Quantum Linear Algebra – Matrix and Vector Operations

Mathematically, which of the following corresponds to the action of applying multiple quantum gates sequentially to a single qubit?
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What is the dimension of the resulting state vector when taking the tensor product of two independent single-qubit state vectors?
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The matrix representation for the Hadamard gate includes which normalization factor to maintain unitarity?
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A quantum register containing n computation qubits is characterized mathematically by a complex vector space of what dimension?
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