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arXiv:2603.24052

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

Giuseppe Bevilacqua, Valerio Biancalana, Roberto Cecchi

physics.ins-detphysics.app-phquant-phSubmitted Mar 25, 2026• Announced Mar 26, 2026• 0 citations
v1 · Mar 25, 2026v2 · Oct 27, 2026
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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.

Comments
8 Pages, 7 Figs, 18 Refs

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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.
Real-time waveform generation supports dynamic quantum circuits without pre-storing complete waveforms for every execution path. However, long-lived distortions in flux-control lines degrade gate fidelity, requiring compensation to account for the actual pulse history. A frequency-domain inversion and time-domain fitting method is proposed for resource-efficient real-time flux distortion compensation. The method fits the reconstructed compensation impulse response with a compact hybrid infinite impulse response (IIR) and finite impulse response (FIR) filter. Look-ahead parallelization enables this filter to process synthesized waveforms at 1.2GSa/s on a field-programmable gate array (FPGA). Two-qubit cross-entropy benchmarking shows that real-time IIR filtering achieves a median controlled-Z Pauli fidelity close to the software-reference value of 99.57%. Numerical analysis and FPGA synthesis indicate approximately logarithmic growth in hardware resource use with compensation timescale. Extending compensation from microsecond to hundred-microsecond timescales increases look-up table (LUT) and digital signal processing (DSP) resource use by only about 14% and 4%, respectively, while maintaining a relative arithmetic error below 10−410^{-4}10−4. This work provides a scalable hardware foundation for high-fidelity flux control in dynamic superconducting quantum circuits.
Quantum control protocols are typically devised in the time domain, leaving their spectral behavior to emerge only a posteriori. Here, we invert this paradigm. Starting from a target frequency-domain filter, we employ the dynamical-invariant framework to derive the continuous driving fields that enact the chosen spectral response on a qubit. This approach, Quantum Invariant Filtering (QIF), maps arbitrary finite-impulse responses, including multi-band and phase-sensitive profiles, into experimentally feasible Hamiltonian modulations. Implemented on a single nitrogen-vacancy center in diamond, the method realizes the prescribed passbands with high fidelity, suppresses noise, and preserves coherence for milliseconds, two orders of magnitude longer than Carr-Purcell-Meiboom-Gill sequences, while remaining robust to 50% drive-amplitude errors. Our results establish QIF as a broadly applicable framework for enhanced quantum control and sensing across diverse physical platforms, including superconducting qubits, trapped ions, and nuclear magnetic resonance systems.
A pulse drive system capable of converting an arbitrary input signal into a delta sigma encoded pulse code stream in real time has been demonstrated. This system is based on the use of analog and digital hardware controlled by a Field Programmable Gate Array (FPGA) rather than using software to produce the delta sigma code and then loading it into the memory of a commercial Pulse Pattern Generator (PPG). The results of using the system to drive a Josephson junction array to synthesize quantum-accurate voltage waveforms are presented. The advantage of such a system includes the significant reduction in time required to change waveform parameters. This provides an easily tunable source of high-fidelity stable voltage waveforms at low temperature for future applications including validation of components for use in quantum technologies.
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We describe how the transient behavior of a tuned and matched resonator circuit and a ringdown suppression pulse may be integrated into an optimal control theory (OCT) pulse-design algorithm to derive control sequences with limited ringdown that perform a desired quantum operation in the presence of resonator distortions of the ideal waveform. Inclusion of ringdown suppression in numerical pulse optimizations significantly reduces spectrometer deadtime when using high quality factor (high-Q) resonators, leading to increased signal-to-noise ratio (SNR) and sensitivity of inductive measurements. To demonstrate the method, we experimentally measure the free-induction decay of an inhomogeneously broadened solid-state free radical spin system at high Q. The measurement is enabled by using a numerically optimized bandwidth-limited OCT pulse, including ringdown suppression, robust to variations in static and microwave field strengths. We also discuss the applications of pulse design in high-Q resonators to universal control of anisotropic-hyperfine coupled electron-nuclear spin systems via electron-only modulation even when the bandwidth of the resonator is significantly smaller than the hyperfine coupling strength. These results demonstrate how limitations imposed by linear response theory may be vastly exceeded when using a sufficiently accurate system model to optimize pulses of high complexity.
Execution of quantum algorithms requires a quantum computer architecture with a dedicated quantum instruction set that is capable of supporting translation of workloads into actual quantum operations acting on the qubits. State-of-the-art qubit control setups typically utilize general purpose test instruments such as arbitrary waveform generators (AWGs) to generate a limited set of waveforms or pulses. These waveforms are precomputed and stored prior to execution, and then used to produce control pulses during execution. Besides their prohibitive cost and limited scalability, such instruments suffer from poor programmability due to the absence of an instruction set architecture (ISA). Limited memory for pulse storage ultimately determines the total number of supported quantum operations. In this work, we present a scalable qubit control system that enables efficient qubit control using a flexible ISA to drive a direct digital synthesis (DDS) pipeline producing nanosecond-accurate qubit control signals dynamically. The designed qubit controller provides a higher density of control channels, a scalable design, better programmability, and lower cost compared to state-of-the-art systems. In this work, we discuss the new qubit controller's capabilities, its architecture and instruction set, and present experimental results for coherent qubit control.