(color online) Experimental layout. (a) Device schematic showing two Xmon qutrits coupled to a resonator in the middle (left), and the corresponding potential-well landscapes and energy levels (right). (b) Energy level arrangement of the resonator and the test qutrit ignoring their interaction (left), and the resonator’s conditional frequency shifts due to the qutrit’s dispersion (right). The microwave drive with a tone ω_d is detuned from ω_c by an amount δ_d. The dispersive coupling to the qutrit shifts the resonator frequency by an amount δ_g (δ_e), and hence the effective drive-resonator detuning is Δ_g ≡ ω_d − ω_c,g = δ_d − δ_g (Δ_e ≡ ω_d − ω_c,e = δ_d − δ_e) for the qutrit state |g⟩ (|e⟩). (c) Ideal resonator’s phase-space trajectories. The resonator, initially in its vacuum state, is displaced by the microwave drive along a circular loop in its phase space with the radium Ω/Δ_g (Ω/Δ_e) and the angular velocity Δ_g (Δ_e) for the qutrit state |g⟩ (|e⟩), where Ω is the drive amplitude. When the resonator traverses the loop once, it will acquire a geometric phase that is proportional to the enclosed phase-space area. When Δ_g/Δ_e = k_g/k_e, with k_g and k_e being integers, at time T = 2π (k_g − k_e)/(Δ_g − Δ_e) the resonator makes a cyclic evolution and returns to the vacuum state no matter whether the qutrit is in the state |g⟩ or |e⟩; however, it acquires different geometric phases for these two qutrit states. (d) Ramsey sequence. The geometric operation, which is achieved by the combination of the microwave driving pulse (red sinusoid) and the dispersive resonator-qubit coupling, is sandwiched in between two π/2 qubit rotations (blue sinusoids) whose rotation axes differ by an angle Φ. The geometric phase difference β is manifested in the test qubit’s Ramsey interference, obtained by a dispersive measurement using a 700 ns-long microwave pulse (light brown sinusoid).