Abstract Quantum computing in the noisy intermediate-scale quantum (NISQ) era has foregrounded the importance of Variational Quantum algorithms (VQAs). These algorithms are crucial for addressing complex quantum mechanical problems that challenge classical computers. One such problem is the electron-phonon (e-ph) interaction, which is essential for determining the zero-point renormalization (ZPR) of electronic structure properties. The calculation of ZPR of fundamental gap relies on the accurate computation of ionization potential (IP) and electron affinity (EA) energy levels in molecular systems, where the VQAs offer the promising solutions. Despite the critical importance of IP, EA energies and ZPR in quantum chemistry calculations, research into the application of quantum algorithms for these calculations remains limited. To address these challenges, we propose two quantum algorithms for ZPR of fundamental gap calculation using Variational Quantum Deflation (VQD) and Quantum equation of Motion (QEOM) algorithm for several molecular systems. This work opens up new possibilities for the accurate and efficient study of e-ph interaction in electronic structure calculations, even with NISQ-era hardware.
Abstract Quantum computing in the noisy intermediate-scale quantum (NISQ) era has foregrounded the importance of Variational Quantum algorithms (VQAs). These algorithms are crucial for addressing complex quantum mechanical problems that challenge classical computers. One such problem is the electron-phonon (e-ph) interaction, which is essential for determining the zero-point renormalization (ZPR) of electronic structure properties. The calculation of ZPR of fundamental gap relies on the accurate computation of ionization potential (IP) and electron affinity (EA) energy levels in molecular systems, where the VQAs offer the promising solutions. Despite the critical importance of IP, EA energies and ZPR in quantum chemistry calculations, research into the application of quantum algorithms for these calculations remains limited. To address these challenges, we propose two quantum algorithms for ZPR of fundamental gap calculation using Variational Quantum Deflation (VQD) and Quantum equation of Motion (QEOM) algorithm for several molecular systems. This work opens up new possibilities for the accurate and efficient study of e-ph interaction in electronic structure calculations, even with NISQ-era hardware.
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 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.
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.
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.
In this work, we present a comprehensive comparative study between two different Ansatz quantum circuits , specifically the Unitary Vibrational Coupled Cluster (UVCC) and the Compact Heuristic Circuit (CHC) with use in computational chemistry . By incorporating these circuits into the Variational Quantum Eigensolver (VQE), we aim to find the vibrational ground state energy of small molecules. Our results, obtained using both the UVCC and CHC ansatzes with and without quantum hardware noise, are benchmarked against classical computational methods for energy state determination. We emphasize the efficiency and accuracy of the CHC Ansatz , which significantly reduces circuit complexity without sacrificing the fidelity of the results. This characteristic demonstrates the potential of the CHC Ansatz for scalable quantum chemistry applications, particularly in the Noisy Intermediate-Scale Quantum (NISQ) era. Furthermore, we employ the CHC Ansatz in conjunction with the Variational Quantum Deflation (VQD) algorithm to determine the excited vibrational state energies, which is compared against the reliable method of quantum Equation of Motion(qEOM). Through this comparative study, we aim to provide valuable insights into the practical applications of these Ansatz in quantum simulations of molecular systems, highlighting their respective advantages and potential for future quantum chemistry research.
Ab initio molecular dynamics (AIMD) is a valuable technique for studying molecules and materials at finite temperatures where the nuclei evolve on potential energy surfaces obtained from accurate electronic structure calculations. In this work, we present an approach to running AIMD simulations on noisy intermediate-scale quantum (NISQ)-era quantum computers. The electronic energies are calculated on a quantum computer using the variational quantum eigensolver (VQE) method. Algorithms for computation of analytical gradients entirely on a quantum computer require quantum fault-tolerant hardware, which is beyond NISQ-era. Therefore, we compute the energy gradients numerically using finite differences, the Hellmann–Feynman theorem, and a correlated sampling technique. This method only requires additional classical calculations of electron integrals for each degree of freedom without any additional computations on a quantum computer beyond the initial VQE run. As a proof of concept, AIMD simulations are demonstrated for the H2 molecule on IBM quantum devices. In addition, we demonstrate the validity of the method for larger molecules using full configuration interaction wave functions. As quantum hardware and noise mitigation techniques continue to improve, the method can be utilized for studying larger molecular systems.