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Quantum computing promises a computational advantage over classical methods in electronic-structure calculations, with expected applications in drug design and materials science. Accessing a quantitative description of chemical systems while minimizing quantum resources, such as the number of qubits, is an essential challenge given the limited capabilities of current quantum processors. We provide a shortcut towards quantum computations at chemical accuracy by approaching the complete-basis-set limit (CBS) through integrating density-functional theory into quantum algorithms via density-based basis-set corrections coupled to basis-sets crafted on-the-fly and specifically adapted to a given system/user-defined qubit budget. The approach self-consistently accelerates the basis-set convergence, improving electronic densities, ground-state energies, and first-order properties such as dipole moments. It can also serve as a classical, a posteriori, energy correction to quantum hardware calculations. The strategy is assessed using GPU-accelerated state-vector emulation up to 32 qubits. We converge the ground-state energies of four systems (He, Be, H$_2$, LiH) within chemical accuracy of the CBS full-configuration-interaction reference, while offering a systematic increase of accuracy beyond a double-zeta quality for various molecules up to the H$_8$ hydrogen chain. We also obtain dissociation curves for H$_2$ and LiH that reach the CBS limit whereas for the challenging simulation of the N$_2$ triple-bond breaking, we achieve a near-triple-zeta quality at the cost of a minimal basis-set. This hybrid strategy allows us to obtain quantitative results that would otherwise require brute-force quantum simulations using far more than 100 logical qubits, thereby opening up opportunities to explore real-world chemistry with reasonable computational resources.

We present the first application to real molecular systems of the recently proposed linear-response theory for the density-based basis-set correction method [J. Chem. Phys. 158, 234107 (2023)]. We apply this approach to accelerate the basis-set convergence of excitation energies in the equation-of-motion coupled-cluster singles doubles (EOM-CCSD) method. We use an approximate linear-response framework which neglects the second-order derivative of the basis-set correction density functional and consists in simply adding to the usual Hamiltonian the one-electron potential generated by the first-order derivative of the functional. This additional basis-set correction potential is evaluated at the Hartree-Fock density, leading to a very computationally cheap basis-set correction. We tested this approach over a set of about 30 excitation energies computed for five small molecular systems and found that the excitation energies from the ground state to Rydberg states are the main source of basis-set error. These excitation energies systematically increase when the size of the basis set is increased, suggesting a biased description in favour of the excited state. Despite the simplicity of the present approach, the results obtained with the basis-set corrected EOM-CCSD method are encouraging as they yield to a mean absolute deviation of 0.02 eV for the aug-cc-pVTZ basis set, while it is of 0.04 eV using the standard EOM-CCSD method. This might open the path to an alternative to explicitly correlated approaches to accelerate the basis-set convergence of excitation energies.

The basis-set correction method based on density-functional theory consists in correcting the energy calculated by a wave-function method with a given basis set by a density functional. This basis-set correction density functional incorporates the short-range electron correlation effects missing in the basis set. This results in accelerated basis convergences of ground-state energies to the complete-basis-set limit. In this work, we extend the basis-set correction method to a linear-response formalism for calculating excited-state energies. We give the general linear-response equations, as well as the more specific equations for configuration-interaction wave functions. As a proof of concept, we apply this approach to the calculations of excited-state energies in a one-dimensional two-electron model system with harmonic potential and a Dirac-delta electron-electron interaction. The results obtained with full-configuration-interaction wave functions expanded in a basis of Hermite functions and a local-density-approximation basis-set correction functional show that the present approach does not help in accelerating the basis convergence of excitation energies. However, we show that it significantly accelerates basis convergences of excited-state total energies.

ADAPT-VQE is a robust algorithm for hybrid quantum-classical simulations of quantum chemical systems on near-term quantum computers. While its iterative process systematically reaches the ground state energy, ADAPT-VQE is sensitive to local energy minima, leading to over-parameterized ans\"atze. We introduce the Overlap-ADAPT-VQE to grow wave-functions by maximizing their overlap with any intermediate target wave-function that already captures some electronic correlation. By avoiding building the ansatz in the energy landscape strewn with local minima, the Overlap-ADAPT-VQE produces ultra-compact ans\"atze suitable for high-accuracy initializations of a new ADAPT procedure. Spectacular advantages over ADAPT-VQE are observed for strongly correlated systems including massive savings in circuit depth. Since this compression strategy can also be initialized with accurate Selected-Configuration Interaction (SCI) classical target wave-functions, it paves the way for chemically accurate simulations of larger systems, and strengthens the promise of decisively surpassing classical quantum chemistry through the power of quantum computing.

The present work proposes an approach to obtain a basis-set correction based on density-functional theory (DFT) for the computation of molecular properties in wave-function theory (WFT). This approach allows one to accelerate the basis-set convergence of any energy derivative of a non-variational WFT method, generalizing previous works on the DFT-based basis-set correction where either only ground-state energies could be computed with non-variational wave functions [J. Phys. Chem. Lett. 10, 2931 (2019)] or properties where computed as expectation values over variational wave functions [J. Chem. Phys. 155, 044109 (2021)]. This work focuses on the basis-set correction of dipole moments in coupled-cluster with single, double, and perturbative triple excitations (CCSD(T)), which is numerically tested on a set of fourteen molecules with dipole moments covering two orders of magnitude. As the basis-set correction relies only on Hartree-Fock densities, its computational cost is marginal with respect to the one of the CCSD(T) calculations. Statistical analysis of the numerical results shows a clear improvement of the basis convergence of the dipole moment with respect to the usual CCSD(T) calculations.

We reexamine the recently introduced basis-set correction theory based on density-functional theory consisting in correcting the basis-set incompleteness error of wave-function methods using a density functional. We use a one-dimensional model Hamiltonian with delta-potential interactions which has the advantage of making easier to perform a more systematic analysis than for three-dimensional Coulombic systems while keeping the essence of the slow basis convergence problem of wave-function methods. We provide some mathematical details about the theory and propose a new variant of basis-set correction which has the advantage of being suited to the development of an adapted local-density approximation. We show indeed how to develop a local-density approximation for the basis-set correction functional which is automatically adapted to the basis set employed, without resorting to range-separated density-functional theory as in previous works, but using instead a finite uniform electron gas whose electron-electron interaction is projected on the basis set. The work puts the basis-set correction theory on firmer grounds and provides an interesting strategy for the improvement of this approach.

This work provides a self-consistent extension of the recently proposed density-based basis-set correction method for wave-function electronic-structure calculations [J. Chem. Phys. 149, 194301 (2018)]. In contrast to the previously used approximation where the basis-set correction density functional was a posteriori added to the energy from a wave-function calculation, here the energy minimization is performed including the basis-set correction. Compared to the non-self-consistent approximation, this allows one to lower the total energy and change the wave function under the effect of the basis-set correction. This work addresses two main questions: i) What is the change in total energy compared to the non-self-consistent approximation, and ii) can we obtain better properties, namely dipole moments, with the basis-set corrected wave functions? We implement the present formalism with two different basis-set correction functionals and test it on different molecular systems. The main results of the study are that i) the total energy lowering obtained by the self-consistent approach is extremely small, which justifies the use of the non-self-consistent approximation, and ii) the dipole moments obtained from the basis-set corrected wave functions are improved, being already close to their complete-basis-set values with triple-zeta basis sets. Thus, the present study further confirms the soundness of the density-based basis-set correction scheme.