Calculation of Core-Excited and Core-Ionized States Using Variational Quantum Deflation Method and Applications to Photocatalyst Modeling

Abstract

The possibility of performing quantum-chemical calculations using quantum computers has attracted much interest. Variational quantum deflation (VQD) is a quantum-classical hybrid algorithm for the calculation of excited states with noisy intermediate-scale quantum 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 examined 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 (TiO 2 ) and nitrogen-doped TiO 2 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.

Quantum simulation of excited states from parallel contracted quantum eigensolvers

“…Yet, in contrast to many previously published VQE-inspired algorithms (e.g. [10,[13][14][15][16][17]), our CQE algorithms do not identify an energy cost function to be minimized by classical means but a residual that guides the parameters of a unitary towards the ones that transform the input states into the desired set of eigenstates. Moreover, by construction, in CQE the number of variational parameters is fixed by the total number of two-body parameters present in the Hamiltonian which ensures the scalability of the algorithm.…”

“…So far, several quantum algorithms have been developed to approximate eigenstates of many-body Hamiltonians, including quantum phase estimation (QPE) [6,7] and the variational quantum eigensolver (VQE) [8,9]. VQE has also inspired several related approaches for excited states: The two dominant variants rely on either targeting specific states through adding nonorthogonal penalties to the Hamiltonian [10][11][12][13][14] or by building subspaces while ensuring orthogonality of the lowest-lying eigenstates [15,16]. Yet, QPE requires circuit depths beyond what is currently achievable, and VQE relies on high-dimensional classical optimization, which has computational costs that scale rapidly with the system size [17].…”