Data-Driven Qubit Characterization and Optimal Control using Deep Learning

TL;DR

This work addresses the challenge of designing high-fidelity quantum gates without detailed dynamical models by training a recurrent neural network to predict qubit responses to random probe pulses. The neural network serves as a differentiable surrogate, enabling gradient-based offline pulse optimization via a gate-syndrome loss $\mathcal{L}_{GSC}$, demonstrated on an $ST_0$ qubit. The method is validated on general and specific device simulations, achieving gate infidelities around 1% and showing comparable performance to model-based optimization while relying only on easily obtainable data. The approach promises practical scalability, potential experimental deployment, and applicability to other qubit platforms and multi-qubit extensions.

Abstract

Quantum computing requires the optimization of control pulses to achieve high-fidelity quantum gates. We propose a machine learning-based protocol to address the challenges of evaluating gradients and modeling complex system dynamics. By training a recurrent neural network (RNN) to predict qubit behavior, our approach enables efficient gradient-based pulse optimization without the need for a detailed system model. First, we sample qubit dynamics using random control pulses with weak prior assumptions. We then train the RNN on the system's observed responses, and use the trained model to optimize high-fidelity control pulses. We demonstrate the effectiveness of this approach through simulations on a single $ST_0$ qubit.

Figures (19)

• Figure 1: Diagram of our model training and pulse optimization pipeline. We model the qubit using a . The network is trained on $N$ randomly chosen control pulses and the measurement outcome from the device or a simulation sampled with these pulses (left). Once the network is trained, it is used as a proxy for the qubit to perform pulse optimization by means of Cerfontaine_2020 (right). To this end, randomly initialized pulses are first concatenated to form sequences inspired by . For each sequence, the qubit model predicts measurement outcomes, from which the loss $\mathcal{L}_{GSC}$ is calculated. The pulse parameters are then updated in a gradient-based optimization scheme by minimizing $\mathcal{L}_{GSC}$.
• Figure 2: Network error for different control sequence lengths measured on the test set. The network is only trained on lengths corresponding to the solid line. Pulses of lengths corresponding to dotted lines have not been seen in the training phase and are not used for optimizing pulses, as the syndromes only require pulses of length $L<=50$.
• Figure 3: The exchange interactions used for simulations of the approximative general model and the more accurate specific model. $\epsilon_{min}$ and $\epsilon_{max}$ describe the voltage range in which random pulses are sampled. The same $\epsilon_{min}$ is chosen for both models. $\epsilon_0$ refers to the parameter in the exchange interaction (Eq. \ref{['eq:exchange_interaction']}).
• Figure 4: The approximated transfer function kernels used to model pulse distortions introduced by the signaling hardware. The transfer function in the general simulation is an idealized, symmetric Gaussian kernel, while the transfer function in the specific simulation is based on the measured system response and captures only the behavior after the begin outputting the corresponding pulse segment.
• Figure 5: The transfer functions in relation to the programmed pulse (control) and the actually measured signal (measured). The qubit model using rough approximations is depicted as the dotted blue line (general). The qubit model based on more realistic measurements is shown in dashed orange (specific).