Analytical Modeling of Power Amplification Requirements for Magnetic Resonance Qubit Control Systems

Precise manipulation of a quantum bit (qubit) magnetic dipole moment requires exact control over the radiofrequency (RF) excitation field amplitude, pulse envelope, and duration. This paper presents a complete analytical derivation linking target quantum logic gate flip angles (α = π/2, π) to the necessary physical RF power amplifier (PA) parameters—specifically voltage gain (G) and peak output power (P ). Starting from a digital direct synthesis (DDS) driving model, we map unitless digital baseband signals through a digital-to-analog converter (DAC) and an impedance-matched resonant LC tank into the physical transverse magnetic field (B1). Applying a coordinate transformation to the rotating frame under the Rotating Wave Approximation (RWA) and modeling Gaussian pulse truncation (τ = nσ), closed-form expressions are derivedfor G and P . This analytical framework provides a direct link between physical hardware specifications and target quantum state rotations.