Quantum Learning Revolutionizes Molecular Simulations

By Muhammad OsamaReviewed by Susha Cheriyedath, M.Sc.Jul 29 2024

A recent study published in the journal Machine Learning: Science and Technology, explored how quantum machine learning (QML) algorithms could be used to simulate the potential energy surfaces (PES) and force fields (FF) of molecular systems. The researchers proposed a quantum extreme learning machine (QELM) paradigm that enables resource-efficient training and accurate predictions.

Background

QML is an emerging field that combines quantum computing and ML techniques to address problems that are challenging or infeasible for classical computers. A promising application of QML is quantum chemistry, which simulates the properties and dynamics of molecules and materials using quantum mechanics. However, these simulations are often computationally demanding and require high accuracy and precision.

One key challenge in quantum chemistry simulations is determining the PES and FF of a molecular system. These describe how energy and interatomic forces vary with molecular geometry, essential for molecular dynamics (MD) simulations that reveal the structure, function, and reactivity of molecules. However, computing the PES and FF on the fly using methods like density functional theory (DFT) is costly and limits the size and time of the simulations.

About the Research

In this paper, the authors introduced a novel QML method to learn the PES and FF of molecular systems from a small set of training data, consisting of molecular geometries and their corresponding energies and forces computed classically. Their method is based on the QELM paradigm, a supervised learning model with two stages: a quantum encoding stage and a classical linear regression stage.

In the quantum encoding stage, the classical input data (molecular coordinates) are mapped to a quantum state of input qubits using a parameterized unitary transformation. A measurement is then performed on the input qubits, resulting in a probability vector that encodes the input data. In the classical linear regression stage, the output data (molecular energy and forces) are obtained by multiplying the probability vector by a weight matrix, optimized to fit the training data.

The QELM has several advantages over other QML methods, such as the variational quantum eigensolver (VQE), also used for PES and FF learning. QELM does not require optimization of parameters in the quantum circuit, reducing quantum resources and noise sensitivity. It also allows simple and efficient implementation on different quantum platforms, such as gate-based or continuous-variable devices.

The researchers proposed a specific QELM setup adaptable to molecules of any dimension, optimized for noisy intermediate-scale quantum (NISQ) devices with a limited number of native gates. They used a Fourier encoding scheme to map the molecular coordinates to the quantum state and a reservoir technique to generate an informationally complete measurement of the input qubits. They also used a generator operator that minimizes circuit depth and maximizes model expressivity.

Research Findings

The authors tested their QELM setup on three case studies: lithium hydride, water, and formamide, which represented molecules of increasing complexity and relevance for quantum chemistry. They generated datasets for each molecule using standard quantum chemistry routines, such as DFT or the Hartree-Fock (HF) approximation and then trained the QELM on a subset of the data. Additionally, they evaluated QELM performance on a separate test set using the root mean square error (RMSE) metric.

Noiseless simulations of QELM, assuming infinite statistics, showed that QELM achieved high predictive accuracy for both energy and forces, well below typical dataset fluctuations. Accuracy improved as the number of encoding qubits increased, and QELM outperformed VQE in terms of both RMSE and quantum resources.

Furthermore, simulations of QELM with finite statistics were performed using the QASM simulator of the Qiskit package. The researchers found that RMSE increased due to statistical error but remained of the same order of magnitude as in the noiseless case. They also implemented QELM on the IBM BRISBANE quantum device, a superconducting transmon processor with 127 qubits, and found that noise did not significantly affect performance, with QELM predictions in good agreement with classical calculations.

Applications

The newly proposed technique has potential implications for quantum chemistry simulations, especially for ab initio MD simulations that require on-the-fly calculations of the PES and FF of molecular systems. It can provide fast and accurate predictions of these quantities, using minimal quantum resources and classical post-processing.

The technique can also be applied to more complex molecules, as the setup is scalable and adaptable to any number of atoms and degrees of freedom. It can be implemented on different quantum platforms, such as trapped-ion or photonic devices, by changing the native gates.

Conclusion

In summary, the novel methodology proved effective, feasible, and accurate for learning the PES and FF of molecular systems on IBM quantum hardware. It showed advantages over other QML methods, such as VQE, in terms of quantum resources, noise sensitivity, and implementation flexibility. It could accelerate ab initio MD simulations and explore the quantum nature of molecular systems.

Moving forward, the authors suggested applying the QELM to more complicated molecules, studying the effect of different encoding and measurement schemes, and developing efficient methods to overcome the limitations of finite statistics.