 1 tabl

Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions

Magnetic skyrmions, which are topological particle-like excitations in ferromagnets, have attracted a lot of attention recently. Skyrmionics is an attempt to use magnetic skyrmions as information carriers in next generation spintronic devices. Proposals of manipulations and operations of skyrmions are highly desired. Here, we show that the conversion, duplication and merging of isolated skyrmions with different chirality and topology are possible all in one system. We also demonstrate the conversion of a skyrmion into another form of a skyrmion, i.e., a bimeron. We design spin logic gates such as the AND and OR gates based on manipulations of skyrmions. These results provide important guidelines for utilizing the topology of nanoscale spin textures as information carriers in novel magnetic sensors and spin logic devices.Comment: 17 pages, 6 figure

All-spin logic operations: Memory device and Reconfigurable computing

Exploiting spin degree of freedom of electron a new proposal is given to characterize spin-based logical operations using a quantum interferometer that can be utilized as a programmable spin logic device (PSLD). The ON and OFF states of both inputs and outputs are described by {\em spin} state only, circumventing spin-to-charge conversion at every stage as often used in conventional devices with the inclusion of extra hardware that can eventually diminish the efficiency. All possible logic functions can be engineered from a single device without redesigning the circuit which certainly offers the opportunities of designing new generation spintronic devices. Moreover we also discuss the utilization of the present model as a memory device and suitable computing operations with proposed experimental setups.Comment: 6 pages, 7 figure