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arXiv:2203.07219 · AIP Advances

Extending the reach of quantum computing for materials science with machine learning potentials

Julian Schuhmacher, Guglielmo Mazzola, Francesco Tacchino, Olga Dmitriyeva, Tai Bui, Shanshan Huang, Ivano Tavernelli

Published Nov 1, 2022• 17 citations
arXivHTMLPDF

Abstract

Solving electronic structure problems represents a promising field of applications for quantum computers. Currently, much effort is spent in devising and optimizing quantum algorithms for near-term quantum processors, with the aim of outperforming classical counterparts on selected problem instances using limited quantum resources. These methods are still expected to feature a runtime preventing quantum simulations of large scale and bulk systems. In this work, we propose a strategy to extend the scope of quantum computational methods to large scale simulations using a machine learning potential trained on quantum simulation data. The challenge of applying machine learning potentials in today’s quantum setting arises from the several sources of noise affecting the quantum computations of electronic energies and forces. We investigate the trainability of a machine learning potential selecting various sources of noise: statistical, optimization, and hardware noise. Finally, we construct the first machine learning potential from data computed on actual IBM Quantum processors for a hydrogen molecule. This already would allow us to perform arbitrarily long and stable molecular dynamics simulations, outperforming all current quantum approaches to molecular dynamics and structure optimization.

DOI
10.1063/5.0099469

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Solving electronic structure problems represents a promising field of applications for quantum computers. Currently, much effort is spent in devising and optimizing quantum algorithms for near-term quantum processors, with the aim of outperforming classical counterparts on selected problem instances using limited quantum resources. These methods are still expected to feature a runtime preventing quantum simulations of large scale and bulk systems. In this work, we propose a strategy to extend the scope of quantum computational methods to large scale simulations using a machine learning potential trained on quantum simulation data. The challenge of applying machine learning potentials in today’s quantum setting arises from the several sources of noise affecting the quantum computations of electronic energies and forces. We investigate the trainability of a machine learning potential selecting various sources of noise: statistical, optimization, and hardware noise. Finally, we construct the first machine learning potential from data computed on actual IBM Quantum processors for a hydrogen molecule. This already would allow us to perform arbitrarily long and stable molecular dynamics simulations, outperforming all current quantum approaches to molecular dynamics and structure optimization.
Abstract Quantum machine learning algorithms are expected to play a pivotal role in quantum chemistry simulations in the immediate future. One such key application is the training of a quantum neural network to learn the potential energy surface and force field of molecular systems. We address this task by using the quantum extreme learning machine paradigm. This particular supervised learning routine allows for resource-efficient training, consisting of a simple linear regression performed on a classical computer. We have tested a setup that can be used to study molecules of any dimension and is optimized for immediate use on NISQ devices with a limited number of native gates. We have applied this setup to three case studies: lithium hydride, water, and formamide, carrying out both noiseless simulations and actual implementation on IBM quantum hardware. Compared to other supervised learning routines, the proposed setup requires minimal quantum resources, making it feasible for direct implementation on quantum platforms, while still achieving a high level of predictive accuracy compared to simulations. Our encouraging results pave the way towards the future application to more complex molecules, being the proposed setup scalable.
Abstract Accurate molecular force fields are of paramount importance for the efficient implementation of molecular dynamics techniques at large scales. In the last decade, machine learning (ML) methods have demonstrated impressive performances in predicting accurate values for energy and forces when trained on finite size ensembles generated with ab initio techniques. At the same time, quantum computers have recently started to offer new viable computational paradigms to tackle such problems. On the one hand, quantum algorithms may notably be used to extend the reach of electronic structure calculations. On the other hand, quantum ML is also emerging as an alternative and promising path to quantum advantage. Here we follow this second route and establish a direct connection between classical and quantum solutions for learning neural network (NN) potentials. To this end, we design a quantum NN architecture and apply it successfully to different molecules of growing complexity. The quantum models exhibit larger effective dimension with respect to classical counterparts and can reach competitive performances, thus pointing towards potential quantum advantages in natural science applications via quantum ML.
A long-standing goal of science is to accurately solve the Schrödinger equation for large molecular systems. The poor scaling of current quantum chemistry algorithms on classical computers imposes an effective limit of about a few dozen atoms for which we can calculate molecular electronic structure. We present a machine learning (ML) method to break through this scaling limit and make quantum chemistry calculations of very large systems possible. We show that Euclidean Neural Networks can be trained to predict the electron density with high fidelity from limited data. Learning the electron density allows us to train a machine learning model on small systems and make accurate predictions on large ones. We show that this ML electron density model can break through the quantum scaling limit and calculate the electron density of systems of thousands of atoms with quantum accuracy.
The convergence of machine learning (ML) and quantum computing is quickly becoming a game-changing new frontier in computational science. The most intriguing area of overlap may be quantum optimization, which seeks to reduce the exponentially increasing complexity and computational cost of ML algorithms. As they grow larger and more complicated, traditional optimization methods, particularly in high-dimensional and non-convex space, will inevitably hit performance limits. Quantum optimization is the whole new paradigm that leverages quantum mechanical effects like superposition, entanglement, and tunnelling to explore solution spaces more efficiently. The chapter outlines the theory, practice, and potential of hybrid quantum-classical optimization algorithms for machine learning. The most brilliant research direction in the current NISQ (noisy intermediate-scale quantum) era is mixed systems leveraging classical computing capability augmented by quantum capacity. In such designs, computationally intensive subroutines like optimization for global optima or escape from local minima are left to quantum processors and data preprocessing, iterative refinement, and model testing are performed by classical processors. We start by defining the fundamental principles of quantum computing and acquainting readers with the fundamentals like qubits, quantum gates, and quantum circuits. These are the building blocks for quantum algorithms, which hopefully can be utilized for optimization, for example, the QAOA (quantum approximate optimization algorithm), the VQE (variational quantum Eigensolver), and quantum annealing. They all build to optimize the problems in some way differently: QAOA through parameterized quantum circuits, VQE through approximations of ground states of the Hamiltonians, and quantum annealing through quantum evolution to low-energy solutions. We then form a loop between these quantum algorithms and regular machine learning tasks. Optimization impacts virtually all ML phases, from training neural networks, where one reduces loss functions; feature selection, where one aims to discover the most relevant subset of input variables; and hyperparameter optimization, which often involves expensive search procedures over extremely large combinatorial spaces. Quantum optimization techniques can therefore, in principle, accelerate such procedures through computational complexity reduction and enhancing solutions over challenging landscapes. Realistic simulations and case studies emphasize the degree to which hybrid quantum-classical algorithms have been employed in solving ML problems, that is, QSVMs, quantum-enhanced clustering, and quantum reinforcement learning. Despite their experimental nature, these applications already show encouraging results in terms of improved performance metrics as well as reduction in time-to-solution compared to classical-only solutions. Notwithstanding that, this new field is not bereft of real challenges. Quantum hardware suffers from hard limits on qubit fidelity, decoherence, and scalability in the current times. Furthermore, quantum circuit integration into broad ML pipelines requires novel architectures and software platforms. As a counter to those issues, this chapter surveys recent advances in quantum programming languages, simulators, and hybrid platforms like PennyLane, Qiskit, and TensorFlow Quantum. We conclude by looking to the future possibility that quantum optimization will revolutionize the machine learning landscape. As hardware improves and algorithmic complexity increases, the possibility of quantum-powered learning systems solving hard problems becomes increasingly accessible. From speeding up deep network training to enabling new types of unsupervised learning, quantum optimization holds the potential to recast computational tractability in machine learning. This chapter is an all-encompassing introduction and state-of-the-art work for students, researchers, and practitioners interested in using quantum optimization for practical ML applications. It sets the foundation for understanding how to pursue hybrid approaches (how they may be applied today in the real world and bracing oneself for disruption in the future).
Machine learning (ML) has emerged into formidable force for identifying hidden but pertinent patterns within a given data set with the objective of subsequent generation of automated predictive behavior. In the recent years, it is safe to conclude that ML and its close cousin deep learning (DL) have ushered unprecedented developments in all areas of physical sciences especially chemistry. Not only the classical variants of ML , even those trainable on near-term quantum hardwares have been developed with promising outcomes. Such algorithms have revolutionzed material design and performance of photo-voltaics, electronic structure calculations of ground and excited states of correlated matter, computation of force-fields and potential energy surfaces informing chemical reaction dynamics, reactivity inspired rational strategies of drug designing and even classification of phases of matter with accurate identification of emergent criticality. In this review we shall explicate a subset of such topics and delineate the contributions made by both classical and quantum computing enhanced machine learning algorithms over the past few years. We shall not only present a brief overview of the well-known techniques but also highlight their learning strategies using statistical physical insight. The objective of the review is to not only to foster exposition to the aforesaid techniques but also to empower and promote cross-pollination among future-research in all areas of chemistry which can benefit from ML and in turn can potentially accelerate the growth of such algorithms.
The ability to perform ab initio molecular dynamics simulations using potential energies calculated on quantum computers would allow virtually exact dynamics for chemical and biochemical systems, with substantial impacts on the fields of catalysis and biophysics. However, noisy hardware, the costs of computing gradients, and the number of qubits required to simulate large systems present major challenges to realizing the potential of dynamical simulations using quantum hardware. Here, we demonstrate that some of these issues can be mitigated by recent advances in machine learning. By combining transfer learning with techniques for building machine-learned potential energy surfaces, we propose a new path forward for molecular dynamics simulations on quantum hardware. We use transfer learning to reduce the number of energy evaluations that use quantum hardware by first training models on larger, less accurate classical datasets and then refining them on smaller, more accurate quantum datasets. We demonstrate this approach by training machine learning models to predict a molecule's potential energy using Behler-Parrinello neural networks. When successfully trained, the model enables energy gradient predictions necessary for dynamics simulations that cannot be readily obtained directly from quantum hardware. To reduce the quantum resources needed, the model is initially trained with data derived from low-cost techniques, such as Density Functional Theory, and subsequently refined with a smaller dataset obtained from the optimization of the Unitary Coupled Cluster ansatz. We show that this approach significantly reduces the size of the quantum training dataset while capturing the high accuracies needed for quantum chemistry simulations.