Knowledge is power. And the power of knowing about the electronic structure of molecules is invaluable. By knowing the electronic structure of molecules, one can know more about their properties and behaviours, and this would be very useful in fields such as materials design, drug development, semiconductor research, and energy storage.
Further to this, modern researchers are also enamoured with the ground state of a molecule. The ground state of a molecule is its lowest energy state, and it provides important information about the molecule such as its chemical reactivity, relative stability with respect to other molecules, and optimal arrangement of atoms in a molecule. The ground state of a molecule can be computed based on the principles of quantum chemistry. However, the ground state computed using the classical computers is often not accurate.
With the advent of quantum computers, which are built based on the principles of quantum mechanics, researchers are hoping that accurate ground states of molecules can be obtained.
Currently, the quantum computers being used are called ‘noisy intermediate-scale quantum’ (NISQ) computers.
In order to study the electronic structures and ground states of molecules, quantum algorithms are needed. Of all the quantum algorithms for this purpose, ‘variational quantum eigensolver’(VQE) is the most common one used.
However, NISQ computers and the VQE algorithm have many limitations. They cannot be used for larger molecules, and optimizing circuit parameters for these is a daunting task.
One of the main objectives of this work is to perform calculations on real quantum devices. Therefore quantum circuits that are as shallow as possible are required.
There has been a lot of buzz surrounding the implementation of deep neural networks (DNN) with the VQE algorithm to get better results. A DNN model is used to predict the final optimized variational parameters for the quantum circuit.
The DNN-VQE model has been used to simulate small molecules such as hydrogen and lithium hydride, but so far there have been no simulations on real quantum devices.
In this study, the authors Mr. Kalpak Ghosh, Mr. Sumit Kumar, and Prof. Sharma S. R. K. C. Yamijala from the Department of Chemistry, Indian Institute of Technology Madras, Chennai, India (these authors are also affiliated with the Centre for Quantum Information, Communication, and Computing, Indian Institute of Technology Madras, Chennai, India), and Mr. Nirmal Mammavalappil Rajan from TCS Research, Tata Consultancy Services, Mumbai, India, have studied the potential of the DNN-VQE method on NISQ devices.
Two types of DNN models – DNN1 and DNNF were trained.
In the DNN1 approach, the predicted parameters were considered as the final optimized parameters obtained from the VQE algorithm, and the ground state energy was computed directly by using these parameters (i.e., in a single step).
In the DNNF approach, the predicted parameters were taken as the initial guess parameters for the VQE calculation, and the ground state energy was computed after optimizing these parameters.
In conclusion, the potential of DNN-VQE and VQE methods were thoroughly investigated for estimating the ground state energies of molecules on NISQ computers. It was found that the DNN-VQE approach was more accurate than VQE. Amongst all the methods, DNN1 was found to be the best for the current quantum hardware.
The accuracy of the DNN-VQE approaches can be further enhanced by exploring lower-depth ansatzes. Ansatzes are trial wavefunctions used as a starting point for optimizations. These can be used to study larger molecular systems.
Prof. Bryan M. Wong, from the Chemical Environmental Engineering Department, University of California, Riverside, California, United States, gave his analysis and appreciation of the work done by the authors with the following comments: “Quantum computing has recently emerged as a promising approach to accurately predict the electronic structure of molecules and materials. Despite their applicability, the performance of most quantum algorithms is highly dependent on mitigating the noise that is intrinsic to these approaches. This recent paper by Yamijala and co-workers harnessed machine learning algorithms known as deep neural networks (DNNs) to predict the quantum mechanical energies of molecules in the presence of noise. Based on their extensive tests and simulations, the Yamijala group found that one DNN variant, known as DNN1, shows great promise for giving quick and accurate predictions of molecular energies. These impressive results can pave the way for future developments in quantum hardware that could provide both faster and more accurate results.”
Article by Akshay Anantharaman
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