Quantum Computing

By the end, you can

• Write and interpret the qubit state α|0⟩ + β|1⟩ and explain the normalization constraint.
• Apply the Born rule to compute the probability of each measurement outcome from given amplitudes.
• Locate |0⟩, |1⟩, and |+⟩ on the Bloch sphere and explain what the equator represents.
• Describe what measurement does to a qubit and why repeated shots are needed to estimate probabilities.
• Identify the action of the X, H, Z, and CNOT gates and classify them as single- or two-qubit gates.
• Explain how H followed by CNOT builds the Bell state, and why it sends no faster-than-light signal.
• State the speedups Grover and Shor achieve and name the problem each solves.
• Explain why quantum speedups are problem-specific and what decoherence means for practical hardware.