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Quantum Re-Uploading for Calorimetry: Optimized Architectures with Extended Expressivity

Léa Cassé, Bernhard Pfahringer, Albert Bifet, Frédéric Magniette

TL;DR

The paper investigates single-qubit quantum re-uploading units (QRUs) for a three-feature calorimetry classification task, comparing them to a mono-encoded VQC under matched parameter budgets. It demonstrates that QRUs achieve high accuracy with shallow depths and that data re-encoding broadens harmonic support, enabling richer functional expressivity as shown by Fourier analysis. A comprehensive hyperparameter study, Bayesian and Hyperband global optimization, and a parameter-matched comparison to VQC and MLP establish QRUs as competitive and sometimes superior in this setting. The work further validates practical deployability with an end-to-end proof-of-execution on a real superconducting QPU via a cloud workflow, highlighting near-term applicability under current hardware constraints.

Abstract

Near-term quantum machine learning must balance expressivity, optimization, and hardware constraints. We study quantum re-uploading units (QRUs) as compact circuits and compare them, at matched parameter count, to a standard mono-encoded variational quantum circuit (VQC) baseline. On a three-feature calorimetry classification task, we train a single-qubit QRU that outputs a scalar in $[-1,1]$ and map it to three classes via fixed thresholds. In this setting, QRUs obtain higher accuracy than the mono-encoded baseline. A controlled ablation over depth, input scaling, circuit template, optimizer, and gradient accumulation indicates that most gains occur at small depths, with diminishing returns as depth increases while training cost grows approximately linearly. To interpret these observations, we analyze reachable Fourier components and find that repeated data re-encoding expands the per-coordinate harmonic support relative to mono-encoding, consistent with a spectral activation study over random initializations. Finally, we report an end-to-end proof-of-execution of the trained model on a superconducting QPU via a cloud workflow, illustrating practical deployability under current constraints.

Quantum Re-Uploading for Calorimetry: Optimized Architectures with Extended Expressivity

TL;DR

The paper investigates single-qubit quantum re-uploading units (QRUs) for a three-feature calorimetry classification task, comparing them to a mono-encoded VQC under matched parameter budgets. It demonstrates that QRUs achieve high accuracy with shallow depths and that data re-encoding broadens harmonic support, enabling richer functional expressivity as shown by Fourier analysis. A comprehensive hyperparameter study, Bayesian and Hyperband global optimization, and a parameter-matched comparison to VQC and MLP establish QRUs as competitive and sometimes superior in this setting. The work further validates practical deployability with an end-to-end proof-of-execution on a real superconducting QPU via a cloud workflow, highlighting near-term applicability under current hardware constraints.

Abstract

Near-term quantum machine learning must balance expressivity, optimization, and hardware constraints. We study quantum re-uploading units (QRUs) as compact circuits and compare them, at matched parameter count, to a standard mono-encoded variational quantum circuit (VQC) baseline. On a three-feature calorimetry classification task, we train a single-qubit QRU that outputs a scalar in and map it to three classes via fixed thresholds. In this setting, QRUs obtain higher accuracy than the mono-encoded baseline. A controlled ablation over depth, input scaling, circuit template, optimizer, and gradient accumulation indicates that most gains occur at small depths, with diminishing returns as depth increases while training cost grows approximately linearly. To interpret these observations, we analyze reachable Fourier components and find that repeated data re-encoding expands the per-coordinate harmonic support relative to mono-encoding, consistent with a spectral activation study over random initializations. Finally, we report an end-to-end proof-of-execution of the trained model on a superconducting QPU via a cloud workflow, illustrating practical deployability under current constraints.

Paper Structure

This paper contains 23 sections, 1 theorem, 25 equations, 25 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Theoretical Foundations
  3. Experimental Methodology
  4. Dataset
  5. Baseline Setups and Computational Environment
  6. Results and Hyperparameter Optimization Studies
  7. Impact of individual hyperparameters
  8. Model hyperparameters
  9. Circuit depth
  10. Input normalization
  11. Rotation gates
  12. Number of trainable parameters per input
  13. Training hyperparameters
  14. Batch Size
  15. Optimizer
  16. ...and 8 more sections

Key Result

Theorem 1

In a three-dimensional space, any rotation can be represented by a combination of elementary rotations around the $x$, $y$and $z$ axes, respectively denoted as $R_x$, $R_y$and $R_z$. More precisely, any rotation can be expressed as a single rotation by an angle $\theta$ around a fixed axis, accordin where $\theta$ is the total rotation angle and $\hat{n}$ is the unit vector describing the rotation

Figures (25)

  • Figure 1: Empirical activation rate $p_n$ of DFT coefficients for QRU (blue) and VQC (orange) under equal parameter budgets ($P=9L$). The QRU activates harmonics up to order $\pm4$ while the VQC remains confined to $\pm1$.
  • Figure 2: Left: Final test accuracy; right: Final loss over 50 runs
  • Figure 3: Evolution of the loss over epochs for different circuit depths.
  • Figure 4: Evolution of test accuracy over epochs for different circuit depths.
  • Figure 5: Comparison of execution time, final loss and final accuracy as a function of circuit depth.
  • ...and 20 more figures

Theorems & Definitions (1)

  • Theorem 1: Euler's theorem on rotations