Toward Chemical Accuracy with Shallow Quantum Circuits: A Clifford-Based Hamiltonian Engineering Approach.

Achieving chemical accuracy with shallow quantum circuits is a significant challenge in quantum computational chemistry, particularly for near-term quantum devices. In this work, we present a Clifford-based Hamiltonian engineering algorithm, namely CHEM, that addresses the trade-off between circuit depth and accuracy. Based on a variational quantum eigensolver and hardware-efficient ansatz, our method designs the Clifford-based Hamiltonian transformation that (1) ensures a set of initial circuit parameters corresponding to the Hartree-Fock energy can be generated, (2) effectively maximizes the initial energy gradient with respect to circuit parameters, (3) imposes negligible overhead for classical processing and does not require additional quantum resources, and (4) is compatible with any circuit topology. We demonstrate the efficacy of our approach using a quantum hardware emulator, achieving chemical accuracy for systems as large as 12 qubits with fewer than 30 two-qubit gates. Our Clifford-based Hamiltonian engineering approach offers a promising avenue for practical quantum computational chemistry on near-term quantum devices.

TenCirChem: An Efficient Quantum Computational Chemistry Package for the NISQ Era.

TenCirChem is an open-source Python library for simulating variational quantum algorithms for quantum computational chemistry. TenCirChem shows high-performance in the simulation of unitary coupled-cluster circuits, using compact representations of quantum states and excitation operators. Additionally, TenCirChem supports noisy circuit simulation and provides algorithms for variational quantum dynamics. TenCirChem's capabilities are demonstrated through various examples, such as the calculation of the potential energy curve of H2O with a 6-31G(d) basis set using a 34-qubit quantum circuit, the examination of the impact of quantum gate errors on the variational energy of the H2 molecule, and the exploration of the Marcus inverted region for charge transfer rate based on variational quantum dynamics. Furthermore, TenCirChem is capable of running real quantum hardware experiments, making it a versatile tool for both simulation and experimentation in the field of quantum computational chemistry.

Molecular-orbital-based machine learning for open-shell and multi-reference systems with kernel addition Gaussian process regression.

We introduce a novel machine learning strategy, kernel addition Gaussian process regression (KA-GPR), in molecular-orbital-based machine learning (MOB-ML) to learn the total correlation energies of general electronic structure theories for closed- and open-shell systems by introducing a machine learning strategy. The learning efficiency of MOB-ML(KA-GPR) is the same as the original MOB-ML method for the smallest criegee molecule, which is a closed-shell molecule with multi-reference characters. In addition, the prediction accuracies of different small free radicals could reach the chemical accuracy of 1 kcal/mol by training on one example structure. Accurate potential energy surfaces for the H10 chain (closed-shell) and water OH bond dissociation (open-shell) could also be generated by MOB-ML(KA-GPR). To explore the breadth of chemical systems that KA-GPR can describe, we further apply MOB-ML to accurately predict the large benchmark datasets for closed- (QM9, QM7b-T, and GDB-13-T) and open-shell (QMSpin) molecules.

Molecular dipole moment learning via rotationally equivariant derivative kernels in molecular-orbital-based machine learning.

This study extends the accurate and transferable molecular-orbital-based machine learning (MOB-ML) approach to modeling the contribution of electron correlation to dipole moments at the cost of Hartree-Fock computations. A MOB pairwise decomposition of the correlation part of the dipole moment is applied, and these pair dipole moments could be further regressed as a universal function of MOs. The dipole MOB features consist of the energy MOB features and their responses to electric fields. An interpretable and rotationally equivariant derivative kernel for Gaussian process regression (GPR) is introduced to learn the dipole moment more efficiently. The proposed problem setup, feature design, and ML algorithm are shown to provide highly accurate models for both dipole moments and energies on water and 14 small molecules. To demonstrate the ability of MOB-ML to function as generalized density-matrix functionals for molecular dipole moments and energies of organic molecules, we further apply the proposed MOB-ML approach to train and test the molecules from the QM9 dataset. The application of local scalable GPR with Gaussian mixture model unsupervised clustering GPR scales up MOB-ML to a large-data regime while retaining the prediction accuracy. In addition, compared with the literature results, MOB-ML provides the best test mean absolute errors of 4.21 mD and 0.045 kcal/mol for dipole moment and energy models, respectively, when training on 110 000 QM9 molecules. The excellent transferability of the resulting QM9 models is also illustrated by the accurate predictions for four different series of peptides.

Accurate Molecular-Orbital-Based Machine Learning Energies via Unsupervised Clustering of Chemical Space.

We introduce an unsupervised clustering algorithm to improve training efficiency and accuracy in predicting energies using molecular-orbital-based machine learning (MOB-ML). This work determines clusters via the Gaussian mixture model (GMM) in an entirely automatic manner and simplifies an earlier supervised clustering approach [ J. Chem. Theory Comput. 2019, 15, 6668] by eliminating both the necessity for user-specified parameters and the training of an additional classifier. Unsupervised clustering results from GMM have the advantages of accurately reproducing chemically intuitive groupings of frontier molecular orbitals and exhibiting improved performance with an increasing number of training examples. The resulting clusters from supervised or unsupervised clustering are further combined with scalable Gaussian process regression (GPR) or linear regression (LR) to learn molecular energies accurately by generating a local regression model in each cluster. Among all four combinations of regressors and clustering methods, GMM combined with scalable exact GPR (GMM/GPR) is the most efficient training protocol for MOB-ML. The numerical tests of molecular energy learning on thermalized data sets of drug-like molecules demonstrate the improved accuracy, transferability, and learning efficiency of GMM/GPR over other training protocols for MOB-ML, i.e., supervised regression clustering combined with GPR (RC/GPR) and GPR without clustering. GMM/GPR also provides the best molecular energy predictions compared with ones from the literature on the same benchmark data sets. With a lower scaling, GMM/GPR has a 10.4-fold speedup in wall-clock training time compared with scalable exact GPR with a training size of 6500 QM7b-T molecules.

Fast Near Ab Initio Potential Energy Surfaces Using Machine Learning.

A machine-learning based approach for evaluating potential energies for quantum mechanical studies of properties of the ground and excited vibrational states of small molecules is developed. This approach uses the molecular-orbital-based machine learning (MOB-ML) method to generate electronic energies with the accuracy of CCSD(T) calculations at the same cost as a Hartree-Fock calculation. To further reduce the computational cost of the potential energy evaluations without sacrificing the CCSD(T) level accuracy, GPU-accelerated Neural Network Potential Energy Surfaces (NN-PES) are trained to geometries and energies that are collected from small-scale Diffusion Monte Carlo (DMC) simulations, which are run using energies evaluated using the MOB-ML model. The combined NN+(MOB-ML) approach is used in variational calculations of the ground and low-lying vibrational excited states of water and in DMC calculations of the ground states of water, CH5+, and its deuterated analogues. For both of these molecules, comparisons are made to the results obtained using potentials that were fit to much larger sets of electronic energies than were required to train the MOB-ML models. The NN+(MOB-ML) approach is also used to obtain a potential surface for C2H5+, which is a carbocation with a nonclassical equilibrium structure for which there is currently no available potential surface. This potential is used to explore the CH stretching vibrations, focusing on those of the bridging hydrogen atom. For both CH5+ and C2H5+ the MOB-ML model is trained using geometries that were sampled from an AIMD trajectory, which was run at 350 K. By comparison, the structures sampled in the ground state calculations can have energies that are as much as ten times larger than those used to train the MOB-ML model. For water a higher temperature AIMD trajectory is needed to obtain accurate results due to the smaller thermal energy. A second MOB-ML model for C2H5+ was developed with additional higher energy structures in the training set. The two models are found to provide nearly identical descriptions of the ground state of C2H5+.

Improved accuracy and transferability of molecular-orbital-based machine learning: Organics, transition-metal complexes, non-covalent interactions, and transition states.

Molecular-orbital-based machine learning (MOB-ML) provides a general framework for the prediction of accurate correlation energies at the cost of obtaining molecular orbitals. The application of Nesbet's theorem makes it possible to recast a typical extrapolation task, training on correlation energies for small molecules and predicting correlation energies for large molecules, into an interpolation task based on the properties of orbital pairs. We demonstrate the importance of preserving physical constraints, including invariance conditions and size consistency, when generating the input for the machine learning model. Numerical improvements are demonstrated for different datasets covering total and relative energies for thermally accessible organic and transition-metal containing molecules, non-covalent interactions, and transition-state energies. MOB-ML requires training data from only 1% of the QM7b-T dataset (i.e., only 70 organic molecules with seven and fewer heavy atoms) to predict the total energy of the remaining 99% of this dataset with sub-kcal/mol accuracy. This MOB-ML model is significantly more accurate than other methods when transferred to a dataset comprising of 13 heavy atom molecules, exhibiting no loss of accuracy on a size intensive (i.e., per-electron) basis. It is shown that MOB-ML also works well for extrapolating to transition-state structures, predicting the barrier region for malonaldehyde intramolecular proton-transfer to within 0.35 kcal/mol when only trained on reactant/product-like structures. Finally, the use of the Gaussian process variance enables an active learning strategy for extending the MOB-ML model to new regions of chemical space with minimal effort. We demonstrate this active learning strategy by extending a QM7b-T model to describe non-covalent interactions in the protein backbone-backbone interaction dataset to an accuracy of 0.28 kcal/mol.

Regression Clustering for Improved Accuracy and Training Costs with Molecular-Orbital-Based Machine Learning.

Machine learning (ML) in the representation of molecular-orbital-based (MOB) features has been shown to be an accurate and transferable approach to the prediction of post-Hartree-Fock correlation energies. Previous applications of MOB-ML employed Gaussian Process Regression (GPR), which provides good prediction accuracy with small training sets; however, the cost of GPR training scales cubically with the amount of data and becomes a computational bottleneck for large training sets. In the current work, we address this problem by introducing a clustering/regression/classification implementation of MOB-ML. In the first step, regression clustering (RC) is used to partition the training data to best fit an ensemble of linear regression (LR) models; in the second step, each cluster is regressed independently, using either LR or GPR; and in the third step, a random forest classifier (RFC) is trained for the prediction of cluster assignments based on MOB feature values. Upon inspection, RC is found to recapitulate chemically intuitive groupings of the frontier molecular orbitals, and the combined RC/LR/RFC and RC/GPR/RFC implementations of MOB-ML are found to provide good prediction accuracy with greatly reduced wall-clock training times. For a data set of thermalized (350 K) geometries of 7211 organic molecules of up to seven heavy atoms (QM7b-T), both RC/LR/RFC and RC/GPR/RFC reach chemical accuracy (1 kcal/mol prediction error) with only 300 training molecules, while providing 35000-fold and 4500-fold reductions in the wall-clock training time, respectively, compared to MOB-ML without clustering. The resulting models are also demonstrated to retain transferability for the prediction of large-molecule energies with only small-molecule training data. Finally, it is shown that capping the number of training data points per cluster leads to further improvements in prediction accuracy with negligible increases in wall-clock training time.

A universal density matrix functional from molecular orbital-based machine learning: Transferability across organic molecules.

We address the degree to which machine learning (ML) can be used to accurately and transferably predict post-Hartree-Fock correlation energies. Refined strategies for feature design and selection are presented, and the molecular-orbital-based machine learning (MOB-ML) method is applied to several test systems. Strikingly, for the second-order Møller-Plessett perturbation theory, coupled cluster with singles and doubles (CCSD), and CCSD with perturbative triples levels of theory, it is shown that the thermally accessible (350 K) potential energy surface for a single water molecule can be described to within 1 mhartree using a model that is trained from only a single reference calculation at a randomized geometry. To explore the breadth of chemical diversity that can be described, MOB-ML is also applied to a new dataset of thermalized (350 K) geometries of 7211 organic models with up to seven heavy atoms. In comparison with the previously reported Δ-ML method, MOB-ML is shown to reach chemical accuracy with threefold fewer training geometries. Finally, a transferability test in which models trained for seven-heavy-atom systems are used to predict energies for thirteen-heavy-atom systems reveals that MOB-ML reaches chemical accuracy with 36-fold fewer training calculations than Δ-ML (140 vs 5000 training calculations).

Transferability in Machine Learning for Electronic Structure via the Molecular Orbital Basis.

We present a machine learning (ML) method for predicting electronic structure correlation energies using Hartree-Fock input. The total correlation energy is expressed in terms of individual and pair contributions from occupied molecular orbitals, and Gaussian process regression is used to predict these contributions from a feature set that is based on molecular orbital properties, such as Fock, Coulomb, and exchange matrix elements. With the aim of maximizing transferability across chemical systems and compactness of the feature set, we avoid the usual specification of ML features in terms of atom- or geometry-specific information, such atom/element-types, bond-types, or local molecular structure. ML predictions of MP2 and CCSD energies are presented for a range of systems, demonstrating that the method maintains accuracy while providing transferability both within and across chemical families; this includes predictions for molecules with atom-types and elements that are not included in the training set. The method holds promise both in its current form and as a proof-of-principle for the use of ML in the design of generalized density-matrix functionals.

Phytic acid improves intestinal mucosal barrier damage and reduces serum levels of proinflammatory cytokines in a 1,2-dimethylhydrazine-induced rat colorectal cancer model.

Phytic acid (PA) has been demonstrated to have a potent anticarcinogenic activity against colorectal cancer (CRC). Defects of the intestinal mucosal barrier and inflammation processes are involved in the development and progression of CRC. In the present study, we evaluated the effect of PA on the intestinal mucosal barrier and proinflammatory cytokines. After a 1-week acclimatisation period, sixty Wistar male rats were divided into the following five groups, with twelve rats per group: the control group (CG), model group (MG), low-PA-dose group (0·25 g/kg per d), middle-PA-dose group (0·5 g/kg per d), and high-PA-dose group (1 g/kg per d). 1,2-Dimethylhydrazine (DMH) at a dosage of 30 mg/kg of body weight was injected weekly to induce CRC for 18 weeks. We examined the expression of genes related to the intestinal mucosal barrier in the model. The results demonstrated that tumour incidence was decreased following PA treatment. The mRNA and protein expression of mucin 2 (MUC2), trefoil factor 3 (TFF3) and E-cadherin in the MG were significantly lower than those in the CG (P<0·05). The mRNA and protein expression of claudin-1 in the MG were significantly higher than those in the CG (P<0·05). PA elevated the mRNA and protein expression of MUC2, TFF3 and E-cadherin, and diminished the mRNA and protein expression of claudin-1. Furthermore, PA decreased serum levels of proinflammatory cytokines, which included TNF-α, IL-1ß and IL-6. In conclusion, this study suggests that PA has favourable effects on the intestinal mucosal barrier and may reduce serum proinflammatory cytokine levels.

Inositol hexaphosphate suppresses colorectal cancer cell proliferation via the Akt/GSK-3ß/ß-catenin signaling cascade in a 1,2-dimethylhydrazine-induced rat model.

Colorectal cancer (CRC) is common worldwide, and most treatments for CRC have undesirable side effects. Many researchers have demonstrated that inositol hexaphosphate (IP6) has potent anticarcinogenic activity against CRC and no apparent toxicity to normal cells. However, the underlying mechanism is still unclear. In this study, we investigated the anticancer and anti-proliferative properties of IP6 in CRC and its possible mechanisms during this chemopreventive process. We examined the expression of genes related to the PI3K/Akt and Wnt pathways at the transcriptional and translational levels in a DMH-induced rat CRC model following IP6 administration. In addition, we also conducted cell proliferation analysis. The results demonstrated that IP6 could inhibit tumors, in terms of tumor incidence, number, weight and volume in DMH-induced rats. Additionally, Akt and c-Myc mRNA levels were significantly decreased. IP6 was also shown to downregulate Akt, pAkt, pGSK-3ß, and c-Myc protein expression and upregulate pß-catenin protein expression. Furthermore, tumor tissues from IP6-treated rats showed decreased proliferation. In conclusion, the anti-proliferative effect of IP6 may be related to crosstalk between the PI3K/Akt and Wnt pathways, revealing a potential mechanism of CRC inhibition by IP6 in our model.

Chemical Interactions of Polyethylene Glycols (PEGs) and Glycerol with Protein Functional Groups: Applications to Effects of PEG and Glycerol on Protein Processes.

In this work, we obtain the data needed to predict chemical interactions of polyethylene glycols (PEGs) and glycerol with proteins and related organic compounds and thereby interpret or predict chemical effects of PEGs on protein processes. To accomplish this, we determine interactions of glycerol and tetraEG with >30 model compounds displaying the major C, N, and O functional groups of proteins. Analysis of these data yields coefficients (α values) that quantify interactions of glycerol, tetraEG, and PEG end (-CH2OH) and interior (-CH2OCH2-) groups with these groups, relative to interactions with water. TetraEG (strongly) and glycerol (weakly) interact favorably with aromatic C, amide N, and cationic N, but unfavorably with amide O, carboxylate O, and salt ions. Strongly unfavorable O and salt anion interactions help make both small and large PEGs effective protein precipitants. Interactions of tetraEG and PEG interior groups with aliphatic C are quite favorable, while interactions of glycerol and PEG end groups with aliphatic C are not. Hence, tetraEG and PEG300 favor unfolding of the DNA-binding domain of lac repressor (lacDBD), while glycerol and di- and monoethylene glycol are stabilizers. Favorable interactions with aromatic and aliphatic C explain why PEG400 greatly increases the solubility of aromatic hydrocarbons and steroids. PEG400-steroid interactions are unusually favorable, presumably because of simultaneous interactions of multiple PEG interior groups with the fused ring system of the steroid. Using α values reported here, chemical contributions to PEG m-values can be predicted or interpreted in terms of changes in water-accessible surface area (ΔASA) and separated from excluded volume effects.