Superconducting LC circuit with Josephson junction — anharmonic energy levels
The transmon qubit reduces charge noise by operating at E_J/E_C ≫ 1. The Josephson Hamiltonian H = 4E_C(n̂−n_g)² − E_J cos(φ̂) produces anharmonic levels: ω₀₁ ≈ √(8E_JE_C)−E_C (qubit frequency), with anharmonicity α = −E_C ≈ −200 MHz. This small anharmonicity allows selective qubit driving while suppressing leakage to |2⟩. Modern transmons achieve T₁ ~ 100–500 μs and gate fidelities > 99.9%.