Modeling stochastic eye tracking data: A comparison of quantum generative adversarial networks and Markov models

TL;DR

The study compares quantum generative models (QGANs) with classical Markov-chain models for modeling stochastic eye-tracking velocity data. It introduces a hybrid quantum-classical QGAN with a variational quantum circuit generator on $N$ qubits and a classical LSTM discriminator, trained via adversarial losses $L_G$ and $L_D$, and evaluated using Jensen-Shannon divergence. Across experiments with 3- and 4-qubit configurations, Markov models consistently achieve lower $D_{JS}$ than QGANs, though increasing qubit count and depth improves the quantum model's fit. The results underscore the potential of quantum approaches for time-series generation while highlighting current limitations and the need for further quantum algorithm development to surpass traditional Markov benchmarks.

Abstract

We explore the use of quantum generative adversarial networks QGANs for modeling eye movement velocity data. We assess whether the advanced computational capabilities of QGANs can enhance the modeling of complex stochastic distribution beyond the traditional mathematical models, particularly the Markov model. The findings indicate that while QGANs demonstrate potential in approximating complex distributions, the Markov model consistently outperforms in accurately replicating the real data distribution. This comparison underlines the challenges and avenues for refinement in time series data generation using quantum computing techniques. It emphasizes the need for further optimization of quantum models to better align with real-world data characteristics.

Figures (4)

• Figure 1: Generative adversarial network models workflow: the generator generates data samples ($g_t$) to imitate the real-world data and tries to fool the discriminator. The discriminator differentiates the generated and the training data samples by training both the generator and discriminator alternatively until the loss converges towards the Nash equilibrium.
• Figure 2: The quantum generator circuit in variational form with $L$ layers acting on $n$ qubits. Each layer in the circuit is composed of single qubit rotation gates ($R_Z, R_Y$) and two-qubit controlled-phase gates.
• Figure 3: Comparative histograms of log-transformed real and generated eye movement velocity data across different circuit layers (1 - 5) for three and four-qubit QGAN. Each subplot illustrates the distribution of real data (in blue) with the corresponding generated data (in magenta) at respective circuit layers. The use of log transformation ensures a focus on the distribution's dynamics rather than its absolute scale to facilitate a clearer understanding of the model's performance across varying complexities.
• Figure 4: Comparative histograms of log-transformed eye movement velocities: real versus Markov model.