Stochastic Security as a Performance Metric for Quantum-enhanced Generative AI

TL;DR

The paper investigates whether quantum Gibbs sampling can offer practical advantages for continuous-energy-based models trained on classical data by using diffusion-based Monte Carlo as a classical stand-in. It trains deep EBMs with varying diffusion budgets via persistent contrastive divergence and evaluates the downstream WRN classifier on robustness to adversarial attacks and on calibration via expected calibration error, observing improvements with longer sampling budgets. The authors frame stochastic security as a pragmatic metric for quantifying potential quantum gains and demonstrate that diffusion-based purification improves both robustness and calibration of the classifier. The work provides empirical evidence supporting the potential utility of quantum Gibbs samplers in ML and motivates further resource estimation and hardware development for fault-tolerant quantum computers.

Abstract

Motivated by applications of quantum computers in Gibbs sampling from continuous real-valued functions, we ask whether such algorithms can provide practical advantages for machine learning models trained on classical data and seek measures for quantifying such impacts. In this study, we focus on deep energy-based models (EBM), as they require continuous-domain Gibbs sampling both during training and inference. In lieu of fault-tolerant quantum computers that can execute quantum Gibbs sampling algorithms, we use the Monte Carlo simulation of diffusion processes as a classical alternative. More specifically, we investigate whether long-run persistent chain Monte Carlo simulation of Langevin dynamics improves the quality of the representations achieved by EBMs. We consider a scheme in which the Monte Carlo simulation of a diffusion, whose drift is given by the gradient of the energy function, is used to improve the adversarial robustness and calibration score of an independent classifier network. Our results show that increasing the computational budget of Gibbs sampling in persistent contrastive divergence improves both the calibration and adversarial robustness of the model, suggesting a prospective avenue of quantum advantage for generative AI using future large-scale quantum computers.

Figures (12)

• Figure 1: The oracle for the energy potential. All registers receive float-point representations of real numbers. The first register receives the current model parameters $\theta \in \mathbb R^D$. The second register receives a data sample $x \in \Omega \subseteq \mathbb R^d$. And, the third register is used to evaluate the energy potential.
• Figure 2: The EBM architecture of nijkamp2019learning. The neural network parameterizes a real-valued energy function which defines the energy potential used by the quantum Gibbs sampler.
• Figure 3: The oracle of \ref{['fig:EBM-circuit']} receiving an augmented sample in superposition as the state $\ket{\Psi_x}= \sum_{b \in \{0, 1\}^d}\ket{(-1)^{b_i} \arccos x_i}$.
• Figure 4: Training of an EBM using persistent contrastive divergence (PCD) applied to stochastic gradient Langevin dynamics (SGLD). The use of a replay buffer that retains samples from older shorter runs of Langevin dynamics significantly expedites the training process at the cost of creating some instabilities as shown in \ref{['eq:cd-gradient']}.
• Figure 5: The projected gradient descent (PGD) attack scheme of madry2017towards. We perform white-box PGD attacks on the classifier. We then pass the attacked image through Langevin dynamics of EBMs to purify it from the attack.