Marko Kuzmanović and colleagues have designed and experimentally implemented a quantum gate with 99.95% accuracy using a novel approach to pulse engineering. The researchers used neural ordinary differential equations to construct control fields as outputs of trainable neural networks, eliminating the need for predefined bases or discrete parametrization. This method achieved greater than 99.9% efficiency for photon number parity measurements in superconducting transmon circuits across a detuning range of approximately ±20MHz, outperforming traditional techniques while maintaining comparable gate durations. This work demonstrates the potential of neural ODEs for high-performance quantum control in experimentally relevant settings.

Neural ODEs Enable Smooth Quantum Control Waveform Generation

By modeling the control field as a continuous function of time, the system optimizes quantum dynamics through differentiable simulation, a departure from conventional methods. Standard pulse designs, like Rabi or DRAG pulses, often struggle with noise, detuning and fluctuations in drive amplitude, requiring specific error modeling for operator cancellation. Neural networks, however, use batch-optimization techniques to achieve high-fidelity operations even with parameter variations, simplifying the process of error mitigation. The primary goal of this work was to introduce and experimentally validate a neural-ODE-based parameterization for quantum control pulses that naturally produces smooth, hardware-compatible waveforms.

The framework’s practicality extends beyond single-qubit operations; it can, in principle, be extended to multiqubit gates while remaining tractable for simulation. “This positions neural ODEs as a useful and easy to use framework for quantum control,” the researchers write, “capable of addressing challenges that are difficult for traditional approaches, with a minimal increase in technical complexity and without requiring extensive training resources.” The team’s experimental setup verified the design, motivated by its central role in parity-measurement sequences, Wigner tomography and related circuit quantum electrodynamics experiments.

Neural Networks Surpass Discrete Methods for Pulse Design

Unlike methods like GRAPE or CRAB, which require either specifying a basis for expansion or adopting a discretized approach, this framework generates smooth, hardware-agnostic pulses optimized through differentiable integrators. To train the neural network, the discrepancy between the implemented and target operation is quantified as a loss function, and the network weights are updated based on the gradients of that loss and a learning rate.

This cycle repeats until convergence, resulting in a pulse with a specific amplitude and phase profile. A pulse duration was chosen as a balance between pulse bandwidth, amplitude and the width of the robustness region, all of which scale proportionally. The resulting pulse amplitude and phase, optimized for both true qubits and qutrits, demonstrate the system’s versatility.

95% Fidelity Achieved with Optimized 𝜋/2 Pulse

A newly designed 𝜋/2 pulse achieved 99.95% accuracy in photon number parity measurements using superconducting transmon circuits, exceeding the performance of established quantum gate techniques. The pulse’s design simultaneously optimized for robustness and minimized unwanted leakage outside the computational basis, a key factor in achieving this level of precision. Minimizing these inherent quantum decoherence effects is important for further improvements in gate fidelity. While these composite sequences outperformed analytical solutions, the neural network-based pulse exhibited a more stable amplitude and phase profile, suggesting a potential advantage in hardware compatibility and ease of implementation.

The loss function used to train the neural network was identical to that used for the composite pulse sequences, ensuring a fair comparison of performance metrics. The team measured the and components of the optimal pulses, alongside corresponding traces, to assess the effectiveness of the optimization process and confirm the pulse’s performance characteristics.

Transmon Circuits Demonstrate Detuning-Robust Parity Measurement

Achieving 99. The newly designed pulses simultaneously optimize for robustness while minimizing unwanted leakage outside the computational basis, addressing a central experimental limitation in quantum systems. The method employed uses neural ordinary differential equations to produce smooth, hardware-compatible control fields that outperform both rectangular and DRAG pulses in robustness.

Initializing the qubit in the ground state and applying a specific pulse sequence, the team measured the probability of finding it in the excited state, demonstrating precise control over qubit rotations even with variable detuning. This capability has broad applications in areas like error mitigation for quantum computing, bosonic state reconstruction and Wigner tomography, extending beyond parity measurements to a range of quantum experiments.

The figure of merit used to assess performance was the efficiency with which two pulses, applied with a specific delay, transfer the qubit population from the ground to the excited state. “This demonstrates precise control over qubit rotations under variable detuning, which, as stated previously, has wide applications in cQED experiments,” the researchers report. This work confirms that neural-ODE-based continuous-time control parameterizations can effectively enable the experimental realization of detuning-robust quantum gates in superconducting circuits, positioning the approach as a valuable tool for future quantum technologies.

Neural Networks Improve Robustness Without Error Modeling

Neural networks offer a path to quantum control pulses that bypass the need for detailed error modeling, achieving 99. This continuous-time framework allows for optimization through differentiable simulation of quantum dynamics, a significant departure from traditional pulse engineering techniques. The framework’s strength lies in its ability to achieve high-fidelity operations without explicitly modeling specific errors, a common requirement for other robustness strategies.

Existing techniques often demand analytical cancellation of error terms at the propagator level, but this new method optimizes directly against complex noise and parameter variations using standard batch-optimization techniques. During training, the system samples amplitude and detuning perturbations to construct complex drive fields, effectively building robustness into the pulse design itself.

Continuous-Time Control Fields Eliminate Basis Prescriptions

Neural networks now directly model quantum control fields as smooth functions of time, circumventing the need for traditional, discretized approaches to pulse engineering. Unlike previous neural network implementations that either discretized the control field or prescribed a basis for discrete parameters, this approach uses the universal function approximation capabilities of neural networks to express optimal control fields directly. The system’s Hamiltonian incorporates both fixed parameters describing the quantum system and tunable parameters representing the drive fields, allowing for precise manipulation of quantum states.

Experimental implementation of this method achieved 99. The pulses maintained an efficiency greater than 99.

High-Fidelity Pulses Facilitate Bosonic Qubit Applications

The newly designed pulses achieved a fidelity exceeding 99.9% for parity measurement operations in superconducting circuits, a performance level that surpasses both standard rectangular and DRAG pulses across a detuning range of ±20MHz. This improvement in robustness is particularly important for bosonic quantum electrodynamics (QED) experiments, where qubit detuning frequently arises from photon-number-dependent ac Stark shifts due to dispersive coupling to a resonator, complicating precise control.

Maintaining qubit resonance across varying photon occupations typically requires recalibration with each state, a process the new pulses circumvent. Beyond simply maintaining signal integrity, the method’s utility extends to a range of applications requiring accurate state reconstruction, including Wigner tomography and reliable error syndrome extraction in bosonic cat-qubit architectures. The ability to minimize coherent dynamical errors during parity mapping is essential for these processes, and the precision afforded by the neural network-designed pulses directly addresses a central experimental limitation.

The framework’s versatility is further demonstrated by its capacity to generate robust arbitrary rotation gates, and its potential for generalization to more complex multiqubit gates. These pulses also offer advantages in areas outside of quantum computation, including microwave sensing via coherent interaction-free measurements and magnetometry. The team validated the approach by experimentally benchmarking detuning-robust pulses with superconducting qubits, finding they outperformed both GRAPE-optimized and composite pulse sequences.

The framework’s success stems from its use of neural ordinary differential equations (neural ODEs) to construct control fields, offering a continuous-time control parameterization that is an effective tool for realizing detuning-robust quantum gates in superconducting circuits. This approach enables high-fidelity operations even when large, state-dependent frequency shifts are present, and has implications for error-mitigation strategies in quantum computing, as well as bosonic state reconstruction and parity measurements for axion detection. The resulting pulses are smooth and adaptable to different control hardware, offering a significant advantage over traditional pulse engineering methods.

Parity Measurement Advances Axion and Dark Photon Detection

This high fidelity, coupled with greater than 99. The ability to reliably discern photon number parity is central to qubit-based axion detectors, where a shift in qubit frequency signals the presence of these weakly interacting candidates for dark matter. The principle behind this enhanced detection relies on a specific sequence of operations; a qubit interacts with photons within a resonant cavity, causing a frequency shift proportional to the photon count.

Implementing this sequence demands true pulses, control signals unaffected by detuning from the qubit’s resonant frequency, to accurately map photon number to qubit state. The newly designed pulses, however, maintain performance even when detuned, offering a significant advantage in resolving subtle signals. Beyond improved sensitivity to dark matter candidates, the framework used to generate these pulses demonstrates versatility in other quantum applications. “This is a key motivation behind this work, as well as the context in which the results will be presented,” the team notes, highlighting the broad applicability of their continuous-time control parameterizations.

👉 More information
🗞 Neural-network-based design and implementation of fast and robust quantum gates
✍️ Marko Kuzmanović et al.
🧠 DOI: http://link.aps.org/doi/10.1103/4zzl-qbsf

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