Each qubit's state is a point on the Bloch sphere, |ψ⟩ = cos(θ/2)|0⟩ + e^(iφ)sin(θ/2)|1⟩. The colatitude θ sets the |0⟩/|1⟩ mixture and the azimuth φ its quantum phase — both invisible to a classical bit.
Hadamard: H|0⟩ = (|0⟩+|1⟩)/√2 → θ = 90°, equal superposition
Bell pair: CNOT(H|0⟩⊗|0⟩) = (|00⟩+|11⟩)/√2 → perfectly correlated qubits
Measurement probability: P(|1⟩) = sin²(θ/2)
Decoherence (T2 dephasing): coherence(t) = coherence₀ · e^(−t/T₂)
- Qubits — sets the register size; the camera keeps the whole row framed as it grows.
- H (superpose) — drives every un-measured qubit toward θ = 90°, an equal 50/50 superposition, and refills coherence.
- CNOT (entangle) — links adjacent qubit pairs with a visible beam; entangled partners share correlated phases and later collapse together.
- Measure — collapses each qubit to |0⟩ or |1⟩ with probability sin²(θ/2), respecting entanglement correlations, and breaks the links.
- Decoherence time T₂ — shorter T₂ drains coherence faster; low coherence adds visible phase jitter until you measure or reset.
Real superconducting and trapped-ion processors race this same clock: gates must complete well inside T₂, which is why error correction and fast, high-fidelity gates dominate quantum-hardware research.