A two‑qubit system is described by combining the states of two individual qubits into a single joint state. If the first qubit is in state ∣ψ⟩=α∣0⟩+β∣1⟩|\psi\rangle = \alpha|0\rangle + \beta|1\rangle∣ψ⟩=α∣0⟩+β∣1⟩ and the second is in state ∣ϕ⟩=γ∣0⟩+δ∣1⟩|\phi\rangle = \gamma|0\rangle + \delta|1\rangle∣ϕ⟩=γ∣0⟩+δ∣1⟩, the combined state is given by the Kronecker (tensor) product ∣ψ⟩⊗∣ϕ⟩|\psi\rangle \otimes |\phi\rangle∣ψ⟩⊗∣ϕ⟩. This produces a four‑dimensional state space spanned by the basis ∣00⟩,∣01⟩,∣10⟩,∣11⟩|00\rangle, |01\rangle, |10\rangle, |11\rangle∣00⟩,∣01⟩,∣10⟩,∣11⟩. Two‑qubit circuits apply unitary operations on this joint space, allowing correlations between the qubits that cannot be represented as separate single‑qubit states.
