The quantum dot spin chain system represents a significant platform for quantum simulation and investigating the collective behaviors of electrons. As such, understanding its mechanisms and control protocols is crucial. Chapter 1 of the thesis introduces the fundamental concepts of the quantum dot chain system, focusing on the extended Hubbard model, the double quantum dot system, and electron-phonon coupling within these systems. Chapter 2 delves into the electron-phonon coupling mechanism within a multielectron double quantum dot system. Here, I examine two distinct scenarios based on the detuning variations of the system: the unbiased case and the biased case. In the unbiased case, the dephasing rate due to electron-phonon coupling generally increases with the number of electrons in the right dot. However, this trend is inconsistent in the biased case, indicating that multielectron quantum dots may offer advantages under certain conditions. Chapter 3 investigates the entanglement entropy in a multielectron quantum dot spin chain system, as the extended Hubbard model describes. Local and pairwise entanglement is influenced by the Coulomb interactions and tunneling strengths settings, shaped by the system’s electronic configurations and potential energy of sites. The entanglement diagram exhibits clear phase transitions, significantly impacted by the ratios of coupling strength and potential energy variations. Adjusting the potential energy of a particular dot crucially influences the ground state configurations and, as a result, the entanglement entropy. Chapter 4 explores the possible operation sequences in the quantum dot spin chain system as defined by the Heisenberg model, inspired by the concept of a decoherence-free subspace. This chapter describes a nine-spin system within a nine-quantum-dot arrangement, where the bases are determined by the total angular quantum number. By employing the Krotov method of quantum optimal control, we identify a more efficient pulse-level operation sequence for an exchange-only quantum dot spin chain system, which offers a superior alternative to conventional quantum gate decomposition methods. This approach could enhance the development of more concise quantum algorithm representations.