This thesis devotes three introductory chapters to outlining basic recipes for constructing the quantum Hamiltonian of an arbitrary superconducting circuit, starting from classical circuit design. Since a superconducting circuit is one of the most promising platforms for realizing a practical quantum computer, anyone who is starting out in the field will benefit greatly from this introduction. The second focus of the introduction is the ultrastrong light-matter interaction (USC), where the latest developments are described. This is followed by three main research works comprising quantum memory in USC; scaling up the 1D circuit to a 2D lattice configuration; creation of Noisy Intermediate-Scale Quantum era quantum error correction codes and polariton-mediated qubit-qubit interaction. The research work detailed in this thesis will make a major contribution to the development of quantum random access memory, a prerequisite for various quantum machine learningalgorithms and applications.​