Design a detailed 14-week syllabus for an advanced graduate-level course titled 'Quantum Algorithms and Complexity'. The curriculum should progress from linear algebra prerequisites to quantum gates, then move to core algorithms like Deutsch-Jozsa, Shor's, and Grover's. For each week, provide learning objectives, required reading from academic papers, and a practical lab component using Qiskit or Cirq. Include a final project proposal that requires students to implement or simulate a novel quantum algorithm.