Optimal charging of a quantum battery

I here report a theoretical study about storage and transportation of energy in quantum systems. In the thesis, I have learnt the fundamentals of quantum physics, which helped me understand the processes involved in quantum computing. I have examined and learnt the nomenclature used to represent a system's quantum states, the nature of the measurements of a quantum system's attributes, and the phenomena of superposition and entanglement. I have employed this knowledge to explore the key properties of the fundamental unit of quantum information, the qubit. I then studied the principles of quantum computing, namely the basics of quantum logic. I realized how to understand the basic single qubit gates thanks to the visualization of quantum states with the Bloch sphere, where states are represented as vectors. I have studied the means of transformation of quantum systems: single qubit gates, including Pauli operators, Hadamard gate, and other gates that create quantum superpositions. Also, I studied the CNOT gate, which allows two qubits to be entangled, and the Toffoli gate, which permits the development of basic algorithms such as the practical implementation of the half-adder algorithm. In the second part of the project, I have learnt the fundamentals of primitive algorithm implementation using "IBM Quantum" tools, namely the "Quantum Composer" tool and the "Qiskit" Python framework. These tools were used to create all of the visuals and algorithms reported in the thesis. Following this section of the implementation of fundamental algorithms and quantum computing notation, I have delved deeper into several parts of the mathematical treatment for the management of mixed-state systems. In contrast to pure states, mixed states have the distinction of not being able to be described in a unique fashion, hence their representation requires probabilistic treatment and is difficult to display using charts such as the Bloch sphere. This section is critical for fully comprehending the thesis's last section, which is concerned with the creation of a quantum battery prototype. The thesis concludes with a definition of a quantum battery, a number of qubits in which we store energy, outlining the physical principles of operation and modelling the battery using the concepts gained in earlier sections. One can show that a quantum system can evolve faster by harnessing entanglement, outperforming a system that operates in a "classical" manner. This phenomenon is well known and is used here to boost the power of the battery, as seen in the thesis conclusions.