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Quantum Machine Learning in High Energy Physics

Wen Guan, Gabriel Perdue, Arthur Pesah, Maria Schuld, Koji Terashi, Sofia Vallecorsa, Jean-Roch Vlimant

arXiv:2005.08582v2quant-phhep-ph

TL;DR

High-energy physics needs methods that can address the enormous computational demands of experiments such as the HL-LHC, motivating questions about quantum machine learning. This review surveys early quantum-machine-learning applications in high-energy physics, including trainable circuits and quantum annealing, and discusses their promise alongside current hardware and benchmarking limitations.

  • Problem

    The HL-LHC and particle-physics experiments require enormous computing resources, motivating investigation of whether quantum machine learning can help with data processing and analysis.

  • Method

    The paper reviews quantum machine-learning applications in high-energy physics, covering quantum circuits, quantum annealing, and prospects for quantum data analysis.

  • Results

    Reviewed applications show promising preliminary quantum-machine-learning performance, but reported circuit-based tracking accuracy remains below the classical case and annealing classifiers show no accuracy advantage over classical approaches.

  • Takeaways & Limitations

    Quantum machine learning is a developing approach for high-energy physics whose future impact includes differentiating through quantum computations for adaptive experiment design and quantum data analysis.

  • Takeaways & Limitations

    Current quantum hardware and classical simulation constraints restrict experiments and benchmarks to small proof-of-principle settings with few qubits and features.

Abstract

from arXiv · show

Machine learning has been used in high energy physics for a long time, primarily at the analysis level with supervised classification. Quantum computing was postulated in the early 1980s as way to perform computations that would not be tractable with a classical computer. With the advent of noisy intermediate-scale quantum computing devices, more quantum algorithms are being developed with the aim at exploiting the capacity of the hardware for machine learning applications. An interesting question is whether there are ways to apply quantum machine learning to High Energy Physics. This paper reviews the first generation of ideas that use quantum machine learning on problems in high energy physics and provide an outlook on future applications.

1. Introduction

High-energy physics faces increasingly demanding data-processing challenges, motivating interest in quantum machine learning and other quantum approaches. The review introduces quantum-computing paradigms and explains their promise, constraints, and open questions for particle-physics applications.

  • 1. Introduction: The HL-LHC will require enormous computing resources, motivating investigation of whether quantum machine learning can help address particle-physics computational challenges.
  • 1. Introduction: Quantum machine learning learns quantum algorithms or uses quantum computers for machine-learning tasks, complementing explicitly designed quantum algorithms.
  • Quantum-computing paradigms: Current devices are limited by noise, small qubit counts, low connectivity, and engineering challenges involving cross-talk and qubit quality.
  • Quantum-computing paradigms: Near-term quantum devices motivate variational circuits with trainable parameters, while quantum annealing approximates solutions to QUBO optimization problems.
  • Quantum annealing: Quantum annealing may lose potential advantage when adiabatic evolution becomes very slow with system size, leaving its useful problem classes an open research question.

3. Quantum Machine Learning

Quantum machine learning spans foundational theory, complexity-driven algorithms, and applications tailored to near-term devices. In practice, trainable circuits encode data and parameters into quantum gates, whereas quantum annealers optimize or sample for classical models.

  • Quantum Machine Learning: Quantum machine learning research comprises foundational quantum learning theory, algorithms seeking computational speedups, and applications tailored to NISQ devices.
  • Quantum Machine Learning: Near-term circuit methods commonly use quantum computers for predictions trained with classical optimization, while quantum annealers optimize classical models.
  • 3.1. Quantum circuits as trainable models: A variational circuit encodes input features and trainable parameters as rotation angles, applies a parameterized unitary, and interprets an observable expectation value as the prediction.
  • 3.1. Quantum circuits as trainable models: Classical optimization trains variational circuits by adjusting parameters to minimize a cost function comparing predictions with target outputs.
  • 3.1. Quantum circuits as trainable models: Quantum circuits support exact gradient estimation through shifted circuit evaluations, enabling gradient-based optimization and differentiable programming.
  • 3.2. Quantum Annealers as Optimizers: Quantum annealers can optimize QUBO-formulated losses, including binary-weight perceptron ensembles, or sample distributions used in restricted Boltzmann-machine training.

4. Quantum Annealing Applications

Quantum annealing applications in HEP map classification and generative-model training onto optimization or sampling problems, but reported performance generally remains comparable to classical methods.

  • 4.1. Di-photon Event Classification: The di-photon classifier selects weak-classifier weights by transforming a QUBO into a problem Hamiltonian and embedding it on the quantum device.The optimized weights define the strong classifier used for comparison with classical methods.
  • 4.1. Di-photon Event Classification: Quantum annealing and simulated annealing were generally on par and showed no obvious classification advantage over BDT and DNN baselines.A slight advantage was noted with a small training dataset, but the difference was not conclusive.
  • 4.1. Di-photon Event Classification: The continuous QAML-Z extension outperformed original QAML but remained without an accuracy advantage over classical approaches, with quantum and simulated annealing results on par.The method iteratively approximates continuous optimization using discretized quantum-annealing steps.
  • 4.2. Classification in Cosmology with Quantum Restricted Boltzmann Machine: Restricted Boltzmann Machines use quantum annealers as sampling engines, with qubit couplings representing graph weights and annealing supplying graph configurations.The bipartite RBM structure scales more favorably in embedding than a fully connected graph.
  • 4.2. Classification in Cosmology with Quantum Restricted Boltzmann Machine: RBM training uses positive and negative phases, but exact model expectations scale as 2^min(n_v,n_h), making the model expectation computationally costly.Quantum annealers can estimate expectations over unclamped variables, although their output distribution is not practically Boltzmann without substantial post-processing.
  • 4.2. Classification in Cosmology with Quantum Restricted Boltzmann Machine: For galaxy morphology classification, RBMs were generally less effective than gradient-boosted trees, while retaining an advantage on very small datasets.Classical discriminative training outperformed quantum generative training overall, but quantum generative training performed better early in small-dataset runs.

5. Quantum Circuit Applications

Quantum circuit applications in HEP explore hierarchical quantum classifiers and variational quantum algorithms for track reconstruction and particle-physics classification. Preliminary results approach classical baselines in some settings, while performance remains constrained by reduced model size, limited iterations, and training-sample or simulation costs.

  • 5.1. Quantum Graph Neural Networks for particle track reconstruction: Quantum circuit applications target demanding HEP tasks including particle tracking, whose computational cost grows with detector occupancy and simultaneous collisions.The reviewed tracking work explores quantum graph-based representations and hierarchical quantum classifiers as an alternative to classical approaches.
  • 5.1. Quantum Graph Neural Networks for particle track reconstruction: The TTN-based quantum edge and node networks encode data with Ry rotations, use CNOT gates, and measure a single output qubit.The TTN contains 11 trainable rotation parameters optimized with ADAM and binary cross entropy on 1450 TrackML subgraphs.
  • 5.1. Quantum Graph Neural Networks for particle track reconstruction: QGNN validation loss decreased smoothly and accuracy increased with iterations, but converged accuracy remained below the classical GNN.The quantum model used fewer hidden features and iterations because of computational constraints.
  • 5.2. Classification Using Variational Quantum Circuits: VQML encodes inputs into quantum states, applies a parameterized ansatz, measures an output, and optimizes its parameters against classification loss.The reviewed implementations use optimizers including COBYLA and SPSA, with quantum circuits and simulators supporting the training procedure.
  • 5.2. Classification Using Variational Quantum Circuits: VQML achieved performance very close to the classical BDT with 800 events and 5 qubits for ttH data analysis.On IBM Q hardware, performance was compatible with the quantum simulator within limited testing iterations, and the simulator approached BDT performance with enough iterations.
  • 5.2. Classification Using Variational Quantum Circuits: In SUSY classification, QCL performance was relatively flat as training size increased, whereas BDT and DNN performance improved with training size.Simulating QCL with 10,000 events or more required computational resources beyond the reported setup.

6. Applications Coming Soon

The review identifies generative models and quantum-enhanced support vector machines as promising but underexploited directions for HEP. These approaches aim to address simulation and classification problems through probability modeling or quantum feature spaces.

  • 6. Applications Coming Soon: Quantum counterparts of Boltzmann machines, variational auto-encoders, and generative adversarial networks are identified as possible tools for HEP generative modeling.Classical generative models are being investigated to accelerate Monte Carlo simulation by modeling complex probability distributions at lower prediction cost.
  • 6. Applications Coming Soon: Generative models could support faster Monte Carlo simulation, although training those models is described as difficult.The review connects this direction to the need for modeling complex probability distributions in HEP.
  • 6. Applications Coming Soon: Quantum-enhanced SVM kernels can map inputs into an exponential Hilbert space, potentially making class-separating hyperplanes easier to construct.The review presents quantum SVMs as an attractive approach that has not yet been fully exploited in HEP.

7. Discussion and Outlook

The review concludes that it is too early to determine whether quantum machine learning is particularly suited to HEP. Large datasets, controversial speed-up claims, and near-term data-loading and measurement constraints limit current evidence.

  • 7. Discussion and Outlook: Whether quantum machine learning is particularly suited to HEP remains unresolved and requires further investigation.The review explicitly states that the available evidence is currently insufficient to answer this question for near-term or universal quantum computers.
  • 7. Discussion and Outlook: Significant quantum machine-learning speed-ups remain controversial and may depend on data sparsity or specialized data-loading oracles.These dependencies limit how broadly claimed speed-ups can be interpreted for large HEP datasets.
  • 7. Discussion and Outlook: Encoding large datasets with sufficient precision and measuring outputs for every event are beyond the scope of near-term quantum computing.Near-term platforms nevertheless allow small-scale testing through quantum programming languages, cloud hardware, and software packages.
  • 7. Discussion and Outlook: Quantum annealers remain noisy and limited in qubit number and connectivity, constraining their current use for HEP applications.These hardware limitations add to the broader uncertainty about practical quantum advantages in the field.

Solver Heuristics.

Solver heuristics help adapt larger optimization problems to hardware with limited connectivity, but this comes with additional computational cost and weakens direct tests of device-only capabilities.

  • Solver Heuristics.: qbsolve splits large QUBOs into smaller problems solvable on available hardware, enabling experiments with larger formulations.The trade-off is additional computing-resource demand and loss of a direct probe of the stand-alone quantum device.
  • Solver Heuristics.: Mapping reformulated problems onto limited-connectivity devices can require connectivity constraints to be incorporated directly into the loss.Hardware connectivity therefore affects the optimization formulation itself.
  • Solver Heuristics.: Digital annealers can prototype fully connected systems with 4,096 qubits at 64-bit precision or 8,192 qubits at 16-bit precision.The review notes a potential cluster scale of up to 1,000,000 qubits using multi-chip support.

Digital Devices.

Current quantum hardware limits experiments to small systems because qubit count, connectivity, and decoherence constrain circuit size.

  • Few qubits and four-feature datasets are typical in current implementations.
  • Limited qubit connectivity and short decoherence times make large, long variational circuits difficult to test.
  • Current hardware limitations constrain practical experimentation with quantum machine learning.

Circuit Architecture.

Reviewed quantum machine learning studies generally fix circuit architectures and optimize only their gate parameters, while circuit-assembly search remains an additional possibility.

  • The reviewed quantum circuits use fixed gate types and numbers, with optimization applied to gate parameters.
  • Reinforcement learning has been used to derive circuits for combinatorial problems.
  • Searching for optimal gate assemblies could provide another route to better-performing quantum machine learning models.

Error Mitigation.

Quantum machine learning experiments face noise and classical simulation costs, motivating error mitigation and smaller device studies.

  • Few circuit gates can be executed before noise overwhelms the signal on practical qubit devices.
  • Error mitigation and machine learning methods can improve measurement fidelity or learn directly from device-dependent noise.
  • Classical simulation enabled testing up to seven variables or approximately 10,000 training events, but simulation cost grows exponentially with input variables.
  • Because large-qubit simulation remains computationally demanding, smaller circuits can be studied through time-to-solution or complexity scaling.

Optimization in Quantum Machine Learning.

The review frames quantum machine learning in HEP as an exploratory field spanning classical-data methods and future quantum-data applications, with differentiation through quantum computations as a major opportunity.

  • Quantum data: Quantum machine learning could process quantum objects directly, such as photons from sensors, before final measurement.
  • Quantum data: Quantum simulations could be followed on the same device by quantum machine learning that analyzes generated quantum states without costly state tomography.
  • Quantum data: Differentiation through quantum computations can provide partial derivatives of measurement results with respect to physical experiment parameters.
  • Concluding remarks: The reviewed studies are exploratory, and current quantum machine learning performance on HEP data remains limited.
  • Concluding remarks: The review covers quantum annealing, restricted Boltzmann machines, quantum graph networks, and variational quantum circuits for HEP classification.
  • Concluding remarks: Current quantum-circuit machine learning has limited performance because HEP problems must be downscaled for devices or simulations.
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