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Theory

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Simulation

Posttest

References

Contributors

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Applied Linear Algebra – Quantum Gates in Action

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What is the normalization condition for a single qubit state |ψ⟩ = α|0⟩ + β|1⟩?

a: |α| + |β| = 1 Explanation

Explanation

b: |α|² + |β|² = 1 Explanation

Explanation

c: α + β = 1 Explanation

Explanation

d: α² + β² = 1 Explanation

Explanation

What property must a quantum gate matrix U satisfy to be valid?

a: U × U = I (identity matrix) Explanation

Explanation

b: U† × U = U × U† = I (unitary property) Explanation

Explanation

c: U is always symmetric Explanation

Explanation

d: U has no complex numbers Explanation

Explanation

What does the Hadamard gate do to the |0⟩ state?

a: It leaves it unchanged Explanation

Explanation

b: It converts it to (1/√2)(|0⟩ - |1⟩) Explanation

Explanation

c: It converts it to (1/√2)(|0⟩ + |1⟩) Explanation

Explanation

d: It converts it to |1⟩ Explanation

Explanation

For a two-qubit state with amplitudes [1/√2, 0, 0, 1/√2], what are the measurement probabilities?

a: 100% |00⟩, 0% others Explanation

Explanation

b: 50% |00⟩, 50% |11⟩, 0% others Explanation

Explanation

c: 25% each state Explanation

Explanation

d: 50% |00⟩, 25% |01⟩, 25% |10⟩, 0% |11⟩ Explanation

Explanation

In a quantum circuit, what does CNOT stand for?

a: Complex NOT gate Explanation

Explanation

b: Controlled-NOT gate Explanation

Explanation

c: Conjugate NOT gate Explanation

Explanation

d: Combined NOT operation Explanation

Explanation

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