Long-lived Particles Anomaly Detection with Parametrized Quantum Circuits

1. Problem Statement

The paper addresses the challenge of Anomaly Detection (AD) in High-Energy Physics (HEP), specifically targeting the identification of Long-Lived Particles (LLPs).

• Context: In collider experiments (like ATLAS at the LHC), new physics often manifests as particles with macroscopic lifetimes that decay far from the primary interaction vertex. These produce "displaced" signatures distinct from standard prompt decays.
• Challenge: Traditional trigger systems struggle with the computational demands and lack of flexibility required to reconstruct these complex, non-standard decay patterns in real-time.
• Goal: To investigate whether Quantum Machine Learning (QML), specifically using Parametrized Quantum Circuits (PQCs) as quantum autoencoders, can effectively detect these anomalies. The authors aim to prove the feasibility of running such algorithms on current Noisy Intermediate-Scale Quantum (NISQ) hardware.

2. Methodology

The authors propose a Quantum Autoencoder architecture implemented via PQCs. The methodology involves three main stages:

A. Algorithm Design (Quantum Autoencoder)

• Architecture: Similar to classical autoencoders, the quantum version consists of an Encoder (unitary transformation $U$) and a Decoder (inverse transformation $U^\dagger$).
• Mechanism: The encoder compresses input data by disentangling a subset of qubits, forcing them into the $|0\rangle$ state (latent space). The decoder attempts to reconstruct the original state.
• Loss Function: Defined as the expectation value of measuring the "compressed" qubits. If the reconstruction is poor (i.e., the compressed qubits are not in the $|0\rangle$ state), the loss is high.
• Training: Parameters (rotation angles) are optimized using stochastic gradient descent (backpropagation) on classical simulators.

B. Data Encoding

• Amplitude Encoding: Classical data (images) are encoded into the amplitudes of the quantum state. This allows $N$ qubits to represent $2^N$ features.
• Datasets:
  1. MNIST (Proof of Concept): "0" digits as normal data, "1" digits as anomalies. Images compressed to $8\times8$ pixels (64 features $\to$ 6 qubits).
  2. LLP Simulation (HEP Application): Simulated muon drift tube (MDT) hits from ATLAS. Normal data = prompt decays; Anomalous data = displaced decays (250–450 cm). Images ($100\times20$ pixels) encoded into 11 qubits.

C. Hardware Adaptation (NISQ Constraints)

To run on the IBM Hanoi quantum processor, significant adaptations were required due to noise and connectivity limits:

1. Connectivity: The original ring-topology circuit required non-neighboring C-NOT gates. The authors modified the circuit to a linear topology, removing specific C-NOT gates to eliminate the need for SWAP gates (which introduce significant noise).
2. Approximated Amplitude Encoding: Exact amplitude encoding requires an exponential number of gates, which is infeasible on NISQ devices. The authors trained a separate, shallow PQC to approximate the amplitude encoding for each data point, minimizing the Mean Squared Error (MSE) between the target state and the circuit output.
3. Loss Function Modification: Due to hardware noise, the standard loss function (sum of probabilities of $|0\rangle$) became indistinguishable. They switched to a new metric: $1 - P(|111\rangle)$, leveraging the fact that the target state $|111\rangle$ has the highest probability and is less susceptible to noise-induced fluctuations.

3. Key Contributions

1. First QML Application for LLPs: This is the first study applying QML specifically to the anomaly detection of long-lived particles in a collider context.
2. NISQ Implementation: Successfully demonstrated the execution of a quantum anomaly detection algorithm on real IBM quantum hardware, including the development of specific hardware-driven adaptations (approximated encoding and connectivity optimization).
3. Hybrid Workflow: Established a workflow where classical simulators are used for training the main autoencoder, while specific encoding circuits are trained individually for hardware execution.
4. Noise Mitigation Strategy: Proposed a novel loss function adaptation ($1 - P(|111\rangle)$) that improves discrimination in noisy environments compared to standard reconstruction losses.

4. Results

MNIST Dataset (Handwritten Digits)

• Simulation: The quantum autoencoder (6 layers, 3 compressed qubits) achieved a clear separation between normal and anomalous data.
  • Average Loss (Normal): 0.307
  • Average Loss (Anomalous): 1.026
  • AUC: High performance, comparable to classical baselines.
• Real Hardware (IBM Hanoi):
  • After adapting the circuit (4 layers, approximated encoding), the algorithm still detected anomalies.
  • AUC: 0.896 (Hardware) vs. 0.983 (Noise-free Simulation).
  • While performance degraded due to noise, a clear separation remained, proving feasibility.

High-Energy Physics (LLP) Dataset

• Simulation Only: The full HEP task (11 qubits) was too complex for current hardware.
• Performance: The quantum algorithm (8 layers, 3 compressed qubits) showed separation between prompt and displaced decays.
  • Comparison: The classical CNN-based autoencoder outperformed the quantum version (AUC: Classical > Quantum).
  • Reason: The quantum circuit's expressive power was limited by the constraint on the number of usable qubits and gates.
  • Observation: Interestingly, anomalous data (displaced decays) had lower reconstruction loss than normal data in both models because the displaced decay patterns were structurally simpler (narrower cone of hits) and thus easier to compress.

5. Significance and Conclusion

• Feasibility: The work proves that quantum anomaly detection is possible on current NISQ devices, provided the algorithms are heavily adapted to hardware constraints.
• Current Limitations: Due to noise and the overhead of amplitude encoding, current quantum implementations do not yet outperform classical deep learning algorithms on classical data.
• Future Outlook:
  • Hardware Evolution: As qubit quality improves and error correction becomes viable, PQCs are expected to surpass classical methods.
  • Quantum Data: The authors highlight a unique advantage for QML: the ability to process native quantum data (e.g., from future quantum sensors in particle detectors) without the need for classical encoding, potentially offering exponential speedups or better feature extraction in the future.

In summary, this paper serves as a critical "proof of concept" for integrating QML into the HEP workflow, bridging the gap between theoretical quantum algorithms and practical, noisy hardware execution.