Unbiasing fermionic quantum Monte Carlo with a quantum computer.

Interacting many-electron problems pose some of the greatest computational challenges in science, with essential applications across many fields. The solutions to these problems will offer accurate predictions of chemical reactivity and kinetics, and other properties of quantum systems1-4. Fermionic quantum Monte Carlo (QMC) methods5,6, which use a statistical sampling of the ground state, are among the most powerful approaches to these problems. Controlling the fermionic sign problem with constraints ensures the efficiency of QMC at the expense of potentially significant biases owing to the limited flexibility of classical computation. Here we propose an approach that combines constrained QMC with quantum computation to reduce such biases. We implement our scheme experimentally using up to 16 qubits to unbias constrained QMC calculations performed on chemical systems with as many as 120 orbitals. These experiments represent the largest chemistry simulations performed with the help of quantum computers, while achieving accuracy that is competitive with state-of-the-art classical methods without burdensome error mitigation. Compared with the popular variational quantum eigensolver7,8, our hybrid quantum-classical computational model offers an alternative path towards achieving a practical quantum advantage for the electronic structure problem without demanding exceedingly accurate preparation and measurement of the ground-state wavefunction.

Quantum computation of stopping power for inertial fusion target design.

Stopping power is the rate at which a material absorbs the kinetic energy of a charged particle passing through it-one of many properties needed over a wide range of thermodynamic conditions in modeling inertial fusion implosions. First-principles stopping calculations are classically challenging because they involve the dynamics of large electronic systems far from equilibrium, with accuracies that are particularly difficult to constrain and assess in the warm-dense conditions preceding ignition. Here, we describe a protocol for using a fault-tolerant quantum computer to calculate stopping power from a first-quantized representation of the electrons and projectile. Our approach builds upon the electronic structure block encodings of Su et al. [PRX Quant. 2, 040332 (2021)], adapting and optimizing those algorithms to estimate observables of interest from the non-Born-Oppenheimer dynamics of multiple particle species at finite temperature. We also work out the constant factors associated with an implementation of a high-order Trotter approach to simulating a grid representation of these systems. Ultimately, we report logical qubit requirements and leading-order Toffoli costs for computing the stopping power of various projectile/target combinations relevant to interpreting and designing inertial fusion experiments. We estimate that scientifically interesting and classically intractable stopping power calculations can be quantum simulated with roughly the same number of logical qubits and about one hundred times more Toffoli gates than is required for state-of-the-art quantum simulations of industrially relevant molecules such as FeMoco or P450.

Reliably assessing the electronic structure of cytochrome P450 on today's classical computers and tomorrow's quantum computers.

An accurate assessment of how quantum computers can be used for chemical simulation, especially their potential computational advantages, provides important context on how to deploy these future devices. To perform this assessment reliably, quantum resource estimates must be coupled with classical computations attempting to answer relevant chemical questions and to define the classical algorithms simulation frontier. Herein, we explore the quantum computation and classical computation resources required to assess the electronic structure of cytochrome P450 enzymes (CYPs) and thus define a classical-quantum advantage boundary. This is accomplished by analyzing the convergence of density matrix renormalization group plus n-electron valence state perturbation theory (DMRG+NEVPT2) and coupled-cluster singles doubles with noniterative triples [CCSD(T)] calculations for spin gaps in models of the CYP catalytic cycle that indicate multireference character. The quantum resources required to perform phase estimation using qubitized quantum walks are calculated for the same systems. Compilation into the surface code provides runtime estimates to compare directly to DMRG runtimes and to evaluate potential quantum advantage. Both classical and quantum resource estimates suggest that simulation of CYP models at scales large enough to balance dynamic and multiconfigurational electron correlation has the potential to be a quantum advantage problem and emphasizes the important interplay between classical computations and quantum algorithms development for chemical simulation.

Stochastic Resolution of Identity to CC2 for Large Systems: Ground State and Triplet Excitation Energy Calculations.

An implementation of stochastic resolution of identity to the CC2 (sRI-CC2) ground state energy followed by triplet excitation energy calculations is presented. A set of stochastic orbitals is introduced to further decouple the expensive 4-index electron repulsion integrals on the basis of RI approximation. A Laplace transformation of the orbital energy difference denominators into numerical summations is adopted to obtain a third-order overall scaling. We select a series of hydrogen dimer chains with nearly thousands of electrons, as well as some other molecules, for sRI-CC2 energies and test the accuracy and time consumption in comparison with those of RI-CC2. Our sRI-CC2 results reproduce a modest agreement with the RI-CC2 in Q-Chem program package and it allows a steep scaling reduction from O(N5) to O(N3). Besides, the unrestricted sRI-CC2 calculations also fit well with the restricted results. Thus, our sRI-CC2 implementation of ground state energy and triplet excitation energy provides a cost-efficient alternative approach, especially for some large-sized systems.

Improved modularity and new features in ipie: Toward even larger AFQMC calculations on CPUs and GPUs at zero and finite temperatures.

ipie is a Python-based auxiliary-field quantum Monte Carlo (AFQMC) package that has undergone substantial improvements since its initial release [Malone et al., J. Chem. Theory Comput. 19(1), 109-121 (2023)]. This paper outlines the improved modularity and new capabilities implemented in ipie. We highlight the ease of incorporating different trial and walker types and the seamless integration of ipie with external libraries. We enable distributed Hamiltonian simulations of large systems that otherwise would not fit on a single central processing unit node or graphics processing unit (GPU) card. This development enabled us to compute the interaction energy of a benzene dimer with 84 electrons and 1512 orbitals with multi-GPUs. Using CUDA and cupy for NVIDIA GPUs, ipie supports GPU-accelerated multi-slater determinant trial wavefunctions [Huang et al. arXiv:2406.08314 (2024)] to enable efficient and highly accurate simulations of large-scale systems. This allows for near-exact ground state energies of multi-reference clusters, [Cu2O2]2+ and [Fe2S2(SCH3)4]2-. We also describe implementations of free projection AFQMC, finite temperature AFQMC, AFQMC for electron-phonon systems, and automatic differentiation in AFQMC for calculating physical properties. These advancements position ipie as a leading platform for AFQMC research in quantum chemistry, facilitating more complex and ambitious computational method development and their applications.

Impacts of Tocolytics on Maternal and Neonatal Glucose Levels in Women With Gestational Diabetes Mellitus.

BACKGROUND: We investigated the impacts of tocolytic agents on maternal and neonatal blood glucose levels in women with gestational diabetes mellitus (GDM) who used tocolytics for preterm labor. METHODS: This multi-center, retrospective cohort study included women with GDM who were admitted for preterm labor from twelve hospitals in South Korea. We excluded women with multiple pregnancies, anomalies, overt DM diagnosed before pregnancy or 23 weeks of gestation, and women who received multiple tocolytics. The patients were divided according to the types of tocolytics; atosiban, ritodrine, and nifedipine group. We collected baseline maternal characteristics, pregnancy outcomes, maternal glucose levels during hospitalization, and neonatal glucose levels. We compared the frequency of maternal hyperglycemia and neonatal hypoglycemia among three groups. A multivariate logistic regression analysis was performed to evaluate the contributing factors to the occurrence of maternal hyperglycemia and neonatal hypoglycemia. RESULTS: A total of 128 women were included: 44 (34.4%), 51 (39.8%), and 33 (25.8%) women received atosiban, ritodrine, and nifedipine, respectively. Mean fasting blood glucose (FBG) (112.3, 109.6, and 89.5 mg/dL, P < 0.001) and 2-hour postprandial glucose (PPG2) levels (145.4, 148.3, and 116.5 mg/dL, P = 0.004) were significantly higher in atosiban and ritodrine group than those in nifedipine group. Even after adjusting for covariates including antenatal steroid use, gestational age at admission, and pre-pregnancy body mass index, there was an increased risk of high maternal mean FBG (≥ 95 mg/dL) and PPG2 (≥ 120 mg/dL) levels in the atosiban and ritodrine group than in nifedipine group. The atosiban and ritodrine groups are also at increased risk of neonatal hypoglycemia (< 47 mg/dL) compared to the nifedipine group with the odds ratio of 4.58 and 4.67, respectively (P < 0.05). CONCLUSION: There is an increased risk of maternal hyperglycemia and neonatal hypoglycemia in women with GDM using atosiban and ritodrine tocolytics for preterm labor compared to those using nifedipine.

Microscopic Theory of Multimode Polariton Dispersion in Multilayered Materials.

We develop a microscopic theory for the multimode polariton dispersion in materials coupled to cavity radiation modes. Starting from a microscopic light-matter Hamiltonian, we devise a general strategy for obtaining simple matrix models of polariton dispersion curves based on the structure and spatial location of multilayered 2D materials inside the optical cavity. Our theory exposes the connections between seemingly distinct models that have been employed in the literature and resolves an ambiguity that has arisen concerning the experimental description of the polaritonic band structure. We demonstrate the applicability of our theoretical formalism by fabricating various geometries of multilayered perovskite materials coupled to cavities and demonstrating that our theoretical predictions agree with the experimental results presented here.

Response properties in phaseless auxiliary field quantum Monte Carlo.

We present a method for calculating first-order response properties in phaseless auxiliary field quantum Monte Carlo by applying automatic differentiation (AD). Biases and statistical efficiency of the resulting estimators are discussed. Our approach demonstrates that AD enables the calculation of reduced density matrices with the same computational cost scaling per sample as energy calculations, accompanied by a cost prefactor of less than four in our numerical calculations. We investigate the role of self-consistency and trial orbital choice in property calculations. We find that orbitals obtained using density functional theory perform well for the dipole moments of selected molecules compared to those optimized self-consistently.

An in-silico NMR laboratory for nuclear magnetic shieldings computed via finite fields: Exploring nucleus-specific renormalizations of MP2 and MP3.

We developed and implemented a method-independent, fully numerical, finite difference approach to calculating nuclear magnetic resonance shieldings, using gauge-including atomic orbitals. The resulting capability can be used to explore non-standard methods, given only the energy as a function of finite-applied magnetic fields and nuclear spins. For example, standard second-order Møller-Plesset theory (MP2) has well-known efficacy for 1H and 13C shieldings and known limitations for other nuclei such as 15N and 17O. It is, therefore, interesting to seek methods that offer good accuracy for 15N and 17O shieldings without greatly increased compute costs, as well as exploring whether such methods can further improve 1H and 13C shieldings. Using a small molecule test set of 28 species, we assessed two alternatives: κ regularized MP2 (κ-MP2), which provides energy-dependent damping of large amplitudes, and MP2.X, which includes a variable fraction, X, of third-order correlation (MP3). The aug-cc-pVTZ basis was used, and coupled cluster with singles and doubles and perturbative triples [CCSD(T)] results were taken as reference values. Our κ-MP2 results reveal significant improvements over MP2 for 13C and 15N, with the optimal κ value being element-specific. κ-MP2 with κ = 2 offers a 30% rms error reduction over MP2. For 15N, κ-MP2 with κ = 1.1 provides a 90% error reduction vs MP2 and a 60% error reduction vs CCSD. On the other hand, MP2.X with a scaling factor of 0.6 outperformed CCSD for all heavy nuclei. These results can be understood as providing renormalization of doubles amplitudes to partially account for neglected triple and higher substitutions and offer promising opportunities for future applications.

The Effect of Vanishing Twin on First- and Second-Trimester Maternal Serum Markers and Nuchal Translucency: A Multicenter Prospective Cohort Study.

BACKGROUND: The purpose of this study was to evaluate the effect of vanishing twin (VT) on maternal serum marker concentrations and nuchal translucency (NT). METHODS: This is a secondary analysis of a multicenter prospective cohort study in 12 institutions. Serum concentrations of pregnancy-associated plasma protein-A in the first trimester and alpha-fetoprotein (AFP), total human chorionic gonadotrophin, unconjugated estriol, and inhibin A in the second trimester were measured, and NT was measured between 10 and 14 weeks of gestation. RESULTS: Among 6,793 pregnant women, 5,381 women were measured for serum markers in the first or second trimester, including 65 cases in the VT group and 5,316 cases in the normal singleton group. The cases in the VT group had a higher median multiple of the median value of AFP and inhibin A than the normal singleton group. The values of other serum markers and NT were not different between the two groups. After the permutation test with adjustment, AFP and inhibin A remained significant differences. The frequency of abnormally increased AFP was also higher in the VT group than in the normal singleton group. CONCLUSION: VT can be considered as an adjustment factor for risk assessment in the second-trimester serum screening test.

Accurate core excitation and ionization energies from a state-specific coupled-cluster singles and doubles approach.

We investigate the use of orbital-optimized references in conjunction with single-reference coupled-cluster theory with single and double substitutions (CCSD) for the study of core excitations and ionizations of 18 small organic molecules, without the use of response theory or equation-of-motion (EOM) formalisms. Three schemes are employed to successfully address the convergence difficulties associated with the coupled-cluster equations, and the spin contamination resulting from the use of a spin symmetry-broken reference, in the case of excitations. In order to gauge the inherent potential of the methods studied, an effort is made to provide reasonable basis set limit estimates for the transition energies. Overall, we find that the two best-performing schemes studied here for ΔCCSD are capable of predicting excitation and ionization energies with errors comparable to experimental accuracies. The proposed ΔCCSD schemes reduces statistical errors against experimental excitation energies by more than a factor of two when compared to the frozen-core core-valence separated (FC-CVS) EOM-CCSD approach - a successful variant of EOM-CCSD tailored towards core excitations.

Near-exact nuclear gradients of complete active space self-consistent field wave functions.

In this paper, we study the nuclear gradients of heat bath configuration interaction self-consistent field (HCISCF) wave functions and use them to optimize molecular geometries for various molecules. We show that HCISCF nuclear gradients are fairly insensitive to the size of the "selected" variational space, which allows us to reduce the computational cost without introducing significant errors. The ability of the HCISCF to treat larger active spaces combined with the flexibility for users to control the computational cost makes the method very attractive for studying strongly correlated systems, which require a larger active space than possible with a complete active space self-consistent field. Finally, we study the realistic catalyst, Fe(PDI), and highlight some of the challenges this system poses for density functional theory (DFT). We demonstrate how HCISCF can clarify the energetic stability of geometries obtained from DFT when the results are strongly dependent on the functional. We also use the HCISCF gradients to optimize geometries for this species and study the adiabatic singlet-triplet gap. During geometry optimization, we find that multiple near-degenerate local minima exist on the triplet potential energy surface.

Selected configuration interaction wave functions in phaseless auxiliary field quantum Monte Carlo.

We present efficient algorithms for using selected configuration interaction (sCI) trial wave functions in phaseless auxiliary field quantum Monte Carlo (ph-AFQMC). These advances, geared toward optimizing computational performance for longer configuration interaction expansions, allow us to use up to a million configurations in the trial state for ph-AFQMC. In one example, we found the cost of ph-AFQMC per sample to increase only by a factor of about 3 for a calculation with 104 configurations compared to that with a single one, demonstrating the tiny computational overhead due to a longer expansion. This favorable scaling allows us to study the systematic convergence of the phaseless bias in auxiliary field quantum Monte Carlo calculations with an increasing number of configurations and provides a means to gauge the accuracy of ph-AFQMC with other trial states. We also show how the scalability issues of sCI trial states for large system sizes could be mitigated by restricting them to a moderately sized orbital active space and leveraging the near-cancellation of out of active space phaseless errors.

Insecticide resistance in pepper greenhouse populations of Aphis gossypii (Hemiptera: Aphididae) in Korea.

The cotton aphid or melon aphid, Aphis gossypii Glover (Hemiptera: Aphididae), is a polyphagous insect pest with a wide host range. Two distinct genetic clusters were found in A. gossypii populations in Korea. To determine whether the division of the genetic clusters was driven by insecticide selection pressure, the frequencies of insecticide resistance-associated mutations on three representative insecticide target genes [i.e., nicotinic acetylcholine receptor gene (nAChR), voltage-gated sodium channel gene (vgsc), and acetylcholinesterase 1 gene (ace-1)] were predicted in A. gossypii populations with known genetic structures. Most populations revealed heterozygosity-resistant alleles for the nAChR R81T and vgsc M918L mutations, but homozygous-resistant alleles for the ace-1 S431F mutation. However, assessment of the three mutation frequencies revealed no apparent correlation between the genetic structures and the resistance profiles. The regression analysis revealed no correlation between the genetic cluster ratios and resistance allele frequencies (R81T, S431F, and M918L). We used three insecticides that are commonly used in greenhouses: imidacloprid (neonicotinoid), acephate (organophosphate), and esfenvalerate (pyrethroid), to test resistance and susceptibility in A. gossypii populations. The bioassay results revealed that the BS_19 (Busan) and JE_19 (Jeongeup) populations were resistant to imidacloprid and acephate, the HS_19 (Honseong) population was resistant to acephate and esfenvalerate, and susceptible lab strains only exhibited resistance to acephate. The bioassay results were correlated with mutation frequency, but no correlation was detected among genetic clusters. These results suggest that the distinct genetic structure observed in the Korean populations of A. gossypii is not likely influenced by insecticide resistance traits, but rather by other factors.

A non-perturbative pairwise-additive analysis of charge transfer contributions to intermolecular interaction energies.

Energy decomposition analysis (EDA) based on absolutely localized molecular orbitals (ALMOs) decomposes the interaction energy between molecules into physically interpretable components like geometry distortion, frozen interactions, polarization, and charge transfer (CT, also sometimes called charge delocalization) interactions. In this work, a numerically exact scheme to decompose the CT interaction energy into pairwise additive terms is introduced for the ALMO-EDA using density functional theory. Unlike perturbative pairwise charge-decomposition analysis, the new approach does not break down for strongly interacting systems, or show significant exchange-correlation functional dependence in the decomposed energy components. Both the energy lowering and the charge flow associated with CT can be decomposed. Complementary occupied-virtual orbital pairs (COVPs) that capture the dominant donor and acceptor CT orbitals are obtained for the new decomposition. It is applied to systems with different types of interactions including DNA base-pairs, borane-ammonia adducts, and transition metal hexacarbonyls. While consistent with most existing understanding of the nature of CT in these systems, the results also reveal some new insights into the origin of trends in donor-acceptor interactions.

A phaseless auxiliary-field quantum Monte Carlo perspective on the uniform electron gas at finite temperatures: Issues, observations, and benchmark study.

We investigate the viability of the phaseless finite-temperature auxiliary-field quantum Monte Carlo (ph-FT-AFQMC) method for ab initio systems using the uniform electron gas as a model. Through comparisons with exact results and FT coupled cluster theory, we find that ph-FT-AFQMC is sufficiently accurate at high to intermediate electronic densities. We show, both analytically and numerically, that the phaseless constraint at FT is fundamentally different from its zero-temperature counterpart (i.e., ph-ZT-AFQMC), and generally, one should not expect ph-FT-AFQMC to agree with ph-ZT-AFQMC in the low-temperature limit. With an efficient implementation, we are able to compare exchange-correlation energies to the existing results in the thermodynamic limit and find that the existing parameterizations are highly accurate. In particular, we found that ph-FT-AFQMC exchange-correlation energies are in better agreement with a known parameterization than is restricted path-integral MC in the regime of Θ ≤ 0.5 and rs ≤ 2, which highlights the strength of ph-FT-AFQMC.

Revealing the nature of electron correlation in transition metal complexes with symmetry breaking and chemical intuition.

In this work, we provide a nuanced view of electron correlation in the context of transition metal complexes, reconciling computational characterization via spin and spatial symmetry breaking in single-reference methods with qualitative concepts from ligand-field and molecular orbital theories. These insights provide the tools to reliably diagnose the multi-reference character, and our analysis reveals that while strong (i.e., static) correlation can be found in linear molecules (e.g., diatomics) and weakly bound and antiferromagnetically coupled (monometal-noninnocent ligand or multi-metal) complexes, it is rarely found in the ground-states of mono-transition-metal complexes. This leads to a picture of static correlation that is no more complex for transition metals than it is, e.g., for organic biradicaloids. In contrast, the ability of organometallic species to form more complex interactions, involving both ligand-to-metal σ-donation and metal-to-ligand π-backdonation, places a larger burden on a theory's treatment of dynamic correlation. We hypothesize that chemical bonds in which inter-electron pair correlation is non-negligible cannot be adequately described by theories using MP2 correlation energies and indeed find large errors vs experiment for carbonyl-dissociation energies from double-hybrid density functionals. A theory's description of dynamic correlation (and to a less important extent, delocalization error), which affects relative spin-state energetics and thus spin symmetry breaking, is found to govern the efficacy of its use to diagnose static correlation.

Exploring spin symmetry-breaking effects for static field ionization of atoms: Is there an analog to the Coulson-Fischer point in bond dissociation?

Löwdin's symmetry dilemma is an ubiquitous issue in approximate quantum chemistry. In the context of Hartree-Fock (HF) theory, the use of Slater determinants with some imposed constraints to preserve symmetries of the exact problem may lead to physically unreasonable potential energy surfaces. On the other hand, lifting these constraints leads to the so-called broken symmetry solutions that usually provide better energetics, at the cost of losing information about good quantum numbers that describe the state of the system. This behavior has previously been extensively studied in the context of bond dissociation. This paper studies the behavior of different classes of HF spin polarized solutions (restricted, unrestricted, and generalized) in the context of ionization by strong static electric fields. We find that, for simple two electron systems, unrestricted Hartree-Fock (UHF) is able to provide a qualitatively good description of states involved during the ionization process (neutral, singly ionized, and doubly ionized states), whereas RHF fails to describe the singly ionized state. For more complex systems, even though UHF is able to capture some of the expected characteristics of the ionized states, it is constrained to a single Ms (diabatic) manifold in the energy surface as a function of field intensity. In this case, a better qualitative picture can be painted by using generalized Hartree-Fock as it is able to explore different spin manifolds and follow the lowest solution due to lack of collinearity constraints on the spin quantization axis.

Approaching the basis set limit in Gaussian-orbital-based periodic calculations with transferability: Performance of pure density functionals for simple semiconductors.

Simulating solids with quantum chemistry methods and Gaussian-type orbitals (GTOs) has been gaining popularity. Nonetheless, there are few systematic studies that assess the basis set incompleteness error (BSIE) in these GTO-based simulations over a variety of solids. In this work, we report a GTO-based implementation for solids and apply it to address the basis set convergence issue. We employ a simple strategy to generate large uncontracted (unc) GTO basis sets that we call the unc-def2-GTH sets. These basis sets exhibit systematic improvement toward the basis set limit as well as good transferability based on application to a total of 43 simple semiconductors. Most notably, we found the BSIE of unc-def2-QZVP-GTH to be smaller than 0.7 mEh per atom in total energies and 20 meV in bandgaps for all systems considered here. Using unc-def2-QZVP-GTH, we report bandgap benchmarks of a combinatorially designed meta-generalized gradient approximation (mGGA) functional, B97M-rV, and show that B97M-rV performs similarly (a root-mean-square-deviation of 1.18 eV) to other modern mGGA functionals, M06-L (1.26 eV), MN15-L (1.29 eV), and Strongly Constrained and Appropriately Normed (SCAN) (1.20 eV). This represents a clear improvement over older pure functionals such as local density approximation (1.71 eV) and Perdew-Burke-Ernzerhof (PBE) (1.49 eV), although all these mGGAs are still far from being quantitatively accurate. We also provide several cautionary notes on the use of our uncontracted bases and on future research on GTO basis set development for solids.

What the foundations of quantum computer science teach us about chemistry.

With the rapid development of quantum technology, one of the leading applications that has been identified is the simulation of chemistry. Interestingly, even before full scale quantum computers are available, quantum computer science has exhibited a remarkable string of results that directly impact what is possible in a chemical simulation with any computer. Some of these results even impact our understanding of chemistry in the real world. In this Perspective, we take the position that direct chemical simulation is best understood as a digital experiment. While on the one hand, this clarifies the power of quantum computers to extend our reach, it also shows us the limitations of taking such an approach too directly. Leveraging results that quantum computers cannot outpace the physical world, we build to the controversial stance that some chemical problems are best viewed as problems for which no algorithm can deliver their solution, in general, known in computer science as undecidable problems. This has implications for the predictive power of thermodynamic models and topics such as the ergodic hypothesis. However, we argue that this Perspective is not defeatist but rather helps shed light on the success of existing chemical models such as transition state theory, molecular orbital theory, and thermodynamics as models that benefit from data. We contextualize recent results, showing that data-augmented models are a more powerful rote simulation. These results help us appreciate the success of traditional chemical theory and anticipate new models learned from experimental data. Not only can quantum computers provide data for such models, but they can also extend the class and power of models that utilize data in fundamental ways. These discussions culminate in speculation on new ways for quantum computing and chemistry to interact and our perspective on the eventual roles of quantum computers in the future of chemistry.