A Brief Review on Mathematical Tools Applicable to Quantum Computing for Modelling and Optimization Problems in Engineering

Since its emergence, quantum computing has enabled a wide spectrum of new possibilities and advantages, including its efficiency in accelerating computational processes exponentially. This has directed much research towards completely novel ways of solving a wide variety of engineering problems, especially through describing quantum versions of many mathematical tools such as Fourier and Laplace transforms, differential equations, systems of linear equations, and optimization techniques, among others. Exploration and development in this direction will revolutionize the world of engineering. In this manuscript, we review the state of the art of these emerging techniques from the perspective of quantum computer development and performance optimization, with a focus on the most common mathematical tools that support engineering applications. This review focuses on the application of these mathematical tools to quantum computer development and performance improvement/optimization. It also identifies the challenges and limitations related to the exploitation of quantum computing and outlines the main opportunities for future contributions. This review aims at offering a valuable reference for researchers in fields of engineering that are likely to turn to quantum computing for solutions. Doi: 10.28991/ESJ-2023-07-01-020 Full Text: PD

Computers from plants we never made. Speculations

We discuss possible designs and prototypes of computing systems that could be based on morphological development of roots, interaction of roots, and analog electrical computation with plants, and plant-derived electronic components. In morphological plant processors data are represented by initial configuration of roots and configurations of sources of attractants and repellents; results of computation are represented by topology of the roots' network. Computation is implemented by the roots following gradients of attractants and repellents, as well as interacting with each other. Problems solvable by plant roots, in principle, include shortest-path, minimum spanning tree, Voronoi diagram, $\alpha$-shapes, convex subdivision of concave polygons. Electrical properties of plants can be modified by loading the plants with functional nanoparticles or coating parts of plants of conductive polymers. Thus, we are in position to make living variable resistors, capacitors, operational amplifiers, multipliers, potentiometers and fixed-function generators. The electrically modified plants can implement summation, integration with respect to time, inversion, multiplication, exponentiation, logarithm, division. Mathematical and engineering problems to be solved can be represented in plant root networks of resistive or reaction elements. Developments in plant-based computing architectures will trigger emergence of a unique community of biologists, electronic engineering and computer scientists working together to produce living electronic devices which future green computers will be made of.Comment: The chapter will be published in "Inspired by Nature. Computing inspired by physics, chemistry and biology. Essays presented to Julian Miller on the occasion of his 60th birthday", Editors: Susan Stepney and Andrew Adamatzky (Springer, 2017

Colloidal Robotics: Programming Structure and Function in Colloidal-Scale Material Through Emergence, Design and Logic

Advancements in self-assembly and top-down fabrication approaches have enabled tailoring of colloidal materials, macromolecules and polymers, and both organic and inorganic nanoparticles to build advanced functional materials. Miniature sized robots made using such materials can have huge impacts in biomedical applications such as minimally invasive surgery, tissue engineering, targeted therapy, diagnostics and single-cell manipulation. This dissertation addresses building such robotic systems that are programmable at the elemental level and are tunable at the macroscopic level. Using coarse-grained particle simulations, analytical modeling, and mechanical design, I have developed three systems to this end that correspond to programming approaches for swarm intelligence, morphological control, and mechanical computing respectively. The first two systems use colloids possessing propulsion, a.k.a. active particles, that harness environmental energy into a propulsion force and can be developed using a wide variety of materials. The first system consists of particles that trigger propulsion only when in contact with other particles. An ensemble of such particles can be tuned externally to form and switch among crystals, gels and clusters as emergent behavior. Further, these systems possess enhanced transport dynamics, which is also tunable. In the second system, the active particles are connected end-to-end in a loop. When actuated, the loops fold into programmed shapes while the internal space is available to accommodate additional components such as sensors, controller, chemicals, and communication devices. The shape and motion information is encoded in the arrangement of active particles along the loop. Besides relevance of these systems in understanding the fundamental physics of non-equilibrium systems, they can be used to develop smart materials that can sense, actuate, compute and communicate. Physical experiments using kilobots—centimeter sized robots—are performed to demonstrate the scale invariance and feasibility of the design. The third system is inspired from the development of materials that respond to external stimuli by expanding or contracting, thereby providing a transduction route that integrates sensing and actuation powered directly by the stimuli. Our work motivates building colloidal scale robots using these stimuli-responsive materials. For maximum control using global triggers, computation ability needs to be incorporated within such robots. The challenge is to design an architecture that is compact, material agnostic, stable under stochastic forces, and employs stimuli-responsive materials. The third system resolves these challenges through an architecture that computes combinatorial logic using mechanical gates. It uses linear actuation—-expansion and contraction—-as input-output signals with the additional benefits of logic circuitry being physically flexible.PHDChemical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155257/1/amayank_1.pd