This text describes novel treatments of quantum problems using enhanced quantization procedures. When treated conventionally, certain systems yield trivial and unacceptable results. This book describes enhanced procedures, generally involving extended correspondence rules for the association of a classical and a quantum theory, which, when applied to such systems, yield nontrivial and acceptable results. The text begins with a review of classical mechanics, Hilbert space, quantum mechanics, and scalar quantum field theory. Next, analytical skills are further developed, a special class of models is studied, and a discussion of continuous and discontinuous perturbations is presented. Later chapters cover two further classes of models both of which entail discontinuous perturbations. The final chapter offers a brief summary, concluding with a conjecture regarding interacting covariant scalar quantum field theories. Symmetry is repeatedly used as a tool to help develop solutions for simple and complex problems alike. Challenging exercises and detailed references are included.
Affine quantization is a relatively new procedure, and it can solve many new problems. This essay reviews this new, and novel, procedure for particle problems, as well as those of fields and gravity. New quantization tools, which are extremely close to, and even constructed from, the tools of canonical quantization, are able to fully solve selected problems that using the standard canonical quantization would fail. In particular, improvements can even be found with an affine quantization of fields, as well as gravity.
QML is the quantum machine learning, a new approach to explore the potential of quantum computation allowing us to discover solutions that otherwise would be hard for a classical computer to find. A variety of applied QML areas will be highlighted in the following chapter such as optimization problems NLP, drug discovery. Some foundations of quantum- superposition and entanglement- are designed to provide more efficient approach- towards higher fidelity in all data driven pipelines. This chapter gives some practical use cases for integration of quantum algorithms into pipelines of machine learning as well as some main challenges (i.e., regarding noise, scalability and algorithm selection) concerning it. Hybrid quantum-classical schemes are thought as the key for progress towards practicality on currently available noisy intermediate-scale quantum hardware. In this chapter, we will address QML viewpoints of the operational strategy and future, including potential QML disruptive effects and the future adoption insights of QML.