Single-Qubit Gate Drives

Single-qubit rotations are produced by resonant microwave pulses whose amplitude, phase, and duration set the rotation angle and axis.

Rotations From Pulses

A superconducting qubit is controlled by a microwave drive at or near its transition frequency, delivered through a dedicated drive line coupled capacitively to the qubit. In the frame rotating at the qubit frequency, a resonant drive appears static, and the qubit precesses about an axis in the equatorial plane set by the drive phase. The rotation angle is the integral of the drive amplitude over time, the pulse area.

Choosing the phase selects the rotation axis: an in-phase drive rotates about X, a quadrature drive rotates about Y. This is why control electronics deliver two quadratures, I and Q. A rotation about Z is usually done in software as a virtual gate, by shifting the phase reference of all subsequent pulses, which costs no time and no error.

Pulse Envelopes

• Gaussian and cosine envelopes are common because their smooth spectra limit off-resonant excitation.
• Pulse duration is a few times the envelope width, typically tens of nanoseconds.
• A DRAG quadrature is added to suppress leakage into the second excited level.

Amplitude and Frequency Calibration

Two parameters dominate single-qubit fidelity: the pulse amplitude that produces exactly a pi or pi-over-two rotation, and the drive frequency that must match the qubit. Amplitude is calibrated by repeating a gate many times so that a small over- or under-rotation accumulates into a measurable error. Frequency is calibrated by Ramsey interferometry, which is sensitive to detuning between the drive and the qubit.

Virtual Z and Frame Tracking

Because Z rotations are virtual, an arbitrary single-qubit unitary is decomposed into physical X or Y rotations sandwiched between frame changes. The control system tracks each qubit's phase frame across the whole circuit. This makes single-qubit gates fast, accurate, and essentially free of the leakage and calibration burden that Z-axis physical rotations would carry.

Well-calibrated single-qubit drives routinely reach fidelities that make them a small term in the overall error budget.