  Quantum dot-based system is one of the most promising systems owing to its
integrability with classical computation hardware and its versatility in
realizing qubits and quantum gates. In this work, we investigate the
functionality of the two-qubit CNOT gate and three-qubit Toffoli gate in the
presence of hyperfine fluctuation noise and phononic noise. We model two and
three-qubit gates using the Lindblad Master Equation to estimate the operating
range of the external static magnetic field. In these ranges, we observe a
successful gate operation under decoherence.
