Data Efficient Prediction of excited-state properties using Quantum Neural Networks (2412.09423v2)

Abstract: 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: $H_2$ with four orbitals, LiH with five orbitals, and $H_4$ 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.

• The paper introduces a hybrid quantum-classical neural network model that efficiently predicts molecular excited-state properties by leveraging limited ground-state data.
• Validated on LiH, H_2, and H_4, the model showed superior performance in low-data scenarios compared to classical methods, proving quantum features enhance prediction.
• This approach enables data-efficient excited-state property calculation, offering a promising path to scale up for larger, more complex molecular systems.

Data Efficient Prediction of Excited-State Properties Using Quantum Neural Networks

In the pursuit to efficiently compute excited-state properties of complex molecules, the paper titled "Data Efficient Prediction of Excited-State Properties using Quantum Neural Networks" presents a compelling methodology tied to quantum machine learning (QML). The inherent challenges with excited-state calculations, such as their higher computational cost compared to ground states, are meaningfully addressed through the novel integration of quantum neural networks (QNNs).

Summary and Methodology

The paper introduces and implements a QML model that distinctively merges a symmetry-invariant quantum neural network with a classical neural network (NN) to predict excited-state properties by leveraging molecular ground-state data. This dual-component architecture allows the model to efficiently calculate properties such as transition energies and transition dipole moments (TDMs) using a reduced set of training data, marking a significant reduction in computational resource requirements.

Essentially, the proposed QML framework operates within the realms of noise-intermediate-scale quantum (NISQ) devices, employing a sparse quantum circuit wherein the parameter count scales linearly with the number of molecular orbitals. By configuring the measurement observable solely with Pauli-$Z$ operators, the approach mitigates the overhead associated with non-commuting measurements, optimizing execution on existing quantum hardware.

Implementation

The implementation employs the Jordan-Wigner transformation to convert the fermionic Hamiltonian of the molecular system into a qubit Hamiltonian, making it suitable for quantum computation. The QNN's structure is inspired by quantum convolutional neural networks, which are noted for their efficient parametric scaling and avoidance of barren plateaus, thus enhancing training efficacy. Furthermore, the QNN exploits a symmetry that maintains invariance under electron exchanges, which aligns with the molecular orbital configuration.

A two-stage training regime refines the model, where a preliminary training of the QNN parameters is followed by an end-to-end tuning of the entire framework incorporating the classical NN component. This strategy facilitates pathfinding within the optimization landscape that suits the combined QML model’s capabilities and complexities.

Results

The researchers validated their approach using detailed benchmarks on three molecules: LiH, $\mathrm{H}_2$, and $\mathrm{H}_4$, under various molecular configurations. The model demonstrated superior performance in numerous scenarios, especially in low-data regimes, compared to traditional classical models like support vector regressors and Gaussian process regressors. The QML-based model excelled in capturing the complexity of excited-state behaviors using less data, thereby proving the hypothesis that quantum computational features can significantly enhance model performance for quantum chemistry applications.

Implications and Future Work

The implications of this research extend far into both the theoretical and practical arenas of quantum computing and machine learning in chemistry. By illustrating a sophisticated QML integration that balances quantum and classical resources, this work lays groundwork for upscaling towards larger, more complex molecular systems, potentially reshaping how excited-state properties are predicted. Moreover, the paper’s methodology holds promise for adaptation to other quantum systems where excited-state properties are vital.

Looking forward, further refinement in quantum circuit efficiency and exploration of the model's adaptability to different quantum algorithms may fortify its applicability in real-world chemical simulations. Addressing the classical simulatability of models akin to the presented QNN remains a compelling area of exploration, as does the broader application across diverse quantum systems where intricate state properties need intuitive quantification.

In conclusion, the outlined paper vividly demonstrates how quantum neural networks, intertwined with classical approaches, underpin evolving methodologies in computational chemistry—pointing towards a future enriched with precise, resource-efficient molecular simulations.