Virtual Labs

Applied Linear Algebra – Quantum Gates in Action

What is the final state of the Bell state circuit: initial |00⟩ → Hadamard → CNOT?

a: (1/√2)(|00⟩ - |11⟩) Explanation

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b: (1/√2)(|00⟩ + |11⟩) Explanation

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c: (1/√2)(|01⟩ + |10⟩) Explanation

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d: |00⟩ Explanation

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What quantum property does the Bell state (1/√2)(|00⟩ + |11⟩) demonstrate?

a: Superposition only Explanation

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b: Entanglement - perfect correlation between qubits Explanation

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c: Unitarity of gates Explanation

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d: Measurement collapse Explanation

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If you measure a qubit in the Bell state (1/√2)(|00⟩ + |11⟩) and get |0⟩, what is the measurement outcome for the second qubit?

a: Could be |0⟩ or |1⟩ with equal probability Explanation

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b: Must be |0⟩ Explanation

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c: Must be |1⟩ Explanation

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d: Depends on external factors Explanation

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What is the difference between the Bell state (2-qubit) and GHZ state (3-qubit)?

a: No difference, just more qubits Explanation

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b: Bell state has 2-qubit entanglement; GHZ state has 3-qubit entanglement Explanation

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c: GHZ uses different gates than Bell Explanation

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d: GHZ is used for different applications only Explanation

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When you apply matrix operation |ψ_new⟩ = U|ψ_old⟩, what does U represent?

a: A unitary matrix representing a quantum gate operation Explanation

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b: The measurement outcome Explanation

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c: The probability of each state Explanation

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d: A classical transformation Explanation

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In the simulation, when 1000 measurements are performed on a Bell state, what distribution of outcomes is expected?

a: All 1000 measurements give |00⟩ Explanation

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b: Approximately 500 |00⟩ and 500 |11⟩ Explanation

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c: Approximately 250 each of |00⟩, |01⟩, |10⟩, |11⟩ Explanation

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d: Random distribution varies each time Explanation

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