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arxiv: 2312.04238 · v2 · submitted 2023-12-07 · 🪐 quant-ph · hep-ex

Long-lived Particles Anomaly Detection with Parametrized Quantum Circuits

Simone Bordoni , Denis Stanev , Tommaso Santantonio , Stefano Giagu This is my paper

Pith reviewed 2026-05-24 04:51 UTC · model grok-4.3

classification 🪐 quant-ph hep-ex
keywords anomaly detectionparametrized quantum circuitslong-lived particlesquantum machine learninghigh-energy physicsNISQ hardwareamplitude encoding
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The pith

A parametrized quantum circuit can detect anomalies in particle detector data from long-lived particle decays.

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

The paper tests whether a quantum circuit with trainable parameters can identify unusual patterns in high-energy physics data. It trains the circuit on a classical computer and runs it on both simulations and actual IBM quantum processors after making hardware-specific adjustments. The circuit successfully flags simple anomalies such as mismatched handwritten digits and, in simulation only, the more complex signatures left by long-lived particles in collider detectors. Because the task requires amplitude encoding of classical inputs, noise on present-day hardware stops the quantum approach from beating established classical neural-network methods.

Core claim

A parametrized quantum circuit, after classical training and hardware adaptations, performs anomaly detection on amplitude-encoded classical data; it identifies both simple digit anomalies on real NISQ devices and simulated long-lived-particle decay patterns in detector data, although noise prevents any performance gain over classical deep networks.

What carries the argument

Parametrized quantum circuit with amplitude encoding, adapted for anomaly scoring on NISQ hardware.

If this is right

  • Quantum circuits become a viable tool for anomaly detection once hardware noise drops enough to support amplitude encoding.
  • The same circuit architecture can be reused for other collider signatures that produce localized detector anomalies.
  • Hardware-specific adaptations such as circuit recompilation become standard steps when moving quantum ML models to real devices.

Where Pith is reading between the lines

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

  • Lower-noise quantum processors could remove the current performance gap and allow direct comparison on the full particle dataset.
  • The encoding step may be replaceable by other data-loading methods that avoid amplitude encoding altogether.

Load-bearing premise

Amplitude encoding of classical detector data into a quantum state remains feasible and useful despite the noise levels on current NISQ hardware.

What would settle it

A side-by-side run of the same long-lived-particle dataset on both the quantum circuit and a classical deep network, or successful execution of the full circuit on hardware with substantially lower noise, that shows a clear performance difference.

Figures

Figures reproduced from arXiv: 2312.04238 by Denis Stanev, Simone Bordoni, Stefano Giagu, Tommaso Santantonio.

Figure 1
Figure 1. Figure 1: Schematic representation of an autoencoder. The input data is compressed by the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schematic representation of a quantum autoencoder. The encoder acts as a unitary [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Circuit representation for three qubits of one layer of the PQC used in this work. Single qubit rotation gates with train￾able rotation angles are followed by an entan￾gling layer made of C-NOT gates acting on neighbouring qubits. ing the conventional stochastic gradient de￾scent techniques via backpropagation adopted in the training of ANNs [34]. A quantum circuit implements a unitary, thus invertible, tr… view at source ↗
Figure 4
Figure 4. Figure 4: Example of images for the ”zero” and ”one” digits for the MNIST handwritten digits dataset. Images are compressed to 8×8 pixels. the AUC value (Sec. 2.1). The best configura￾tion has been found with six layers and three compressed qubits. This procedure has been repeated in order to find the best entangling gates ansatz. We have tested different C-NOT configurations, the one that produced the best performa… view at source ↗
Figure 5
Figure 5. Figure 5: Circuit representation of the quantum encoder used for anomaly detection of hand [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Quantum autoencoder loss function values distribution. The graph has been made [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: A normal (left) and an anomalous (right) event used for quantum anomaly detection [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Loss function values distribution for the quantum anomaly detection algorithm (left) [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: ROC curve and AUC for quantum anomaly detection algorithm (blue) and the classic [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Architecture of IBM hanoi quan￾tum computer. The C-NOT connectivity is re￾ported. The colours of single qubits and their connections represent respectively the single qubit readout assignment error and C-NOT error probabilities. Darker colours represent a lower error probability, in a range between 5.9×10−3 and 9.8×10−2 for readout error and 3.3×10−3 and 1 for C-NOT gates. Data from calibration on 19/10/2… view at source ↗
Figure 11
Figure 11. Figure 11: Parametrized quantum circuit used for approximated amplitude encoding. The [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Counts distribution of 2048 shots for a simulated circuit with no noise (top) a simulated circuit with realistic noise (center) and a noisy quantum circuit (bottom). on the right reports the counts for the circuit executed on the quantum hardware. As ex￾plained in Sec. 3.1, the loss function, which the circuit has to minimize, measures the sum of the probabilities of the three compressed qubits to be in t… view at source ↗
Figure 13
Figure 13. Figure 13: Quantum autoencoder loss function values distribution. Simulated circuits with no [PITH_FULL_IMAGE:figures/full_fig_p014_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: ROC curves and AUC for anomaly detection, simulated circuits with no noise [PITH_FULL_IMAGE:figures/full_fig_p015_14.png] view at source ↗
read the original abstract

We investigate the possibility to apply quantum machine learning techniques for data analysis, with particular regard to an interesting use-case in high-energy physics. We propose an anomaly detection algorithm based on a parametrized quantum circuit. This algorithm has been trained on a classical computer and tested with simulations as well as on real quantum hardware. Tests on NISQ devices have been performed with IBM quantum computers. For the execution on quantum hardware specific hardware driven adaptations have been devised and implemented. The quantum anomaly detection algorithm is able to detect simple anomalies like different characters in handwritten digits as well as more complex structures like anomalous patterns in the particle detectors produced by the decay products of long-lived particles produced at a collider experiment. For the high-energy physics application, performance is estimated in simulation only, as the quantum circuit is not simple enough to be executed on the available quantum hardware. This work demonstrates that it is possible to perform anomaly detection with quantum algorithms, however, as amplitude encoding of classical data is required for the task, due to the noise level in the available quantum hardware, current implementation cannot outperform classic anomaly detection algorithms based on deep neural networks.

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

0 major / 2 minor

Summary. The manuscript proposes an anomaly detection algorithm based on parametrized quantum circuits (PQCs). The algorithm is trained on classical hardware and tested on handwritten digit data executed on IBM NISQ devices (with hardware-specific adaptations) as well as on simulated high-energy physics data for detecting anomalous patterns from long-lived particle decays. The authors conclude that anomaly detection is feasible with quantum methods but that amplitude encoding of classical data combined with current NISQ noise levels prevents the approach from outperforming classical deep neural network methods.

Significance. If the results hold, the work supplies a concrete, hardware-validated demonstration of PQC-based anomaly detection on a simple task together with simulation-based evidence for a HEP use case. The explicit discussion of practical limitations arising from amplitude encoding and NISQ noise provides a realistic assessment that is valuable for the field. The combination of classical training, hardware execution for digits, and simulation for the collider application offers a balanced feasibility study.

minor comments (2)
  1. [Abstract] Abstract: the summary states that the quantum implementation 'cannot outperform' classical DNN methods but provides no quantitative performance numbers, error bars, or direct comparison metrics; including at least headline figures from the digit and HEP tests would strengthen the abstract.
  2. The description of the PQC architecture and the specific hardware-driven adaptations would benefit from an accompanying circuit diagram or pseudocode to improve reproducibility and clarity for readers.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the constructive and positive review. The assessment accurately captures the scope of our work, including the hardware execution on IBM devices for the digit task, the simulation-based HEP application, and the explicit discussion of limitations due to amplitude encoding and NISQ noise. We appreciate the recommendation for minor revision and will incorporate clarifications where appropriate.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper reports an empirical machine-learning demonstration: a parametrized quantum circuit is trained on classical hardware to perform anomaly detection, then evaluated on simulated HEP data and (for simpler tasks) on IBM NISQ hardware. No derivation chain, uniqueness theorem, or first-principles result is presented that reduces to its own fitted parameters or to a self-citation by construction. Performance metrics are obtained from explicit training and testing runs; the abstract explicitly caveats that amplitude encoding plus current noise prevents any claimed advantage over classical DNNs. The argument is therefore self-contained against external benchmarks and contains none of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The approach rests on standard quantum circuit execution and classical training of variational parameters; no new physical entities or ad-hoc constants are introduced beyond the circuit architecture itself.

free parameters (1)
  • PQC variational parameters
    Circuit parameters are optimized during classical training to perform the anomaly detection task.
axioms (1)
  • domain assumption Quantum circuit model with amplitude encoding of classical data
    Required to load detector data into the quantum device as stated in the abstract conclusion.

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