Gate-based quantum-computing platform built from Josephson-junction-based microwave circuits (circuit QED). Foundational: Josephson 1962 equations for supercurrent tunneling; Devoret-Martinis-Clarke 1985 macroscopic quantum tunneling;…
superconducting-qubits
Transmon: E_J/E_C ~ 50 for exponentially-suppressed charge-noise sensitivity
Koch-Yu-Gambetta-Houck-Schuster-Blais-Devoret-Girvin-Schoelkopf 2007 transmon qubit: a Cooper-pair box shunted by a large capacitor to…
Fluxonium: E_J/E_L ~ 1 — high anharmonicity (~GHz), long T₁ (ms)
Manucharyan-Koch-Glazman-Devoret 2009 fluxonium: a Josephson junction shunted by a large superinductance (typically L ≈ μH, implemented as…
Dispersive regime |Δ| ≫ g: qubit-state-dependent resonator frequency pull 2χ
Wallraff-Schuster-Blais 2004 dispersive-readout scheme for circuit QED. Starting from the Jaynes-Cummings Hamiltonian H_JC = ℏω_q σ_z/2 +…
Josephson energy: E_J cos φ̂ with I_c = 2πE_J/Φ_0; Φ_0 = h/(2e) flux quantum
Josephson 1962 dc relations: the potential energy of a Josephson junction as a function of the gauge-invariant phase difference φ across…
Transmon anharmonicity: α = ω_12 − ω_01 ≈ −E_C (leading order in (E_C/E_J)^(1/2))
Transmon (E_J/E_C ≫ 1) is effectively a weakly-anharmonic oscillator. Duffing-oscillator expansion of the H_trans = 4E_C(n̂−n_g)² − E_J…
Dispersive shift χ = g²/Δ for two-level limit; χ = g² α/(Δ(Δ+α)) for transmon
Blais-Huang-Wallraff-Girvin-Schoelkopf 2004 dispersive shift for circuit-QED. In the two-level (σ_z) truncation of the Jaynes-Cummings…