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.

Instantons and the quantum bound to chaos.

The rate at which information scrambles in a quantum system can be quantified using out-of-time-ordered correlators. A remarkable prediction is that the associated Lyapunov exponent [Formula: see text] that quantifies the scrambling rate in chaotic systems obeys a universal bound [Formula: see text]. Previous numerical and analytical studies have indicated that this bound has a quantum-statistical origin. Here, we use path-integral techniques to show that a minimal theory to reproduce this bound involves adding contributions from quantum thermal fluctuations (describing quantum tunneling and zero-point energy) to classical dynamics. By propagating a model quantum-Boltzmann-conserving classical dynamics for a system with a barrier, we show that the bound is controlled by the stability of thermal fluctuations around the barrier instanton (a delocalized structure which dominates the tunneling statistics). This stability requirement appears to be general, implying that there is a close relation between the formation of instantons, or related delocalized structures, and the imposition of the quantum-chaos bound.

Remembering the Work of Phillip L. Geissler: A Coda to His Scientific Trajectory.

Phillip L. Geissler made important contributions to the statistical mechanics of biological polymers, heterogeneous materials, and chemical dynamics in aqueous environments. He devised analytical and computational methods that revealed the underlying organization of complex systems at the frontiers of biology, chemistry, and materials science. In this retrospective we celebrate his work at these frontiers.

Electron and Spin Delocalization in [Co6 Se8 (PEt3 )6 ]0/+1 Superatoms.

Molecular clusters can function as nanoscale atoms/superatoms, assembling into superatomic solids, a new class of solid-state materials with designable properties through modifications on superatoms. To explore possibilities on diversifying building blocks, here we thoroughly studied one representative superatom, Co6 Se8 (PEt3 )6 . We probed its structural, electronic, and magnetic properties and revealed its detailed electronic structure as valence electrons delocalize over inorganic [Co6 Se8 ] core while ligands function as an insulated shell. 59 Co SSNMR measurements on the core and 31 P, 13 C on the ligands show that the neutral Co6 Se8 (PEt3 )6 is diamagnetic and symmetric, with all ligands magnetically equivalent. Quantum computations cross-validate NMR results and reveal degenerate delocalized HOMO orbitals, indicating aromaticity. Ligand substitution keeps the inorganic core nearly intact. After losing one electron, the unpaired electron in [Co6 Se8 (PEt3 )6 ]+1 is delocalized, causing paramagnetism and a delocalized electron spin. Notably, this feature of electron/spin delocalization over a large cluster is attractive for special single-electron devices.

Scalable Ab Initio Electronic Structure Methods with Near Chemical Accuracy for Main Group Chemistry.

This study evaluates the precision of widely recognized quantum chemical methodologies, CCSD(T), DLPNO-CCSD(T), and localized ph-AFQMC, for determining the thermochemistry of main group elements. DLPNO-CCSD(T) and localized ph-AFQMC, which offer greater scalability compared to canonical CCSD(T), have emerged over the past decade as pivotal in producing precise benchmark chemical data. Our investigation includes closed-shell, neutral molecules, focusing on their heat of formation and atomization energy sourced from four specific small molecule data sets. First, we selected molecules from the G2 and G3 data sets, noted for their reliable experimental heat of formation data. Additionally, we incorporate molecules from the W4-11 and W4-17 sets, which provide high-level theoretical reference values for atomization energy at 0 K. Our findings reveal that both DLPNO-CCSD(T) and ph-AFQMC methods are capable of achieving a root-mean-square deviation of less than 1 kcal/mol across the combined data set, aligning with the threshold for chemical accuracy. Moreover, we make efforts to confine the maximum deviations within 2 kcal/mol, a degree of precision that significantly broadens the applicability of these methods in fields such as biology and materials science.

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.

On the potentially transformative role of auxiliary-field quantum Monte Carlo in quantum chemistry: A highly accurate method for transition metals and beyond.

Approximate solutions to the ab initio electronic structure problem have been a focus of theoretical and computational chemistry research for much of the past century, with the goal of predicting relevant energy differences to within "chemical accuracy" (1 kcal/mol). For small organic molecules, or in general, for weakly correlated main group chemistry, a hierarchy of single-reference wave function methods has been rigorously established, spanning perturbation theory and the coupled cluster (CC) formalism. For these systems, CC with singles, doubles, and perturbative triples is known to achieve chemical accuracy, albeit at O(N7) computational cost. In addition, a hierarchy of density functional approximations of increasing formal sophistication, known as Jacob's ladder, has been shown to systematically reduce average errors over large datasets representing weakly correlated chemistry. However, the accuracy of such computational models is less clear in the increasingly important frontiers of chemical space including transition metals and f-block compounds, in which strong correlation can play an important role in reactivity. A stochastic method, phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC), has been shown to be capable of producing chemically accurate predictions even for challenging molecular systems beyond the main group, with relatively low O(N3 - N4) cost and near-perfect parallel efficiency. Herein, we present our perspectives on the past, present, and future of the ph-AFQMC method. We focus on its potential in transition metal quantum chemistry to be a highly accurate, systematically improvable method that can reliably probe strongly correlated systems in biology and chemical catalysis and provide reference thermochemical values (for future development of density functionals or interatomic potentials) when experiments are either noisy or absent. Finally, we discuss the present limitations of the method and where we expect near-term development to be most fruitful.

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.

Microscopic observation of two-level systems in a metallic glass model.

The low-temperature quasi-universal behavior of amorphous solids has been attributed to the existence of spatially localized tunneling defects found in the low-energy regions of the potential energy landscape. Computational models of glasses can be studied to elucidate the microscopic nature of these defects. Recent simulation work has demonstrated the means of generating stable glassy configurations for models that mimic metallic glasses using the swap Monte Carlo algorithm. Building on these studies, we present an extensive exploration of the glassy metabasins of the potential energy landscape of a variant of the most widely used model of metallic glasses. We carefully identify tunneling defects and reveal their depletion with increased glass stability. The density of tunneling defects near the experimental glass transition temperature appears to be in good agreement with experimental measurements.

Strongly Correlated Ladders in K-Doped p-Terphenyl Crystals.

Potassium-doped terphenyl has recently attracted attention as a potential host for high-transition-temperature superconductivity. Here, we elucidate the many-body electronic structure of recently synthesized potassium-doped terphenyl crystals. We show that this system may be understood as a set of weakly coupled one-dimensional ladders. Depending on the strength of the interladder coupling, the system may exhibit insulating spin-gapped valence-bond solid or antiferromagnetic phases, both of which upon hole doping may give rise to superconductivity. This terphenyl-based ladder material serves as a new platform for investigating the fate of ladder phases in the presence of three-dimensional coupling as well as for novel superconductivity.

Elastoplasticity Mediates Dynamical Heterogeneity Below the Mode Coupling Temperature.

As liquids approach the glass transition temperature, dynamical heterogeneity emerges as a crucial universal feature of their behavior. Dynamic facilitation, where local motion triggers further motion nearby, plays a major role in this phenomenon. Here we show that long-ranged, elastically mediated facilitation appears below the mode coupling temperature, adding to the short-range component present at all temperatures. Our results suggest deep connections between the supercooled liquid and glass states, and pave the way for a deeper understanding of dynamical heterogeneity in glassy systems.

Revisiting the concept of activation in supercooled liquids.

In this work, we revisit the description of dynamics based on the concepts of metabasins and activation in mildly supercooled liquids via the analysis of the dynamics of a paradigmatic glass former between its onset temperature [Formula: see text] and mode-coupling temperature [Formula: see text]. First, we provide measures that demonstrate that the onset of glassiness is indeed connected to the landscape, and that metabasin waiting time distributions are so broad that the system can remain stuck in a metabasin for times that exceed [Formula: see text] by orders of magnitude. We then reanalyze the transitions between metabasins, providing several indications that the standard picture of activated dynamics in terms of traps does not hold in this regime. Instead, we propose that here activation is principally driven by entropic instead of energetic barriers. In particular, we illustrate that activation is not controlled by the hopping of high energetic barriers and should more properly be interpreted as the entropic selection of nearly barrierless but rare pathways connecting metabasins on the landscape.

Time evolution of ML-MCTDH wavefunctions. I. Gauge conditions, basis functions, and singularities.

We derive a family of equations-of-motion (EOMs) for evolving multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) wavefunctions that, unlike the standard ML-MCTDH EOMs, never require the evaluation of the inverse of singular matrices. All members of this family of EOMs make use of alternative static gauge conditions than those used for standard ML-MCTDH. These alternative conditions result in an expansion of the wavefunction in terms of a set of potentially arbitrary orthonormal functions, rather than in terms of a set of non-orthonormal and potentially linearly dependent functions, as is the case for standard ML-MCTDH. We show that the EOMs used in the projector splitting integrator (PSI) and the invariant EOM approaches are two special cases of this family obtained from different choices for the dynamic gauge condition, with the invariant EOMs making use of a choice that introduces potentially unbounded operators into the EOMs. As a consequence, all arguments for the existence of parallelizable integration schemes for the invariant EOMs can also be applied to the PSI EOMs.

Time evolution of ML-MCTDH wavefunctions. II. Application of the projector splitting integrator.

The multi-layer multi-configuration time-dependent Hartree (ML-MCTDH) approach can suffer from numerical instabilities whenever the wavefunction is weakly entangled. These instabilities arise from singularities in the equations of motion (EOMs) and necessitate the use of regularization of the EOMs. The Projector Splitting Integrator (PSI) has previously been presented as an approach for evolving ML-MCTDH wavefunctions that is free of singularities. Here, we will discuss the implementation of the multi-layer PSI with a particular focus on how the steps required relate to those required to implement standard ML-MCTDH. We demonstrate the efficiency and stability of the PSI for large ML-MCTDH wavefunctions containing up to hundreds of thousands of nodes by considering a series of spin-boson models with up to 106 bath modes and find that for these problems, the PSI requires roughly 3-4 orders of magnitude fewer Hamiltonian evaluations and 2-3 orders of magnitude fewer Hamiltonian applications than standard ML-MCTDH and 2-3/1-2 orders of magnitude fewer evaluations/applications than approaches that use improved regularization schemes. Finally, we consider a series of significantly more challenging multi-spin-boson models that require much larger numbers of single-particle functions with wavefunctions containing up to ∼1.3×109 parameters to obtain accurate dynamics.

Multiple Stable Isoprene-Ozone Complexes Reveal Complex Entrance Channel Dynamics in the Isoprene + Ozone Reaction.

Accurately characterizing isoprene ozonolysis continues to challenge atmospheric chemists. The reaction is believed to be a spontaneous, concerted cycloaddition. However, little information is available about the entrance channel and isoprene-ozone complexes thought to define the long-range portion of the reaction coordinate. Our coupled cluster and auxiliary field quantum Monte Carlo calculations predict multiple stable isoprene-ozone van der Waals complexes for trans-isoprene in the gas phase with moderate association energies. These results indicate that long-range dynamics in the isoprene-ozone entrance channel can impact the overall reaction in the troposphere and provide the spectroscopic information necessary to extend the microwave characterization of isoprene ozonolysis to prereactive complexes. At the air-water interface, Born-Oppenheimer molecular dynamics simulations indicate that the cycloaddition reaction between ozone and trans-isoprene follows a stepwise mechanism, which is quite distinct from our proposed gas-phase mechanism and occurs on a femtosecond time scale. The stepwise nature of isoprene ozonolysis on the aqueous surface is more consistent with the DeMore mechanism than with the Criegee mechanism suggested by the gas-phase calculations, suggesting that the reaction media may play an important role in the reaction. Overall, these predictions aim to provide a missing fundamental piece of molecular insight into isoprene ozonolysis, which has broad tropospheric implications due to its critical role as a nighttime source of hydroxyl radicals.

Molecular Engineering of Chromophores to Enable Triplet-Triplet Annihilation Upconversion.

Triplet-triplet annihilation upconversion (TTA-UC) is an unconventional photophysical process that yields high-energy photons from low-energy incident light and offers pathways for innovation across many technologies, including solar energy harvesting, photochemistry, and optogenetics. Within aromatic organic chromophores, TTA-UC is achieved through several consecutive energy conversion events that ultimately fuse two triplet excitons into a singlet exciton. In chromophores where the singlet exciton is roughly isoergic with two triplet excitons, the limiting step is the triplet-triplet annihilation pathway, where the kinetics and yield depend sensitively on the energies of the lowest singlet and triplet excited states. Herein we report up to 40-fold improvements in upconversion quantum yields using molecular engineering to selectively tailor the relative energies of the lowest singlet and triplet excited states, enhancing the yield of triplet-triplet annihilation and promoting radiative decay of the resulting singlet exciton. Using this general and effective strategy, we obtain upconversion yields with red emission that are among the highest reported, with remarkable chemical stability under ambient conditions.

Depletion of Two-Level Systems in Ultrastable Computer-Generated Glasses.

Amorphous solids exhibit quasiuniversal low temperature anomalies whose origin has been ascribed to localized tunneling defects. Using an advanced Monte Carlo procedure, we create in silico glasses spanning from hyperquenched to ultrastable glasses. Using a multidimensional path-finding protocol, we locate tunneling defects with energy splittings smaller than k_{B}T_{Q}, with T_{Q} the temperature below which quantum effects are relevant (T_{Q}≈1 K in most experiments). We find that as the stability of a glass increases, its energy landscape as well as the manner in which it is probed tend to deplete the density of tunneling defects, as observed in recent experiments. We explore the real-space nature of tunneling defects, and find that they are mostly localized to a few atoms, but are occasionally dramatically delocalized.

Stochastic resolution-of-the-identity auxiliary-field quantum Monte Carlo: Scaling reduction without overhead.

We explore the use of the stochastic resolution-of-the-identity (sRI) with the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) method. sRI is combined with four existing local energy evaluation strategies in ph-AFQMC, namely, (1) the half-rotated electron repulsion integral tensor (HR), (2) Cholesky decomposition (CD), (3) tensor hypercontraction (THC), or (4) low-rank factorization (LR). We demonstrate that HR-sRI achieves no scaling reduction, CD-sRI scales as O(N3), and THC-sRI and LR-sRI scale as O(N2), albeit with a potentially large prefactor. Furthermore, the walker-specific extra memory requirement in CD is reduced from O(N3) to O(N2) with sRI, while sRI-based THC and LR algorithms lead to a reduction from O(N2) extra memory to O(N). Based on numerical results for one-dimensional hydrogen chains and water clusters, we demonstrated that, along with the use of a variance reduction technique, CD-sRI achieves cubic-scaling without overhead. In particular, we find that for the systems studied, the observed scaling of standard CD is O(N3-4), while for CD-sRI, it is reduced to O(N2-3). Once a memory bottleneck is reached, we expect THC-sRI and LR-sRI to be preferred methods due to their quadratic-scaling memory requirements and their quadratic-scaling of the local energy evaluation (with a potentially large prefactor). The theoretical framework developed here should facilitate large-scale ph-AFQMC applications that were previously difficult or impossible to carry out with standard computational resources.

Microscopic model of the doping dependence of linewidths in monolayer transition metal dichalcogenides.

A fully microscopic model of the doping-dependent exciton and trion linewidths in the absorption spectra of monolayer transition metal dichalcogenides in the low temperature and low-doping regime is explored. The approach is based on perturbation theory and avoids the use of phenomenological parameters. In the low-doping regime, we find that the trion linewidth is relatively insensitive to doping levels, while the exciton linewidth increases monotonically with doping. On the other hand, we argue that the trion linewidth shows a somewhat stronger temperature dependence. The magnitudes of the linewidths are likely to be masked by phonon scattering for T ≥ 20 K in encapsulated samples in the low-doping regime. We discuss the breakdown of perturbation theory, which should occur at relatively low-doping levels and low temperatures. Our work also paves the way toward understanding a variety of related scattering processes, including impact ionization and Auger scattering in clean 2D samples.

Multiset Matrix Product State Calculations Reveal Mobile Franck-Condon Excitations Under Strong Holstein-Type Coupling.

We show that the dynamics of (vertical) Franck-Condon excitations in the regime where Holstein-coupled vibrational modes mix strongly with electronic degrees of freedom sharply contrasts with the known self-localized behavior of vibrationally relaxed excitations. Instead, the strongly coupled modes are found to periodically induce resonances between interacting electronic sites, during which effective excitation transfer occurs, allowing Franck-Condon excitations to attain substantial mean square displacements under conditions where relaxed excitations are essentially trapped to a single site. In demonstrating this behavior, we employ a multiset matrix product state formalism. We find this tensor network state method to be a remarkably efficient and accurate approach for the notoriously difficult problem posed by the Holstein model in the regime where the electronic coupling, the vibrational quantum, and the vibrational reorganization energy are comparable in magnitude.