Research-grade circuit-QED instrument for transmon superconducting qubits. Explore the Hilbert-space map, inspect cited claims, ask the research assistant — no fake device metrics.
Primary path: pick a constellation node → read the equation → check notebook tags → ask the assistant. No hunting.
In the circuit-QED Cooper-pair box / transmon picture, charge number n̂ and phase φ̂ are conjugate. With EJ ≫ EC the spectrum approaches a weakly anharmonic oscillator. Exact diagonalization in the charge basis (or Mathieu functions) yields eigenenergies En(ng) with residual gate-charge dependence.
Linked: charge-dispersion · anharmonicity · ej-ec
Canonical form — conjugate charge and phase operators on the Josephson circuit.
Ask about charge dispersion, α vs EJ/EC tradeoffs, Purcell filters, CZ vs iSWAP, or surface-code context. Answers stay rigorous — no invented lab numbers.
Every claim is tagged literature / textbook / assumption. Ranges are illustrative unless a primary citation supplies a measured value. Transmon Lab has no product hardware — never treat UI copy as experimental data.
Charge dispersion is exponentially suppressed as √(8 EJ/EC) grows; anharmonicity α ≈ −EC to leading order in the transmon expansion.
Foundational transmon proposal / analysis. Use for functional forms, not as a claim about any live device.
Koch et al., Phys. Rev. A 76, 042319 (2007)
Circuit QED lecture notes / reviews provide the standard quantized-circuit derivation path from Lagrangian to Hamiltonian.
Pedagogical backbone for undergrad→grad depth.
Girvin, “Circuit QED: Superconducting Qubits Coupled to Microwave Photons” (Les Houches / notes)