$.\mathrm{.}181.$ Explain the theoretical principles of quantum computing and its applications in cryptography, optimization, and simulation. Quantum computing utilizes quantum bits $($qubits$)$ to perform computations based on quantum phenomena such as superposition and entanglement. By understanding quantum gates, quantum algorithms, and quantum error correction, engineers can develop quantum computing systems for applications such as breaking cryptographic protocols, solving optimization problems, and simulating quantum systems, offering potential advantages over classical computing in certain tasks.