# Data Efficient Prediction of excited-state properties using Quantum Neural Networks

arXiv: https://arxiv.org/abs/2412.09423 · HTML: https://mlsanity.com/paper/2412.09423/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 43 references that are in the map.
- First posted on arXiv 12 Dec 2024.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Better than classical? The subtle art of benchmarking quantum machine learning models](https://mlsanity.com/paper/2403.07059/) (2024)
- [Exploiting symmetry in variational quantum machine learning](https://mlsanity.com/paper/2205.06217/) (2022)
- [Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.09974/) (2022)
- [Quantum Convolutional Neural Networks are Effectively Classically Simulable](https://mlsanity.com/paper/2408.12739/) (2024)
- [Reduction of finite sampling noise in quantum neural networks](https://mlsanity.com/paper/2306.01639/) (2023)
- [Symmetry-invariant quantum machine learning force fields](https://mlsanity.com/paper/2311.11362/) (2023)

## Built on by (most cited first, 1 of 1)

- [Quantum Machine Unlearning: Foundations, Mechanisms, and Taxonomy](https://mlsanity.com/paper/2511.00406/) (2025)

## Abstract (arXiv)

Understanding the properties of excited states of complex molecules is crucial for many chemical and physical processes. Calculating these properties is often significantly more resource-intensive than calculating their ground state counterparts. We present a quantum machine learning model that predicts excited-state properties from the molecular ground state for different geometric configurations. The model comprises a symmetry-invariant quantum neural network and a conventional neural network and is able to provide accurate predictions with only a few training data points. The proposed procedure is fully NISQ compatible. This is achieved by using a quantum circuit that requires a number of parameters linearly proportional to the number of molecular orbitals, along with a parameterized measurement observable, thereby reducing the number of necessary measurements. We benchmark the algorithm on three different molecules with three different system sizes: H2 with four orbitals, LiH with five orbitals, and H4 with six orbitals. For these molecules, we predict the excited state transition energies and transition dipole moments. We show that, in many cases, the procedure is able to outperform various classical models (support vector machines, Gaussian processes, and neural networks) that rely solely on classical features, by up to two orders of magnitude in the test mean squared error.