Over the last decade, researchers have been working to improve a crucial aspect of quantum computing to predict Hamiltonian energy of solids. Quantum algorithms such as Variational Quantum Eigensolver (VQE) and Variational Quantum Deflation (VQD) have been used to study the molecular systems. However, there is growing interest in adapting and applying these methods to periodic solid-state materials. In this work, we have integrated first-principles density functional theory with VQE and VQD algorithms and utilizing the Wannier Tight-Binding Hamiltonian (WTBH) method to predict the electronic characteristics of solids. We demonstrate that VQE and VQD algorithms can be used to accurately predict electronic characteristics in a variety of multi-component prototype solid-state materials such as - Silicon (semiconductor), Gold (metallic), Boron Nitrile (insulator), Graphene (semi-metal). Efficient SU2 performs well among all the predefined ansatz used in the study. COBYLA is the fastest optimizer among the classical optimizers with minimum number of iterations for convergence. Results of noise models help to understand the band structure when calculated on real quantum hardware. As quantum hardware advances, our method might be a starting point for using quantum computers to study materials and could help make material discovery more automatic in the future.
Over the last decade, researchers have been working to improve a crucial aspect of quantum computing to predict Hamiltonian energy of solids. Quantum algorithms such as Variational Quantum Eigensolver (VQE) and Variational Quantum Deflation (VQD) have been used to study the molecular systems. However, there is growing interest in adapting and applying these methods to periodic solid-state materials. In this work, we have integrated first-principles density functional theory with VQE and VQD algorithms and utilizing the Wannier Tight-Binding Hamiltonian (WTBH) method to predict the electronic characteristics of solids. We demonstrate that VQE and VQD algorithms can be used to accurately predict electronic characteristics in a variety of multi-component prototype solid-state materials such as - Silicon (semiconductor), Gold (metallic), Boron Nitrile (insulator), Graphene (semi-metal). Efficient SU2 performs well among all the predefined ansatz used in the study. COBYLA is the fastest optimizer among the classical optimizers with minimum number of iterations for convergence. Results of noise models help to understand the band structure when calculated on real quantum hardware. As quantum hardware advances, our method might be a starting point for using quantum computers to study materials and could help make material discovery more automatic in the future.
Quantum chemistry is one of the most promising near-term applications of quantum computers. Quantum algorithms such as variational quantum eigen solver (VQE) and variational quantum deflation (VQD) algorithms have been mainly applied for molecular systems and there is a need to implement such methods for periodic solids. Using Wannier tight-binding Hamiltonian (WTBH) approaches, we demonstrate the application of VQE and VQD to accurately predict both electronic and phonon bandstructure properties of several elemental as well as multi-component solid-state materials. We apply VQE-VQD calculations for 307 spin-orbit coupling based electronic WTBHs and 933 finite-difference based phonon WTBHs. We establish a workflow for using VQD with lattice Greens function that can be used for solving dynamical mean-field theory problems. The WTBH model solvers can be used for testing other quantum algorithms also.
Quantum chemistry is one of the most promising near-term applications of quantum computers. Quantum algorithms such as variational quantum eigen solver (VQE) and variational quantum deflation (VQD) algorithms have been mainly applied for molecular systems and there is a need to implement such methods for periodic solids. Using Wannier tight-binding Hamiltonian (WTBH) approaches, we demonstrate the application of VQE and VQD to accurately predict both electronic and phonon bandstructure properties of several elemental as well as multi-component solid-state materials. We apply VQE-VQD calculations for 307 spin-orbit coupling based electronic WTBHs and 933 finite-difference based phonon WTBHs. Also, we discuss a workflow for using VQD with lattice Green's function that can be used for solving dynamical mean-field theory problems. The WTBH model solvers can be used for testing other quantum algorithms and models also.
Abstract Variational Quantum Eigensolver (VQE) and its extension, Variational Quantum Deflation (VQD), have emerged as promising algorithms for computing ground and excited state energy eigenvalues of Hamiltonians, particularly in quantum physics, chemistry, and materials science. Recently, the VQE and VQD algorithms were implemented to calculate the electronic band structure described by the tight-binding Hamiltonian. Despite their success for simple models, scalability remains a challenge due to the need for a large number of circuit executions, limited qubit coherence times, and low gate fidelities. In this work, we implemented the VQE and VQD algorithms for tight-binding models of diamond and zincblende crystal structures (Sn, C, Si, Ge, AlP, AlAs, AlSb, and GaP) using a quantum computer simulator. We investigate the scalability challenges, focusing on the significant overhead caused by a large number of quantum circuit executions required to find the energy eigenvalues. Our analysis highlights the substantial amount of both measurement and optimization overheads in VQD, particularly as the number of excited states increases. Based on our findings, we critically discuss the implications of implementing VQD on current noisy intermediate-scale quantum (NISQ) devices.
Quantum computing is currently emerging as a useful paradigm for solving highly complex computational problems.Current quantum computers are unfortunately too noisy to provide sufficient accuracy, and quantumclassical hybrid algorithms emerged as a solution.Variational Quantum Deflation (VQD) has gained significant attention for addressing challenges in quantum chemistry, material science, etc. VQDs typically use multiple optimization methods, and the correct choice of optimization method can significantly impact performance.In our study, we focused on the comparison of multiple optimization methods used in VQD when applied to the electronic structure of crystals.The quantum part of VQD ran on a classical simulator with imported noise models from real quantum computers from the IBM Quantum Platform.
Variational Quantum Algorithms (VQAs) provide a promising framework for solving electronic structure problems using the computational capabilities of quantum computers to explore high-dimensional Hilbert spaces efficiently. This research investigates the performance of VQAs in electronic structure calculations of gallium arsenide (GaAs), a semiconductor with a zinc-blende structure. Utilizing a tight-binding Hamiltonian and a Jordan-Wigner-like transformation, we map the problem to a 10-qubit Hamiltonian. We analyze the impact of quantum circuit architectures, algorithm hyperparameters, and optimization methods on two VQAs: Variational Quantum Deflation (VQD) and Subspace Search Variational Quantum Eigensolver (SSVQE). We observed that while both algorithms offer promising results, the choice of ansatz and hyperparameter tuning were especially critical in achieving reliable outcomes, particularly for higher energy states. Adjusting the hyperparameters in VQD significantly enhanced the accuracy of higher energy state calculations, reducing the error by an order of magnitude, whereas tuning the hyperparameters in SSVQE had minimal impact. Our findings provide insights into optimizing VQAs for electronic structure problems, paving the way for their application to more complex systems on near-term quantum devices.
Abstract Variational quantum algorithms such as the variational quantum eigensolver (VQE) and variational quantum deflation (VQD) have emerged as leading candidates for computing electronic structure on near-term quantum hardware. For periodic solids, however, their reach has been limited not by the quantum algorithm itself but by the cost of constructing a faithful second-quantized Hamiltonian for each material, typically via density-functional theory (DFT) followed by Wannierization or by hand-fitted empirical tight-binding parameters. SlaKoNet, a recently developed method, significantly reduces the computational cost of electronic Hamiltonian construction with a small accuracy tradeoff. It integrates modern deep-learning methods and the Slater-Koster tight-binding formalism to fit thousands of onsite and distance-dependent hopping and overlap tight-binding parameters across 65 elements of the periodic table. After fitting, these parameters can be used to deterministically construct an electronic Hamiltonian for any crystal made up of any of the 65 elements in the training set, and the crystal's band structure can subsequently be computed. In this work, we combine a SlaKoNet model trained on the JARVIS-TBmBJ dataset with a Qiskit-based variational quantum deflation algorithm, replacing the traditional and costly Hamiltonian construction step with a universal neural Hamiltonian generator. Within the 65-element set, the resulting SlaKoNet-VQD workflow is structure-agnostic, fully differentiable, fast, and suited to high-throughput screening of band structures. We benchmark the workflow on silicon, recovering the full eight-band band structure along the standard high-symmetry k-path with a mean absolute deviation of 1.78 meV from exact diagonalization on a 3-qubit statevector simulator. We further compute the full band structure for five additional conventional superconductors, Al, Ta, Nb, V, and ZrN, achieving a mean absolute deviation within approximately 1.8 meV, and demonstrate full execution of SlaKoNet-VQD on IBM Quantum hardware for a representative k-point ground-state calculation on aluminum with a mean absolute error of roughly 0.37 eV. Beyond the single-particle level, we promote the same SlaKoNet Hamiltonian to a correlated Hubbard model and solve it with dynamical mean-field theory, recovering the weakening of correlations across the group-5 metals and strong quasiparticle renormalization in the cuprate La₂CuO₄, and we identify the resulting impurity problem as the natural target for a quantum solver. The pipeline opens a path to high-throughput benchmarking of variational quantum algorithms across the periodic table and to gradient-based co-optimization of ansatz and Hamiltonian for materials discovery. An interactive web app is available at https://atomgpt.org/quantum.