The possibility of performing quantum chemical calculations using quantum computers has attracted much interest. In this regard, variational quantum deflation (VQD) is a quantum-classical hybrid algorithm for the calculation of excited states with noisy intermediate-scale quantum (NISQ) devices. Although the validity of this method has been demonstrated, there have been few practical applications, primarily because of the uncertain effect of calculation conditions on the results. In the present study, calculations of the core-excited and core-ionized states for common molecules based on the VQD method were simulated using a classical computer, focusing on the effects of the weighting coefficients applied in the penalty terms of the cost function. Adopting a simplified procedure for estimating the weighting coefficients based on molecular orbital levels allowed these core-level states to be successfully calculated. The O 1s core-ionized state for a water molecule was calculated with various weighting coefficients and the resulting ansatz states were systematically examined. The application of this technique to functional materials was demonstrated by calculating the core-level states for titanium dioxide (TiO2) and nitrogen-doped TiO2 models. The results demonstrate that VQD calculations employing an appropriate cost function can be applied to the analysis of functional materials in conjunction with an experimental approach.
The possibility of performing quantum chemical calculations using quantum computers has attracted much interest. In this regard, variational quantum deflation (VQD) is a quantum-classical hybrid algorithm for the calculation of excited states with noisy intermediate-scale quantum (NISQ) devices. Although the validity of this method has been demonstrated, there have been few practical applications, primarily because of the uncertain effect of calculation conditions on the results. In the present study, calculations of the core-excited and core-ionized states for common molecules based on the VQD method were simulated using a classical computer, focusing on the effects of the weighting coefficients applied in the penalty terms of the cost function. Adopting a simplified procedure for estimating the weighting coefficients based on molecular orbital levels allowed these core-level states to be successfully calculated. The O 1s core-ionized state for a water molecule was calculated with various weighting coefficients and the resulting ansatz states were systematically examined. The application of this technique to functional materials was demonstrated by calculating the core-level states for titanium dioxide (TiO2) and nitrogen-doped TiO2 models. The results demonstrate that VQD calculations employing an appropriate cost function can be applied to the analysis of functional materials in conjunction with an experimental approach.
Variational quantum eigensolver (VQE) is an appealing candidate for the application of near-term quantum computers. A technique introduced in [Higgot et al., Quantum 3, 156 (2019)], which is named variational quantum deflation (VQD), has extended the ability of the VQE framework for finding excited states of a Hamiltonian. However, no method to evaluate transition amplitudes between the eigenstates found by the VQD without using any costly Hadamard-test-like circuit has been proposed despite its importance for computing properties of the system such as electronic oscillator strengths of molecules. Here we propose a method to evaluate transition amplitudes between the eigenstates obtained by the VQD avoiding any Hadamard-test-like circuit. Our method relies only on the ability to estimate overlap between two states, so it does not restrict to the VQD eigenstates and applies for general situations. To support the significance of our method, we provide a comparison of three previously proposed methods to find excited states with numerical simulation of three molecules (lithium hydride, diazene, and azobenzene) and find that the VQD method exhibits the best performance among the three methods within the scope of noiseless simulation. Finally, we demonstrate the validity of our method by calculating the oscillator strength of lithium hydride, comparing results from numerical simulations and real-hardware experiments on the cloud enabled quantum computer IBMQ Rome. Our results illustrate the superiority of the VQD to find excited states and widen its applicability to various quantum systems.
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.
Variational Quantum Algorithms (VQAs) are iterative algorithms suited to implementation on current-era quantum devices. VQAs employ classical optimization to minimize cost functions evaluated on quantum circuits. However, the extent to which VQAs manage noise is often insufficient for quantum chemistry applications. One method of improving VQAs is through accurate ansatz initialization. The CAFQA (Clifford Ansatz For Quantum Accuracy) protocol runs a discrete search through a classically simulatable subset of the entire state space to find a desirable initialization. Prior work has evaluated CAFQA applied to the Variational Quantum Eigensolver (VQE), a VQA that computes grounds states of a Hamiltonian. Motivated by CAFQA's success, we propose Excited-CAFQA initialization for Variational Quantum Deflation (VQD), a quantum algorithm that extends VQE by allowing the computation of excited states. VQD recursively computes excited states, by constraining the kth state to be orthogonal to the previous k-1 computed energy states via a penalty term appended to the standard VQE cost function. Just as with VQE, the VQD cost function can be efficiently computed classically for the states considered in the discrete CAFQA search, allowing for the discrete CAFQA optimizer to find good initial parameters for each energy level computation. Preliminary evaluation shows that Excited-CAFQA achieves 90 to 99+% accuracy across a variety of bond lengths and excited states for H2 and HeH+ molecular systems.
Variational quantum eigensolver (VQE) is an appealing candidate for the application of near-term quantum computers. A technique introduced in [Higgot et al., Quantum 3, 156 (2019)], which is named variational quantum deflation (VQD), has extended the ability of the VQE framework for finding excited states of a Hamiltonian. However, no method to evaluate transition amplitudes between the eigenstates found by the VQD without using any costly Hadamard-test-like circuit has been proposed despite its importance for computing properties of the system such as oscillator strengths of molecules. Here we propose a method to evaluate transition amplitudes between the eigenstates obtained by the VQD avoiding any Hadamard-test-like circuit. Our method relies only on the ability to estimate overlap between two states, so it does not restrict to the VQD eigenstates and applies for general situations. To support the significance of our method, we provide a comprehensive comparison of three previously proposed methods to find excited states with numerical simulation of three molecules (lithium hydride, diazene, and azobenzene) in a noiseless situation and find that the VQD method exhibits the best performance among the three methods. Finally, we demonstrate the validity of our method by calculating the oscillator strength of lithium hydride in numerical simulations with shot noise. Our results illustrate the superiority of the VQD to find excited states and widen its applicability to various quantum systems.
The integration of quantum chemistry, machine learning, and optimization calculations is expected to accelerate materials discovery by making large chemical spaces amenable to computational study, a challenging task for classical computers. In this study, we develop a quantum-classical computing scheme involving the computational-basis variational quantum deflation (cVQD) method for calculating the excited states of a general classical Hamiltonian, such as an Ising Hamiltonian. We apply this scheme to the practical use case of generating photochromic diarylethene (DAE) derivatives for photopharmacology applications. Using a dataset of 384 DAE derivatives from quantum chemistry calculation results, we show that machine learning can accurately predict the wavelength of maximum absorbance, λ max , of 4,096 DAE derivatives. After screening over 4,096 molecules using the computing scheme, we identified 5 DAE candidates that have important applications in photopharmacology. In detail, a 12-qubit cVQD calculation provides the ground state and 4 excited states of an Ising Hamiltonian corresponding to DAE candidates possessing large λ max . On a quantum simulator, results are found to be in excellent agreement with those obtained by an exact eigensolver. Utilizing error suppression and mitigation techniques, cVQD on a real quantum device produces results with accuracy comparable to calculations on the simulator. Finally, we show that quantum chemistry calculations for the DAE candidates provides a path to achieving large λ max and oscillator strengths by means of the molecular engineering of DAE derivatives.
Investigating ultrafast electron-nuclear dynamics in molecules requires robust theoretical methods that offer predictive capabilities beyond interpretation purposes. However, the vast number of electronic and nuclear degrees of freedom often prevents an accurate description of chemical systems on classical computers. To address these challenges, hybrid approaches combining quantum and classical computing can leverage the strengths of both to enhance the computational efficiency and fully exploit hardware capabilities. In this work, we perform excited-state molecular dynamics simulations of the formaldimine molecule by combining the surface hopping nonadiabatic molecular dynamics technique with quantum algorithms. We replace conventional electronic energy and overlap calculations with the variational quantum deflation (VQD) algorithm and the Hadamard test, respectively, employing a configuration state function (CSF) spin-restricted ansatz. Finally, we evaluate the accuracy and feasibility of three different gradient calculation approaches integrated with the quantum computing components, demonstrating the advantages of an analytical gradient method over finite difference approaches for hybrid quantum-classical integration.