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

Davis Borders

Published Sep 24, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.22930827

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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.
Arbitrary Waveform Generators (AWGs) have widespread applications in telecommunications, quantum computing, and biomedical engineering, among others, due to their ability to generate a wide range of waveforms precisely and instantaneously. This work focuses on developing a scalable and energy-efficient AWG for qubit control. A simple methodology for bringing up a Radio-Frequency System-on-Chip (RFSoC) board and using it to generate various arbitrary waveforms has been discussed. A software-hardware codesign paradigm has been used in this work to dynamically control the output frequency, voltage and shape of the arbitrary waveforms. Similarly, the on-the-fly programmability of four Digital to Analog convertor (DAC) channels and four Analog to Digital Converter (ADC) channels have been tested. The voltage and frequency response of the DAC output has also been characterised to better understand the limitations of the RFSoC. The DAC-ADC loopback characterisation was also performed to prepare the RFSoC for qubit state readout measurements. Over the last few decades, the Direct Digital Synthesiser (DDS) has been a popular choice for generating specific waveforms, such as sinusoidal and ramp waveforms, due to its low cost, simple design, and high precision. Several prior-art works were surveyed, and the trade-offs and strengths of each architecture were summarised. A benchmarking table is prepared based on the Power, Performance and Area (PPA) analysis to make design selection easier for DDS designers. Two Figure of Merit definitions and scaling equations have also been used to normalise the specifications to a target process node (28 nm CMOS), to provide a more accurate comparison among state-of-the-art DDS designs on Application Specific Integrated Circuits (ASICs), and to set expectations for future architectural advancements in DDS design. Finally, a viable DDS-based AWG architecture for ASIC implementation has also been proposed based on the benchmarking.
Control electronics for superconducting quantum processors have strict requirements for accurate command of the sensitive quantum states of their qubits. Hinging on the purity of ultra-phase-stable oscillators to upconvert very-low-noise baseband pulses, conventional control systems can become prohibitively complex and expensive when scaling to larger quantum devices, especially as high sampling rates become desirable for fine-grained pulse shaping. Few-gigahertz radio-frequency (RF) digital-to-analog converters (DACs) present a more economical avenue for high-fidelity control while simultaneously providing greater command over the spectrum of the synthesized signal. Modern RF DACs with extra-wide bandwidths are able to directly synthesize tones above their sampling rates, thereby keeping the system clock rate at a level compatible with modern digital logic systems while still being able to generate high-frequency pulses with arbitrary profiles. We have incorporated custom superconducting qubit control logic into off-the-shelf hardware capable of low-noise pulse synthesis up to 7.5 GHz using an RF DAC clocked at 5 GHz. Our approach enables highly linear and stable microwave synthesis over a wide bandwidth, giving rise to high-resolution control and a reduced number of required signal sources per qubit. We characterize the performance of the hardware using a five-transmon superconducting device and demonstrate consistently reduced two-qubit gate error (as low as 1.8%), which we show results from superior control chain linearity compared to traditional configurations. The exceptional flexibility and stability further establish a foundation for scalable quantum control beyond intermediate-scale devices.
Abstract Fast and accurate quantum operations of a single spin in room-temperature solids are required in many modern scientific areas, for instance in quantum information, quantum metrology, and magnetometry. However, the accuracy is limited if the Rabi frequency of the control is comparable with the transition frequency of the qubit due to the breakdown of the rotating wave approximation (RWA). We report here an experimental implementation of a control method based on quantum optimal control theory which does not suffer from such restriction. We demonstrate the most commonly used single qubit rotations, i.e. - and π-pulses, beyond the RWA regime with high fidelity and , respectively. They are in excellent agreement with the theoretical predictions, and . Furthermore, we perform two basic magnetic resonance experiments both in the rotating and the laboratory frames, where we are able to deliberately ‘switch’ between the frames, to confirm the robustness of our control method. Our method is general, hence it may immediately find its wide applications in magnetic resonance, quantum computing, quantum optics, and broadband magnetometry.
Logic gates in superconducting quantum processors are implemented through precise quantum control techniques in the microwave regime. The choice of drive frequency and other control parameters directly determines the duration of quantum gate operations. Because current devices remain too noisy to reach fault tolerance, reducing gate durations, and thereby the overall circuit depth, is of critical importance. In this work, we present a model of single qubit gate execution in both the adiabatic regime, where the rotating wave approximation (RWA) is valid, and the diabatic regime, where the RWA no longer applies. Using parameters representative of superconducting qubits, we investigate how gates can be driven at durations well below conventional timescales, and we examine the associated limitations, performance trade offs. The results demonstrate that ultrashort control pulses in the diabatic regime can achieve fidelities comparable to those obtained under standard RWA conditions, offering a possible route to faster quantum logic without sacrificing accuracy under idealized conditions.
Power amplifiers (PA) are essential for microwavecontrolled trapped-ion and semiconductor spin based quantum computers (QC). They adjust the power level of the control signal and therefore the processing time of the QC. Their nonlinearities and memory effects degrade the signal quality and, thus, the fidelity of qubit gate operations. Driving the PA with a significant input power back-off reduces nonlinear effects but is neither power-efficient nor cost-effective. To overcome this limitation, this letter augments the conventional signal generation system applied in QCs by digital predistortion (DPD) to linearize the radio frequency (RF) channel. Numerical analysis of the qubit behavior based on measured representative control signals indicates that DPD improves its fidelity.