Neural-network-based design and implementation of fast and robust quantum gates
Marko Kuzmanović, Ilya N. Moskalenko, Yu‐Han Chang, Ognjen Stanisavljević, Christopher Warren, Emil Hogedal, Anuj Aggarwal, Irshad Ahmad, Janka Biznárová, Mamta Dahiya, Marcus Rommel, Andreas Nylander, Giovanna Tancredi, Gheorghe Sorin Paraoanu
We present a continuous-time, neural-network-based approach to optimal control in quantum systems, with a focus on pulse engineering for quantum gates. Leveraging the framework of neural ordinary differential equations (neural ODEs), we construct control fields as outputs of trainable neural networks, thereby eliminating the need for discrete parametrization or predefined bases. This allows for the generation of smooth, control-hardware-agnostic pulses that can be optimized directly using differentiable integrators. As a case study, we design and experimentally implement a short and detuning-robust π / 2 pulse for photon number parity measurements in superconducting transmon circuits. This is achieved through simultaneous optimization for robustness and suppressing the leakage outside of the computational basis. These pulses have very high fidelity ( ≈ 99.95 % ) and realize the parity measurement with an efficiency greater than 99.9% over a detuning range of ≈ ± 20 MHz , thereby outperforming traditional techniques while retaining comparable gate durations. This showcases the potential of neural ODEs for high-performance quantum control in experimentally relevant settings.
We present a continuous-time, neural-network-based approach to optimal control in quantum systems, with a focus on pulse engineering for quantum gates. Leveraging the framework of neural ordinary differential equations (neural ODEs), we construct control fields as outputs of trainable neural networks, thereby eliminating the need for discrete parametrization or predefined bases. This allows for the generation of smooth, control-hardware-agnostic pulses that can be optimized directly using differentiable integrators. As a case study, we design and experimentally implement a short and detuning-robust π / 2 pulse for photon number parity measurements in superconducting transmon circuits. This is achieved through simultaneous optimization for robustness and suppressing the leakage outside of the computational basis. These pulses have very high fidelity ( ≈ 99.95 % ) and realize the parity measurement with an efficiency greater than 99.9% over a detuning range of ≈ ± 20 MHz , thereby outperforming traditional techniques while retaining comparable gate durations. This showcases the potential of neural ODEs for high-performance quantum control in experimentally relevant settings.
The presence of decoherence in quantum computers necessitates the suppression of noise. Dynamically corrected gates via specially designed control pulses offer a path forward, but hardware-specific experimental constraints can cause complications. Existing methods to obtain smooth pulses are either restricted to two-level systems, require an optimization over noise realizations, or limited to piecewise-continuous pulse sequences. In this paper, we present the first general method for obtaining truly smooth pulses that minimizes sensitivity to noise, eliminating the need for sampling over noise realizations and making assumptions regarding the underlying statistics of the experimental noise. We parametrize the Hamiltonian using a neural network, which allows the use of a large number of optimization parameters to adequately explore the functional control space. We demonstrate the capability of our approach by finding smooth shapes, which suppress the effects of noise within the logical subspace as well as leakage out of that subspace.
Real-time adaptive control of quantum systems requires rapid generation of robust, high-fidelity pulses across a continuous range of operating conditions. Standard optimization algorithms such as gradient-ascent pulse engineering (GRAPE) solve each instance independently, discarding information between runs and requiring costly reinitialization when parameters change. We present an approach to robust optimal quantum control based on model-based reinforcement learning, in which a single neural network -- embedding the Hamiltonian directly into the training pipeline -- generates robust gates across an entire family of gate configurations, without pre-computed training data. Demonstrated on a single-spin (two-level) system, the trained networks produce pulses for arbitrary rotation angles over a range of pulse durations, detunings, and field inhomogeneities in milliseconds, at fidelities comparable to multi-seed GRAPE. The framework is inherently adaptable: any parameter entering the Hamiltonian can serve as a network input, extending the approach to different systems and control settings. Beyond speed, the network reveals structure in the control landscape: it discovers the same structured phase profiles that appear in GRAPE solutions -- made identifiable through fidelity-invariant symmetry transformations -- but more consistently than independent optimization. This consistency enables smooth interpolation across the entire trained parameter space.
Fault-tolerant quantum computing requires high-fidelity quantum gates that are resilient to control errors and device imperfections. Here, we develop energy-optimal control pulses for single-qubit gates that are simultaneously robust against frequency detuning and waveform inhomogeneities while also suppressing leakage outside the computational subspace. Combining the optimized pulse envelopes with an adaptive control scheme, we experimentally demonstrate optimal robust gates on a superconducting quantum processor. For a gate duration of 90ns, we achieve fidelities above 99.9% for the X gate and 99.6% for Hadamard-type gates. For the X gate, we maintain fidelities above 99.5% for simultaneous drive-amplitude variations up to 20% and qubit detuning up to 4 MHz. This robustness outperforms that of conventional Gaussian pulses by an order of magnitude, without much difference in peak gate fidelity. These results establish a route towards robust single-qubit control in large-scale quantum processors, advancing the development of fault-tolerant quantum computing.
The potential of quantum computing is fundamentally constrained by the inherent susceptibility of qubits to noise and crosstalk, particularly during multi-qubit gate operations.
Existing strategies, such as hardware isolation and dynamical decoupling, face limitations in scalability, experimental feasibility, and robustness against complex noise sources.
In this manuscript, we propose a physics-guided neural control (PGNC) framework to generate robust control pulses for superconducting transmon qubit systems, specifically targeting crosstalk mitigation.
By combining a hardware aware parameterization with a Hamiltonian-informed objective that accounts for condition-dependent crosstalk distortions, PGNC steers the search toward smooth and physically realizable pulses while efficiently exploring high dimensional control landscapes.
Numerical simulations for the CZ gate demonstrate superior fidelity and pulse smoothness compared to a Krotov baseline under matched constraints.
Taken together, the results show consistent and practically meaningful improvements in both nominal and perturbed conditions, with pronounced gains in worst-case fidelity, supporting PGNC as a viable route to robust control on near-term transmon devices.
The potential of quantum computing is constrained by the susceptibility of qubits to noise and crosstalk during multi-qubit gate operations. Existing strategies, such as hardware isolation and dynamical decoupling, face limitations in scalability, feasibility, and robustness against complex noise sources. Here we show a physics-guided neural control framework that generates robust control pulses for superconducting transmon qubit systems, specifically targeting crosstalk mitigation. By combining a hardware-aware parameterization with a Hamiltonian-informed objective that accounts for condition-dependent crosstalk distortions, the framework steers the search toward smooth and physically realizable pulses while exploring high-dimensional control landscapes. Numerical simulations for the controlled-Z gate demonstrate superior fidelity and pulse smoothness compared to the Krotov and GRAPE baselines under matched constraints. The results show consistent and practically meaningful improvements in both nominal and perturbed conditions, with pronounced gains in worst-case fidelity, supporting physics-guided neural control as a route to robust control on near-term transmon devices. Quantum computers are highly sensitive to unwanted crosstalk between qubits, especially during multi-qubit gate operations. Here, the authors show that physics-guided neural control can generate smooth, hardware-compatible pulses that make two-qubit gates more robust against crosstalk.
Implementing quantum gates on quantum computers can require the application of carefully shaped pulses for high-fidelity operations. We explore the use of physics-informed neural networks (PINNs) for quantum optimal control to assess their usefulness in predicting such pulses. Our PINN is a feedforward neural network that utilizes an unsupervised learning approach, whose loss function includes terms that enforce the equations that govern the evolution of a quantum system, measure how close the learned unitary is to the target unitary operation, and ensure state normalization. We use a sinusoidal activation function and adopt variance-type weight initialization, tailored to our activation function. By analyzing the model's performance with important machine learning metrics, we demonstrate that the choice of our architecture is well-suited for this type of problem. We ensure that our network avoids the vanishing and exploding gradients with our relevant choices. We build two different PINNs, one based on the Schrödinger equation and another one based on the Lindblad equation. Our PINNs are able to discover high-fidelity two-qubit gate pulses for a variety of quantum operations, demonstrating its flexibility and robustness. We build two different PINNs, one based on the Schrödinger equation and another one based on the Lindblad equation. Our PINNs are able to discover high-fidelity two-qubit gate pulses for a variety of quantum operations, demonstrating its flexibility and robustness.