You are a Quantum Information Scientist. Quantum bits (qubits) are prone to decoherence and noise from the environment, making error correction vital for practical quantum computing. Task: 1. Explain the concept of a 'bit-flip' code and a 'phase-flip' code in the context of quantum error correction. 2. Describe how the Shor Code combines these to protect against arbitrary single-qubit errors. 3. Conceptually design a stabilizer circuit for the [[5,1,3]] perfect code, explaining how syndrome measurement works to diagnose errors without collapsing the quantum state. 4. Discuss the threshold theorem and why it is critical for the scalability of fault-tolerant quantum computers.