Concept 27 of 42 · Control and Entangling Gates

Single-qubit microwave control

Resonant drives rotate a qubit on its Bloch sphere.

01 / Mathematical framework
$$H_d/\hbar=\frac{\Omega}{2}(\cos\phi\,\sigma_x+\sin\phi\,\sigma_y)$$

Physical intuition

Resonant drives rotate a qubit on its Bloch sphere. This is the starting point for understanding how superconducting circuit parameters determine quantum energy levels and dynamics.

Deep dive: how the mechanism works

Drive amplitude, phase and duration set rotation axis and angle in the rotating frame.

How the quantum phenomenon appears

Gaussian-envelope pulses implement X and Y rotations. To establish the predicted quantum behavior, connect the circuit Hamiltonian to a measured transition, coherence experiment, gate benchmark or calibrated readout signal.

Assumptions and limitations

Calibration drift and off-resonant excitation create coherent errors.

Research and simulation exercise

Identify the tunable parameters, predict the observable from the stated model, and sweep one parameter while holding the others fixed. Compare against a simpler reference model, quantify loss and uncertainty, and state which observations would falsify the hypothesis.

Connect the ideas

See the chapter guide and further reading.

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