NN-AE-VQE: Neural network parameter prediction on autoencoded variational quantum eigensolvers

TL;DR

This work tackles the resource bottlenecks of variational quantum eigensolvers by integrating a quantum auto-encoder with a neural-network that predicts latent-space ansatz parameters (NN-AE-VQE). By compressing the quantum state to a smaller latent space and applying a trained PQC, then decoding for evaluation, it significantly reduces circuit depth and parameter count while preserving accuracy. Empirical results on H$_2$ and LiH show chemical-accuracy energy predictions with up to a $98.3\%$ reduction in circuit length, illustrating a promising near-term pathway for quantum-accelerated chemistry. The study also identifies critical QML challenges—such as optimal QAE compression limits and ansatz construction in compressed spaces—and proposes practical strategies, including pipeline scheduling and warm-start training, to guide future scaling to more complex systems.

Abstract

A longstanding computational challenge is the accurate simulation of many-body particle systems. Especially for deriving key characteristics of high-impact but complex systems such as battery materials and high entropy alloys (HEA). While simple models allow for simulations of the required scale, these methods often fail to capture the complex dynamics that determine the characteristics. A long-theorized approach is to use quantum computers for this purpose, which allows for a more efficient encoding of quantum mechanical systems. In recent years, the field of quantum computing has become significantly more mature. Furthermore, the rise in integration of machine learning with quantum computing further pushes to a near-term advantage. In this work we aim to improve the well-established quantum computing method for calculating the inter-atomic potential, the variational quantum eigensolver, by presenting an auto-encoded VQE with neural-network predictions: NN-AE-VQE. We apply a quantum autoencoder for a compressed quantum state representation of the atomic system, to which a naive circuit ansatz is applied. This reduces the number of circuit parameters to optimize, while still minimal reduction in accuracy. Additionally, we train a classical neural network to predict the circuit parameters to avoid computationally expensive parameter optimization. We demonstrate these methods on a H2 molecule, achieving chemical accuracy. We believe this method shows promise of efficiently capturing highly accurate systems while omitting current bottlenecks of variational quantum algorithms. Finally, we explore options for exploiting the algorithm structure and further algorithm improvements.

Figures (12)

• Figure 1: Computational complexity and accuracy trade-off comparison of direct computations (Force fields, DFT, CCSD, machine learning potentials). The computational efficiency of force fields to DFT allow for MD simulations, while the order of CCSD(T) computations are limited to several atoms. Recent work in ML potentials has improved upon this tradeoff, with different models having different strengths (red dots). The goal of using quantum computing is to improve this trade-off, but this has yet to be reached (purple).
• Figure 2: Overview of the VQE compression scheme. As in VQE, the atom description is used for the Hamiltonian to evaluate the expectation value. Instead of simply using a PQC on the full state space, a PQC is applied to a reduced state space to be decoded to the full state space for evaluation. While VQE generally relies on a classical optimizer to find the optimal parameter values of the PQC, we instead train a neural network to predict these values, omitting this costly subroutine.
• Figure 3: Basic structure of a quantum autoencoder (QAE). A quantum state $|\psi\rangle$ is encoded (E), after which the trash (upper) state is traced away, leaving only the encoded state (called latent space). This encoded state is decoded back into its original state space using the decoder gate $D$, of which the top (trash) input state is initialized with $\ket{0}$.Romero_2017
• Figure 4: Circuit of the fully entangled PQC for 4 qubits.
• Figure 5: Using a classical neural network to predict compressed ansatz parameters. A classical optimizer finds optimal values for the ansatz with a pre-trained decoder circuit. The found parameters are then used as training data for the classical neural network.