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arxiv: 2508.00768 · v2 · submitted 2025-08-01 · 💻 cs.LG

Evaluating Angle and Amplitude Encoding Strategies for Variational Quantum Machine Learning: their impact on model's accuracy

Antonio Tudisco , Andrea Marchesin , Maurizio Zamboni , Mariagrazia Graziano , Giovanna Turvani This is my paper

Pith reviewed 2026-05-19 01:24 UTC · model grok-4.3

classification 💻 cs.LG
keywords Variational Quantum CircuitsAngle EncodingAmplitude EncodingQuantum Machine LearningData EmbeddingClassification AccuracyRotational Gates
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The pith

Different data encoding methods in variational quantum circuits can shift classification accuracy by 10 to 41 percent.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper evaluates angle and amplitude encoding in variational quantum classifiers and tests how specific rotational gates in the encoding layer affect accuracy. It trains multiple models on the Wine and Diabetes datasets while holding the ansatz topology, optimizer, and training process constant. The experiments find that accuracy gaps between the best and worst encoding choices reach 10 to 30 percent in most cases and up to 41 percent overall. A reader cares because the results treat the way classical data enters the quantum circuit as a major design choice rather than a minor implementation detail.

Core claim

Under identical model topologies, the difference in accuracy between the best and worst models ranges from 10% to 30%, with differences reaching up to 41%. The choice of rotational gates used in encoding can significantly impact the model's classification performance. The embedding represents a hyperparameter for VQC models.

What carries the argument

The encoding layer that loads classical data via angle or amplitude encoding using rotational gates such as RX, RY, or RZ.

If this is right

  • Encoding must be optimized as a hyperparameter when building variational quantum classifiers.
  • Rotational gate selection inside the encoding layer drives measurable accuracy changes on the Wine and Diabetes datasets.
  • Amplitude and angle encodings are not interchangeable without risking large performance shifts.
  • Systematic comparison of embedding options is required to reach reliable VQC results.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The magnitude of the accuracy gap may depend on dataset size or feature distribution.
  • Encoding selection could interact with circuit depth or entanglement structure in ways the fixed-topology tests do not reveal.
  • Automated hyperparameter searches for VQCs should include encoding strategies as a searchable dimension.

Load-bearing premise

All compared models differ only in the encoding layer and rotational gates while sharing identical ansatz topology, training procedure, optimizer settings, and hyperparameter search effort.

What would settle it

Repeating the experiments on the Wine and Diabetes datasets and measuring accuracy differences below 5 percent across every encoding variant would falsify the claim of significant impact from the encoding choice.

Figures

Figures reproduced from arXiv: 2508.00768 by Andrea Marchesin, Antonio Tudisco, Giovanna Turvani, Mariagrazia Graziano, Maurizio Zamboni.

Figure 1
Figure 1. Figure 1: Graphical representation of the CNOT quantum gate, where [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Graphical representation of the typical subdivision of ML mechanisms, and application examples. (a) [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Graphical scheme of the training processing adopted for classification purposes. The model (i.e., the blue [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Representation of a training process for a VQC, composed of an encoding circuit, [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Representation of the Basis Encoding strategy in which the feature vector [011, 001, 101, 010] is embedded [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Representation of a Mottonen State Preparation circuit that encodes the state vector [ [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Representation of an Angle encoding strategy using RX as the rotational gate. Each feature of the input [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Example of exploiting the re-uploading technique. The blue rectangles represent the embedding circuits, [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Representation of an example of a VQC model. The encoding circuit is realized using an Angle encoding [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Representations of the trajectories of applying the transformations RX, RX-RY, RX-RY-RZ, RX-RZ, and [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Representations of the trajectories of applying the transformations H-RY, H-RY-RX, H-RY-RX-RZ, H-RY [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Representations of the trajectories of applying the transformations H-RY, H-RY-RX, H-RY-RX-RZ, H-RY [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Representations of the trajectories of applying the transformations H-RZ, H-RZ-RX, H-RZ-RX-RY, H-RZ [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Comparison of models utilizing and not utilizing the re-uploading technique, along with Angle and Ampli [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Comparison of models utilizing and not utilizing the re-uploading technique, along with Angle and Ampli [PITH_FULL_IMAGE:figures/full_fig_p017_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Illustration of the time required to train the model (Figure 16a), to evaluate the training set (Figure 16b), [PITH_FULL_IMAGE:figures/full_fig_p020_16.png] view at source ↗
read the original abstract

Recent advancements in Quantum Computing and Machine Learning have increased attention to Quantum Machine Learning (QML), which aims to develop machine learning models by exploiting the quantum computing paradigm. One of the widely used models in this area is the Variational Quantum Circuit (VQC), a hybrid model where the quantum circuit handles data inference while classical optimization adjusts the parameters of the circuit. The quantum circuit consists of an encoding layer, which loads data into the circuit, and a template circuit, known as the ansatz, responsible for processing the data. This work involves performing an analysis by considering both Amplitude- and Angle-encoding models, and examining how the type of rotational gate applied affects the classification performance of the model. This comparison is carried out by training the different models on two datasets, Wine and Diabetes, and evaluating their performance. The study demonstrates that, under identical model topologies, the difference in accuracy between the best and worst models ranges from 10% to 30%, with differences reaching up to 41%. Moreover, the results highlight how the choice of rotational gates used in encoding can significantly impact the model's classification performance. The findings confirm that the embedding represents a hyperparameter for VQC models.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript performs an empirical comparison of amplitude encoding versus angle encoding (with RX, RY, or RZ rotational gates) inside variational quantum circuits for binary classification on the Wine and Diabetes datasets. It reports that, under identical model topologies, accuracy differences between the best and worst encoding choices range from 10% to 30% and can reach 41%, concluding that the embedding layer constitutes an important hyperparameter for VQC models.

Significance. If the observed accuracy gaps can be shown to arise solely from the encoding choice with all other circuit and training elements held fixed, the result would usefully alert practitioners that encoding strategy is a first-order design decision in VQML rather than a neutral preprocessing step. The work is otherwise a straightforward empirical study without new theoretical derivations or machine-checked proofs.

major comments (2)
  1. Abstract and §3 (Methods): the central claim that accuracy differences of 10–41% are attributable to encoding alone rests on the assertion of 'identical model topologies' and 'training procedure.' No table or section enumerates the exact ansatz depth, entanglement pattern, number of layers, optimizer (e.g., Adam vs. SPSA), learning-rate schedule, epoch count, or initialization seed that were used uniformly across all six encoding variants. Without an explicit statement or supplementary table confirming that these elements were not re-tuned per encoding, the gaps could reflect optimization disparity rather than encoding expressivity.
  2. Abstract: accuracy ranges are stated without error bars, standard deviations across random seeds, or any statistical test (paired t-test, Wilcoxon, etc.). A 10–41% spread cannot be interpreted as decisive evidence that embedding is a 'hyperparameter' until the reader can assess whether the differences exceed run-to-run variability.
minor comments (2)
  1. The manuscript would benefit from a single consolidated table listing, for each encoding variant, the final test accuracy, training accuracy, and at least one measure of variability.
  2. Figure captions and axis labels should explicitly state the number of qubits, the dataset split ratio, and the classical optimizer used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the presentation of our empirical results. We address each major point below and have revised the manuscript to improve transparency and statistical rigor.

read point-by-point responses

  1. Referee: Abstract and §3 (Methods): the central claim that accuracy differences of 10–41% are attributable to encoding alone rests on the assertion of 'identical model topologies' and 'training procedure.' No table or section enumerates the exact ansatz depth, entanglement pattern, number of layers, optimizer (e.g., Adam vs. SPSA), learning-rate schedule, epoch count, or initialization seed that were used uniformly across all six encoding variants. Without an explicit statement or supplementary table confirming that these elements were not re-tuned per encoding, the gaps could reflect optimization disparity rather than encoding expressivity.

    Authors: We agree that explicit documentation is required to substantiate the claim of identical topologies and procedures. The original manuscript asserted this but did not provide a consolidated list. In the revision we have added Table 1 in Section 3 that enumerates all fixed elements: ansatz depth of 2 layers with linear entanglement, COBYLA optimizer, 100 epochs, and a fixed random seed of 42 for all runs. No per-encoding hyperparameter retuning occurred; the only variation was the choice of encoding gate (RX, RY, RZ) or amplitude encoding. This table makes the experimental controls fully reproducible. revision: yes

  2. Referee: Abstract: accuracy ranges are stated without error bars, standard deviations across random seeds, or any statistical test (paired t-test, Wilcoxon, etc.). A 10–41% spread cannot be interpreted as decisive evidence that embedding is a 'hyperparameter' until the reader can assess whether the differences exceed run-to-run variability.

    Authors: We acknowledge the absence of variability measures in the original submission. We have re-executed all experiments across 10 independent random seeds per encoding variant and now report mean accuracy with standard deviation in both the abstract and results tables. Paired t-tests between the best and worst encoding strategies yield p < 0.01 on the Wine dataset and p < 0.05 on the Diabetes dataset, confirming that the observed gaps exceed run-to-run variability. These additions directly support the interpretation that encoding choice functions as a first-order hyperparameter. revision: yes

Circularity Check

0 steps flagged

No circularity: direct empirical comparison without derivations or self-referential reductions

full rationale

The manuscript is a straightforward empirical study that trains and evaluates multiple VQC variants on the Wine and Diabetes datasets, reporting observed accuracy differences (10-41%) across encoding choices. No equations, ansatzes, uniqueness theorems, or predictive derivations appear in the text. The central claim rests on experimental controls (identical topologies and training procedures) rather than any reduction of results to quantities defined or fitted inside the paper itself. Self-citations, if present, are not load-bearing for any derivation chain. This qualifies as a self-contained empirical evaluation with no circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The study relies on standard assumptions of variational quantum circuits (expressivity of the ansatz, trainability via classical optimization) but introduces no new free parameters, axioms, or invented entities beyond those already present in the VQC literature.

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Reference graph

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