Pulsed learning for quantum data re-uploading models

TL;DR

The paper targets the trainability and noise challenges of gate-based variational quantum circuits on NISQ devices by proposing a pulse-level data re-uploading framework that embeds trainable controls directly into hardware dynamics. By integrating quantum optimal control with data re-uploading, and implementing single- and two-qubit pulse-parameterized blocks on transmon architectures, the approach yields hardware-aligned quantum learning that can exploit continuous-time control. Numerical simulations on a superconducting transmon model with realistic noise demonstrate improved generalization and resilience to decoherence compared to gate-based baselines, even as circuit depth increases. The results suggest pulse-native QML can offer a practical and scalable path for near-term quantum learning, potentially reducing calibration overhead and enhancing performance under hardware imperfections. The work also outlines a general methodology to translate other variational quantum algorithms to pulse-level implementations, inviting broader adoption and tooling development.

Abstract

While Quantum Machine Learning (QML) holds great potential, its practical realization on Noisy Intermediate-Scale Quantum (NISQ) hardware has been hindered by the limitations of variational quantum circuits (VQCs). Recent evidence suggests that VQCs suffer from severe trainability and noise-related issues, leading to growing skepticism about their long-term viability. However, the possibility of implementing learning models directly at the pulse-control level remains comparatively unexplored and could offer a promising alternative. In this work, we formulate a pulse-based variant of data re-uploading, embedding trainable parameters directly into the native system's dynamics. We benchmark our approach on a simulated superconducting transmon processor with realistic noise profiles. The pulse-based model consistently outperforms its gate-based counterpart, exhibiting higher test accuracy and improved generalization under equivalent noise conditions. Moreover, by systematically increasing noise strength, we show that pulse-level implementations retain higher fidelity for longer, demonstrating enhanced resilience to decoherence and control errors. These results suggest that pulse-native architectures, though less explored, may offer a viable and hardware-aligned path forward for practical QML in the NISQ era.

Figures (6)

• Figure 1: Capacitive coupling of two transmon qubits via a coupler in form of a linear resonator. Each transmon is made with a Josephson junction and a capacitor. The transmon qubits interact through an intermediate resonator, which is composed of an inductance and a capacitor.
• Figure 2: (a) Virtual Z rotations scheme. $U$ gates represent an arbitrary gate. The upper indices denote the phase offset of the pulse. (b) CNOT gate from the three basic blocks for transmon. Here CR represents a cross resonance gate. Virtual rotations and CNOT gate transpilation with transmon architecture.
• Figure 3: Initialization of the proposed two-qubit QNN training. The parameters of the first qubit are initialized with the optimized values obtained from the previous single-qubit QNN training. The parameters of the entangling gates are set to zero to ensure that both qubits start the training process in a product state. The parameters of the second qubit are initialized randomly. From this initialization, all parameters are subsequently updated to minimize the cost function.
• Figure 4: Pulse-based gate replacement. Each $Z$-rotation gate is implemented as a vz rotation, introducing neither physical errors nor additional duration. The fixed $Y$-rotation gate is replaced by a parameterized single-qubit pulse, enabling arbitrary rotations within the $XY$-plane. As a result, the trainable parameters consist of the pulse phase, pulse amplitude, and the two vz rotation angles. Note that the original $\nu_2$ parameter is linked to the pulse amplitude $\Omega$, the pulse shape $s(t)$, and the pulse duration.
• Figure 5: Schematic representation of the pulsed ansätze $(a)$ compared to the original gate-based ansätze $(b)$ of a data re-uploading model. As in the traditional approach, the pulsed qnn exhibits a layered structure, divided into three basic operations: an encoding block, a single-qubit parameterized block, and a multi-qubit variational gate scheme. In the pulse model, each of these parametric blocks corresponds to a sequence of parameterized pulses, with selected physical parameters left free for optimization. The encoding block remains general and can be replaced with any user- or problem-specific encoding. Here, $\boldsymbol{\phi_l}$ represents the full set of trainable parameters for layer $l$, corresponding to the pulse controls in $(a)$ and to the gate rotations in $(b)$.