Zephyr quantum-assisted hierarchical Calo4pQVAE for particle-calorimeter interactions

TL;DR

High-energy physics HL-LHC simulations with Geant4 are computationally expensive. The paper proposes Zephyr quantum-assisted hierarchical Calo4pQVAE, a VAE with a 4-partite energy-conditioned RBM prior aligned to D-Wave Zephyr topology to accelerate particle-calorimeter shower generation. The authors evaluate on CaloChallenge Dataset 2, demonstrating competitive fidelity relative to baselines while achieving substantial speed-ups through quantum sampling. The work demonstrates the viability of hybrid classical-quantum priors for large-scale generative modeling in HEP and suggests directions for improving connectivity and attention mechanisms to further close the gap with the best-performing methods.

Abstract

With the approach of the High Luminosity Large Hadron Collider (HL-LHC) era set to begin particle collisions by the end of this decade, it is evident that the computational demands of traditional collision simulation methods are becoming increasingly unsustainable. Existing approaches, which rely heavily on first-principles Monte Carlo simulations for modeling event showers in calorimeters, are projected to require millions of CPU-years annually -- far exceeding current computational capacities. This bottleneck presents an exciting opportunity for advancements in computational physics by integrating deep generative models with quantum simulations. We propose a quantum-assisted hierarchical deep generative surrogate founded on a variational autoencoder (VAE) in combination with an energy conditioned restricted Boltzmann machine (RBM) embedded in the model's latent space as a prior. By mapping the topology of D-Wave's Zephyr quantum annealer (QA) into the nodes and couplings of a 4-partite RBM, we leverage quantum simulation to accelerate our shower generation times significantly. To evaluate our framework, we use Dataset 2 of the CaloChallenge 2022. Through the integration of classical computation and quantum simulation, this hybrid framework paves way for utilizing large-scale quantum simulations as priors in deep generative models.

Figures (5)

• Figure 1: (a) Calochallenge dataset showers are voxelized using cylindrical coordinates $(r,\varphi,z)$. For any given event, each voxel value corresponds to the energy (MeV) in that vicinity. Each layer has 144 voxels composed of $16$ angular bins and $9$ radial bins. The data set is parsed onto a 1D vector with $6480$ voxels per each event. (b) Visualization of the voxels in an event in the dataset.
• Figure 2: (a) Overview of Calo4pQVAE training architecture. Preprocessed voxels of a shower, $x$ and their corresponding incident energies, $e$ are inputted to the encoder. The encoder compresses the energy-conditioned shower into 4 partitions, of which 3 are generated from the hierarchies of the encoders and 1 is an encoded conditioning of the incident energy. The conditioned RBM is trained to learn these representations, then the concatenation of the 4 partitions is the latent vector that gets passed through the hierarchical decoder, generating a hits and activations vector to reconstruct the shower. (b) Once the model finishes training classically, the states of the trained RBM with an incidence energy conditioning is loaded onto D-Wave's Zephyr quantum annealer to sample a latent vector that is then passed through the hierarchical decoder to generate a shower. (c) The hierarchical decoder consists of 9 sub-decoders, each generating 5 layers to make up a total of 45 layers and conditions subsequent layers of the shower based on previous layers to simulate the physical propagation of particle scattering in the calorimeter through the evolution of the shower.
• Figure 3: (a) Saturation of RBM log-likelihood vs epochs. Yellow star - freezing of encoder and decoder, Red star - completion of model training. (b) QA inverse temperature estimation vs iterations. (c) RBM energy histogram for classical and QA samples.
• Figure 4: Normalized histograms comparing Geant4 simulated data (ground truth) and Calo4pQVAE's reconstruction, classically sampled synthetic data, and quantum annealed (Zeyphr) synthetic data for 10k events in: (a) sparsity index, ratio of non-hit voxels over all voxels in a shower, (b) energy per event, sum of all voxel energies in a shower, and (c) granularity, randomly shifted differences in voxel energies along angular and radial bins in a shower.
• Figure 5: Solid vs dotted line plots comparing Geant4 simulated data and classical Calo4pQVAE's classically sampled synthetic data for 100k events. (a) Mean energy deposit per layer, (b) angular and (c) radial bin. Relative and absolute errors for each parameter are shown underneath each plot, respectively.