Data-driven synthesis of high-fidelity triaxial magnetic waveforms for quantum control

Abstract

We present a system for generating arbitrary, triaxial magnetic waveforms with a spectral content spanning from DC to tens of kHz, a critical capability for quantum control and spin manipulation. To compensate for amplifier-coil dynamics, we implement a data-driven approach to identify a numerical compensation model. The method parametrizes the system response using a Finite Impulse Response (FIR) filter calibrated on the specific waveform to be generated. The application of a driving signal designed via frequency-domain inversion of the identified model enables the synthesis of complex field sequences with sharp transitions between static and single- or multi-frequency temporal segments. The work is validated with experimental results demonstrating waveform fidelity and transient performance, thereby showcasing the precision and feasibility of the method.

Figures (7)

• Figure 1: Schematics of the load and the compensation network, featuring a parallel $R_\mathrm{comp}$–$C_\mathrm{comp}$ compensation network in series with the coil $L_\mathrm{coil}$ and the monitoring resistor $R_\mathrm{mon}$. The parallel branch compensates for the coil’s inductance: the capacitive reactance enhances the maximum attainable current near the resonant frequency, while the resistive term ensures proper DC operation. The low-side monitor resistor enables the measurement of the actual current $I_\mathrm{out}$ through the voltage $V_\mathrm{mon}$ and hence an estimate of the magnetic field, provided that accurate calibration factors bevilacqua_apdap_25 are available. The physical implementation of this network, with selectable components, is shown in the amplifier schematic of Fig. \ref{['fig:schemacircuito']}.
• Figure 2: The amplifier is built around an LM3886 integrated circuit, its design employs a linear non-inverting topology with full DC-coupling to maintain signal integrity from input to output. It features a reconfigurable conditioning network, adjustable via jumpers, allowing the system to adapt its response and frequency shaping to the specific requirements of the inductive load or of the designed waveforms.
• Figure 3: Workflow for system identification and waveform pre-compensation. The procedure is divided into two main stages: Phase 1 (in blue: identification). A calibration voltage $V_\mathrm{in,0}$, evaluated from an ideal behavior, excites the system. The resulting coil current $I_{coil}$ is measured via a shunt resistor ($R_\mathrm{mon}$), and the magnetic field $B(t)$ is inferred through the coil constant $k$. A FIR model is then identified using a WLS algorithm, which allows for temporal weighting to exclude initial transients and enhance the accuracy in selected critical segments. Phase 2: (in green: assignment). The identified FIR taps ($\hat{h}$) are used to perform a frequency-domain inversion. The target field $B_d(t)$ is processed through a Wiener-regularized deconvolution to derive the final pre-compensated input voltage $V_\mathrm{in}(t)$, ensuring numerical stability even in the presence of non-minimum phase zeros or spectral nulls. This signal excites the system and provides the high-fidelity field needed in the experiment.
• Figure 4: The test field-waveform consists of a constant value held for 20ms followed by a dual frequency signal, as described in Tab. \ref{['tab:testwf']}. Here, only a short portion is shown to facilitate the $t=0$ transient visualization.
• Figure 5: FIR taps (a) and corresponding bode plot (b). In b), the blue curves are evaluated with eq.\ref{['eq:taps2bode']}, while the red points are obtained experimentally, testing the system with harmonic signals whose frequency is scanned. The 8 dB displacement in the $|H|$ plots reflects the conversion factor from $V_\mathrm{mon}$ to $B_m$.