Yukio Kawashima

Quantum computers (QC) could harbor the potential to significantly advance materials simulations, particularly at the atomistic scale involving strongly correlated fermionic systems where an accurate description of quantum many-body effects scales unfavorably with size. While a full-scale treatment of condensed matter systems with currently available noisy quantum computers remains elusive, quantum embedding schemes like dynamical mean-field theory (DMFT) allow the mapping of an effective, reduced subspace Hamiltonian to available devices to improve the accuracy of ab initio calculations such as density functional theory (DFT). Here, we report on the development of a hybrid quantum-classical DFT+DMFT simulation framework which relies on a quantum impurity solver based on the Lehmann representation of the impurity Green's function. Hardware experiments with up to 14 qubits on the IBM Quantum system are conducted, using advanced error mitigation methods and a novel calibration scheme for an improved zero-noise extrapolation to effectively reduce adverse effects from inherent noise on current quantum devices. We showcase the utility of our quantum DFT+DMFT workflow by assessing the correlation effects on the electronic structure of a real material, Ca2CuO2Cl2, and by carefully benchmarking our quantum results with respect to exact reference solutions and experimental spectroscopy measurements.

Quantum computers have the potential to advance material design and drug discovery by performing costly electronic structure calculations. A critical aspect of this application requires optimizing the limited resources of the quantum hardware. Here, we experimentally demonstrate an end-to-end pipeline that focuses on minimizing quantum resources while maintaining accuracy. Using density matrix embedding theory as a problem decomposition technique, and an ion-trap quantum computer, we simulate a ring of 10 hydrogen atoms without freezing any electrons. The originally 20-qubit system is decomposed into 10 two-qubit problems, making it amenable to currently available hardware. Combining this decomposition with a qubit coupled cluster circuit ansatz, circuit optimization, and density matrix purification, we accurately reproduce the potential energy curve in agreement with the full configuration interaction energy in the minimal basis set. Our experimental results are an early demonstration of the potential for problem decomposition to accurately simulate large molecules on quantum hardware.

The method of increments and frozen natural orbital (MI-FNO) framework is introduced to help expedite the application of noisy, intermediate-scale quantum (NISQ) devices for quantum chemistry simulations. The MI-FNO framework provides a systematic reduction of the occupied and virtual orbital spaces for quantum chemistry simulations. The correlation energies of the resulting increments from the MI-FNO reduction can then be solved by various algorithms, including quantum algorithms such as the phase estimation algorithm and the variational quantum eigensolver (VQE). The unitary coupled-cluster singles and doubles VQE framework is used to obtain correlation energies for the case of small molecules (i.e., BeH₂, CH₄, NH₃, H₂O, and HF) using the cc-pVDZ basis set. The quantum resource requirements are estimated for a constrained geometry complex catalyst that is utilized in industrial settings for the polymerization of α-olefins. We show that the MI-FNO approach provides a significant reduction in the quantum bit (qubit) requirements relative to the full system simulations. We propose that the MI-FNO framework can create scalable examples of quantum chemistry problems that are appropriate for assessing the progress of NISQ devices.

Quantum computers have the potential to perform accurate and efficient electronic structure calculations, enabling the simulation of properties of materials. However, today’s noisy, intermediate-scale quantum (NISQ) devices have a limited number of qubits and gate operations due to the presence of errors. Here, we propose a systematically improvable end-to-end pipeline to alleviate these limitations. Our proposed resource-efficient pipeline combines problem decomposition techniques for compact molecular representations, circuit optimization methods for compilation, solving the eigenvalue problem on advanced quantum hardware, and error-mitigation techniques in post-processing the results. Using the density matrix embedding theory for compact representation, and an ion-trap quantum computer, we simulate a ring of 10 hydrogen atoms taking into account all electrons equally and explicitly in the electronic structure calculation. In our experiment, we simulated the largest molecular system on a quantum computer within chemical accuracy with respect to total molecular energy calculated by the full CI method. Our methods reduce the number of qubits required for high-accuracy quantum simulations by an order of magnitude in the present work, enabling the simulation of larger, more industrially relevant molecules using NISQ devices. They are further systematically improvable as devices’ computational capacity continues to grow.

We have developed a combined quantum mechanics/molecular mechanics (QM/MM) method with periodic boundary condition (PBC) treatment of explicit electron-charge interactions in a theoretically rigorous manner, for an accurate description of electronic structures for molecules in the condensed phase. The Ewald summation technique is employed for the calculation of the one-electron Hamiltonian in an ab initio framework. We decompose the Coulomb interactions into two components: those within the same cell and those between different cells. The former is calculated in the same way as the conventional QM/MM calculation for isolated systems; this article focuses on our novel method for calculating the latter type of Coulomb interactions. The detailed formulation of the Hamiltonian of this new QM/MM-PBC method, as well as the necessary one-electron integrals and their gradients, is given. The novel method is assessed by applying it to the dilute water system and a system with a coumarin molecule in water solvent; it successfully reproduces the electronic energies, frontier orbital energies, and Mulliken population charge of the real-space limit calculated by QM/MM using large isolated systems. We investigated the contribution from each term of the Hamiltonian and found that the surface-dipole term in the Ewald summation technique is indispensable for QM/MM-PBC calculations. The newly developed QM/MM-PBC method is promising for tackling chemical reactions and excited states of molecules in the condensed phase.

Fullerenes are sheets of sp² carbon atoms wrapped around to form spheres. With this simple consideration, we have in the present study devised and (with over 3600 DFT data points) successfully validated a simple model, termed R+D, for estimating the relative energies of fullerenes. This model contains a resonance component to account for the intrinsic differences between the π-energies of different fullerenes, and a deformation component for treating the distortions from planarity. Notably, we find that both terms (and they alone) are required to obtain good relative energies, which lends support to the formulation of the R+D model. An interesting finding is that for some medium-sized IPR fullerenes, their isomers show similar variations in the two components. We deduce that these fullerenes may represent a good opportunity for tuning molecular properties for practical applications. We hope that the promising results of the present study will encourage further investigations into fullerenes from a fundamental perspective.

We apply ab initio path integral molecular dynamics simulation employing ωB97XD as the quantum chemical calculation method to acetic acid–arsenic acid anion and acetic acid–phosphoric acid anion clusters to investigate the difference of the hydrogen bond structure and its fluctuation such as proton transfer. We found that the nuclear quantum effect enhanced the fluctuation of the hydrogen bond structure and proton transfer, which shows treatment of the nuclear quantum effect was essential to investigate these systems. The hydrogen bond in acetic acid–arsenic acid anion cluster showed characters related to low‐barrier hydrogen bonds, while acetic acid–phosphoric acid anion cluster did not. We found non‐negligible distinction between these two systems, which could not be found in conventional calculations. We suggest that the difference in amount of atomic charge of the atoms consisting the hydrogen bond is the origin of the difference between acetic acid–arsenic acid and acetic acid–phosphoric acid anion cluster.

In the present study, we have reparametrized the HISS exchange functional. The new “reHISS” exchange provides a balance between short‐ and mid‐range Hartree–Fock exchange (HFX) and a large total HFX coverage, with a fast convergence to zero HFX in the long range. The five parameters in this functional (according to equations 3 and 4 in the main text) are c_SR = 0.15, c_MR = 2.5279, c_LR = 0, ω_SR = 0.27, and ω_LR = 0.2192. The combination of reHISS exchange with a reparametrized B97c‐type correlation functional (Chan et al., J. Comput. Chem. 2017, 38, 2307) and a D2 dispersion term (s₆ = 0.6) gives the reHISSB‐D method. We find it to be more accurate than related screened‐exchange methods and, importantly, its accuracy is more uniform across different properties. Fundamentally, our analysis suggests that the good performance of the reHISS exchange is related to it capturing a near‐optimal proportion of HFX in the range of interelectronic distance that is important for many chemical properties, and we propose this range to be approximately 1–4Å.