6. Multi-Qubit: Tensor Products
Tensor Products
How do we describe two qubits? We multiply their vector spaces using the Tensor Product ($\otimes$).
If qubit A is in state $|0\rangle$ and qubit B is in state $|1\rangle$, the combined state is:
$$|0\rangle \otimes |1\rangle = |01\rangle$$If we have two 2D vectors, their tensor product is a 4D vector. For $n$ qubits, the state space is $2^n$. This exponential growth is why quantum computers are hard to simulate.
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