The articles in this special section compare classical and quantum electromagnetics. The articles introduce the fundamental concepts of quantum electromagnetics and compares them to classical ones. When James Clerk Maxwell published his paper on those equations that bear his name, he could never have imagined that they would have such a wide-ranging impact. These equations are valid from static to X-ray, from subatomic length-scale to galactic length-scale, and also from classical electromagnetics to quantum electromagnetics (this includes quantum electrodynamics and quantum optics). The advent of one of the first computers by Google uses microwave photons, which have a much longer wavelength than do optical ones; therefore, much microwave/electromagnetic engineering is needed for designing many aspects of quantum technologies. Due to the ease of engineering at microwave frequencies because of the component sizes involved, many proof-of-concept works are done at microwave frequencies with well-established electromagnetic engineering.
The articles in this special section compare classical and quantum electromagnetics. The articles introduce the fundamental concepts of quantum electromagnetics and compares them to classical ones. When James Clerk Maxwell published his paper on those equations that bear his name, he could never have imagined that they would have such a wide-ranging impact. These equations are valid from static to X-ray, from subatomic length-scale to galactic length-scale, and also from classical electromagnetics to quantum electromagnetics (this includes quantum electrodynamics and quantum optics). The advent of one of the first computers by Google uses microwave photons, which have a much longer wavelength than do optical ones; therefore, much microwave/electromagnetic engineering is needed for designing many aspects of quantum technologies. Due to the ease of engineering at microwave frequencies because of the component sizes involved, many proof-of-concept works are done at microwave frequencies with well-established electromagnetic engineering.
The articles in this special section focus on quantum computing. After decades of research and development, quantum computing has recently grown into one of the hottest and most promising of all emerging fields. While large-scale quantum computing was just a pipe dream even a decade ago, today there is an intense race around the globe to build a practical quantum computer. So, as a microwave engineer, why should you be interested in quantum computing? It turns out that there is actually a significant amount of microwave engineering involved in the implementation of many controllable quantum systems.
During the past decade, quantum computing has grown from a field known mostly for generating scientific papers to one that is poised to reshape computing as we know it [1]. Major industrial research efforts in quantum computing are currently underway at many companies, including IBM [2], Microsoft [3], Google [4], [5], Alibaba [6], and Intel [7], to name a few. The European Union [8], Australia [9], China [10], Japan [11], Canada [12], Russia [13], and the United States [14] are each funding large national research initiatives focused on the quantum information sciences. And, recently, tens of start-up companies have emerged with goals ranging from the development of software for use on quantum computers [15] to the implementation of full-fledged quantum computers (e.g., Rigetti [16], ION-Q [17], Psi-Quantum [18], and so on). However, despite this rapid growth, because quantum computing as a field brings together many different disciplines, there is currently a shortage of engineers who understand both the engineering aspects (e.g., microwave design) and the quantum aspects required to build a quantum computer [19]. The aim of this article is to introduce microwave engineers to quantum computing and demonstrate how the microwave community's expertise could contribute to that field.
Due to the advent of Quantum Mechanics' 100th anniversary in 2025, we wrote this review paper in order to present a discussion that addresses the foundations of this theory. And since the creation of this Mechanics and other quantum theories was guided, for instance, by correspondence principles that needed to be identified between them and other well-established physical theories, this paper will be devoted to discussing the correspondence between these quantum theories and Maxwell's theory of electromagnetism. More precisely, what we will do throughout this paper is discuss how the Maxwell's electromagnetic theory in free space and the stronger formulation of the correspondence principle already pointed, together, to the basis of a Quantum Mechanics that was only be formulated half a century later. And, in order to make this very clear, we will show that the quantum-mechanical description of a photon can already be identified, simply, by manipulating Maxwell's equations in free space with mathematical resources that, for instance, were already well known before the advent of Quantum Mechanics.
By the end of the nineteenth century all the important elements of classical physics were fully mature. Newton's Laws had been applied with success to everything from industrial machines to planetary orbits. Classical thermodynamics had extended energy conservation arguments into thermal processes, and scientists including J. Willard Gibbs and Ludwig Boltzmann had developed the statistical interpretation of entropy. James Clerk Maxwell had explained all electromagnetic phenomena, from AC generators/motors to light, with the four Maxwell's equations and three material-dependent constitutive relations. There was serious discussion that physics was on the verge of being “finished” – becoming a closed system of knowledge like classical geometry with only essentially routine tasks left of determining how the known laws could be applied to engineering problems. Yet by 1930 the foundations of mechanics, electromagnetics, and atomic-scale systems had been shaken to the core by the new revolutions in the Theory of Relativity, the photon picture of light, and quantum physics. We are still reaping the benefits of the application of these new scientific paradigms in our technology today, including semiconductor electronic devices, lasers, and GPS systems. But the description of reality that these theories provide is still deeply anti-intuitive and disturbing. Nevertheless, quantum physics is one of the most extensively experimentally verified theories that we know. Even when quantum theory and common sense seem to diverge, quantum theory gives the right answers when tested by experiment. In the next chapter we will develop the framework of quantum theory that has been so successful when people “shut up and calculate,” as one scientist suggested as the way through the philosophical thicket of quantum physics. But in this chapter, we will spend a brief time considering the historical development and continuing paradoxical implications of quantum theory. The photoelectric effect and photons In 1905, Albert Einstein, who was a key figure in the revolution of modern physics, was working as a clerk in the patent office in Zurich, Switzerland. Einstein had finished his studies in physics, but had not obtained a coveted position as a university professor. He was intensely interested in the latest developments in classical physics and was aware of a few of the remaining loose ends that were resisting explanation in the classical model.
Quantum electrodynamics presents intrinsic limitations in the description of physical processes that make it impossible to recover from it the type of description we have in classical electrodynamics. Hence one cannot consider classical electrodynamics as reducing to quantum electrodynamics and being recovered from it by some sort of limiting procedure. Quantum electrodynamics has to be seen not as an more fundamental theory, but as an upgrade of classical electrodynamics, which permits an extension of classical theory to the description of phenomena that, while being related to the conceptual framework of the classical theory, cannot be addressed from the classical theory.