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Classical nonlinear dynamical systems are often characterized by their steady-state probability distribution functions (PDFs). Typically, PDFs are accumulated from numerical simulations that involve solving the underlying dynamical equations of motion using integration techniques. An alternative procedure, direct statistical simulation (DSS), solves for the statistics directly. One approach to DSS is the Fokker-Planck Equation (FPE), which can be used to find the PDF of classical dynamical systems. Here, we investigate the utility of Noisy Intermediate-Scale Quantum (NISQ) computers to find steady-state solutions to the FPE. We employ the Quantum Phase Estimation (QPE) and the Variational Quantum Eigensolver (VQE) algorithms to find the zero-mode of the FPE for one-dimensional Ornstein-Uhlenbeck problems enabling comparison with exact solutions. The quantum computed steady-state probability distribution functions (PDFs) are demonstrated to be in reasonable agreement with the classically computed PDFs. We conclude with a discussion of potential extensions to higher-dimensional dynamical systems., Comment: 14 pages, 6 figures

The ability to perform ab initio molecular dynamics simulations using potential energies calculated on quantum computers would allow virtually exact dynamics for chemical and biochemical systems, with substantial impacts on the fields of catalysis and biophysics. However, noisy hardware, the costs of computing gradients, and the number of qubits required to simulate large systems present major challenges to realizing the potential of dynamical simulations using quantum hardware. Here, we demonstrate that some of these issues can be mitigated by recent advances in machine learning. By combining transfer learning with techniques for building machine-learned potential energy surfaces, we propose a new path forward for molecular dynamics simulations on quantum hardware. We use transfer learning to reduce the number of energy evaluations that use quantum hardware by first training models on larger, less accurate classical datasets and then refining them on smaller, more accurate quantum datasets. We demonstrate this approach by training machine learning models to predict a molecule's potential energy using Behler-Parrinello neural networks. When successfully trained, the model enables energy gradient predictions necessary for dynamics simulations that cannot be readily obtained directly from quantum hardware. To reduce the quantum resources needed, the model is initially trained with data derived from low-cost techniques, such as Density Functional Theory, and subsequently refined with a smaller dataset obtained from the optimization of the Unitary Coupled Cluster ansatz. We show that this approach significantly reduces the size of the quantum training dataset while capturing the high accuracies needed for quantum chemistry simulations., Comment: 1- pages, 12 figures

The field of two-dimensional (2D) materials has grown dramatically in the last two decades. 2D materials can be utilized for a variety of next-generation optoelectronic, spintronic, clean energy, and quantum computation applications. These 2D structures, which are often exfoliated from layered van der Waals (vdW) materials, possess highly inhomogeneous electron densities and can possess short- and long-range electron correlations. The complexities of 2D materials make them challenging to study with standard mean-field electronic structure methods such as density functional theory (DFT), which relies on approximations for the unknown exchange-correlation functional. In order to overcome the limitations of DFT, highly accurate many-body electronic structure approaches such as Diffusion Monte Carlo (DMC) can be utilized. In the past decade, DMC has been used to calculate accurate magnetic, electronic, excitonic, and topological properties in addition to accurately capturing interlayer interactions and cohesion and adsorption energetics of 2D materials. This approach has been applied to 2D systems of wide interest including graphene, phosphorene, MoS$_2$, CrI$_3$, VSe$_2$, GaSe, GeSe, borophene, and several others. In this review article, we highlight some successful recent applications of DMC to 2D systems for improved property predictions beyond standard DFT.

The intrinsic dynamics of most proteins are central to their function. Protein tyrosine kinases such as Abl1 undergo significant conformational changes that modulate their activity in response to different stimuli. These conformational changes constitute a conserved mechanism for self-regulation that dramatically impacts kinases' affinities for inhibitors. Few studies have attempted to extensively sample the pathways and elucidate the mechanisms that underlie kinase inactivation. Seeking to bridge this knowledge gap, we present a thorough analysis of the ``DFG flip'' inactivation pathway in Abl1 kinase. By leveraging the power of the Weighted Ensemble methodology, which accelerates sampling without the use of biasing forces, we have comprehensively simulated DFG flip events in Abl1 and its inhibitor-resistant variants, revealing a rugged landscape punctuated by potentially druggable intermediate states. Through our strategy, we successfully simulated dozens of uncorrelated DFG flip events distributed along two principal pathways, identified the molecular mechanisms that govern them, and measured their relative probabilities. Further, we show that the compound Glu255Lys/Val Thr315Ile Abl1 variants owe their inhibitor resistance phenotype to an increase in the free energy barrier associated with completing the DFG flip. This barrier stabilizes Abl1 variants in conformations that can lead to loss of binding for Type-II inhibitors such as Imatinib or Ponatinib. Finally, we contrast our Abl1 observations with the relative state distributions and propensity for undergoing a DFG flip of evolutionarily-related protein tyrosine kinases with diverging Type-II inhibitor binding affinities. Altogether, we expect that our work will be of significant importance for protein tyrosine kinase inhibitor discovery., Comment: 34 pages, 10 figures

The Chemical Master Equation (CME) provides a highly accurate, yet extremely resource-intensive representation of a stochastic chemical reaction network and its kinetics due to the exponential scaling of its possible states with the number of reacting species. In this work, we demonstrate how quantum algorithms and hardware can be employed to model stochastic chemical kinetics as described by the CME using the Schl\"ogl Model of a trimolecular reaction network as an illustrative example. To ground our study of the performance of our quantum algorithms, we first determine a range of suitable parameters for constructing the stochastic Schl\"ogl operator in the mono- and bistable regimes of the model using a classical computer and then discuss the appropriateness of our parameter choices for modeling approximate kinetics on a quantum computer. We then apply the Variational Quantum Deflation (VQD) algorithm to evaluate the smallest-magnitude eigenvalues, $\lambda_0$ and $\lambda_1$, which describe the transition rates of both the mono- and bi-stable systems, and the Quantum Phase Estimation (QPE) algorithm combined with the Variational Quantum Singular Value Decomposition (VQSVD) algorithm to estimate the zeromode (ground state) of the bistable case. Our quantum computed results from both noisy and noiseless quantum simulations agree within a few percent with the classically computed eigenvalues and zeromode. Altogether, our work outlines a practical path toward the quantum solution of exponentially complex stochastic chemical kinetics problems and other related stochastic differential equations.

Descriptors are physically-inspired schemes for representing atomistic systems that play a central role in the construction of models of potential energy surfaces. Although physical intuition can be flexibly encoded into descriptor schemes, they are generally ultimately guided only by the spatial or topological arrangement of atoms in the system. Here, we propose a novel approach for the optimization of descriptors based on encoding information about geodesic distances along potential energy manifolds into the hyperparameters of commonly used descriptor schemes. To accomplish this, we combine two ideas: (1) a differential-geometric approach for the fast estimation of approximate geodesic distances; and (2) an information-theoretic evaluation metric - information imbalance - for measuring the shared information between two distance measures. Using the MD22 datasets of ethanol, malonaldehyde, and aspirin, we first show that Euclidean (in Cartesian coordinates) and geodesic distances are inequivalent distance measures, indicating the need for updated ground-truth distance measures that go beyond the Euclidean distance. We then utilize a Bayesian optimization framework to show that descriptors (in this case, atom-centered symmetry functions) can be optimized to maximally express a certain type of distance information, such as Euclidean or geodesic information. We also show that modifying the Bayesian optimization algorithm to minimize a combined Euclidean+geodesic objective function can yield descriptors that not only express both Euclidean and geodesic distance information simultaneously, but in fact resolve substantial disagreements between descriptors optimized to encode only one type of distance measure. We discuss the relevance of our approach to the design of more physically rich and informative descriptors that can encode useful, alternative information about molecular systems.

Stochastic electronic structure theories, e.g., Quantum Monte Carlo methods, enable highly accurate total energy calculations which in principle can be used to construct highly accurate potential energy surfaces. However, their stochastic nature poses a challenge to the computation and use of forces and Hessians, which are typically required in algorithms for minimum-energy pathway (MEP) and transition state (TS) identification, such as the nudged-elastic band (NEB) algorithm and its climbing image formulation. Here, we present strategies that utilize the surrogate Hessian line-search method - previously developed for QMC structural optimization - to efficiently identify MEP and TS structures without requiring force calculations at the level of the stochastic electronic structure theory. By modifying the surrogate Hessian algorithm to operate in path-orthogonal subspaces and on saddle points, we show that it is possible to identify MEPs and TSs using a force-free QMC approach. We demonstrate these strategies via two examples, the inversion of the ammonia molecule and an SN2 reaction. We validate our results using Density Functional Theory- and coupled cluster-based NEB calculations. We then introduce a hybrid DFT-QMC approach to compute thermodynamic and kinetic quantities - free energy differences, rate constants, and equilibrium constants - that incorporates stochastically-optimized structures and their energies, and show that this scheme improves upon DFT accuracy. Our methods generalize straightforwardly to other systems and other high-accuracy theories that similarly face challenges computing energy gradients, paving the way for highly accurate PES mapping, transition state determination, and thermodynamic and kinetic calculations, at significantly reduced computational expense.

The complicated ways in which electrons interact in many-body systems such as molecules and materials have long been viewed through the lens of local electron correlation and associated correlation functions. However, quantum information science has demonstrated that more global diagnostics of quantum states, like the entanglement entropy, can provide a complementary and clarifying lens on electronic behavior. One particularly useful measure that can be used to distinguish between quantum and classical sources of entanglement is the accessible entanglement, the entanglement available as a quantum resource for systems subject to conservation laws, such as fixed particle number, due to superselection rules. In this work, we introduce an algorithm and demonstrate how to compute accessible and symmetry-resolved entanglements for interacting fermion systems. This is accomplished by combining an incremental version of the swap algorithm with a recursive Auxiliary Field Quantum Monte Carlo algorithm recently developed by the authors. We apply these tools to study the pairing and charge density waves exhibited in the paradigmatic attractive Hubbard model via entanglement. We find that the particle and spin symmetry-resolved entanglements and their related full probability distribution functions show very clear - and unique - signatures of the underlying electronic behavior even when those features are less pronounced in more conventional correlation functions. Overall, this work provides a systematic means of characterizing the entanglement within quantum systems that can grant a deeper understanding of the complicated electronic behavior that underlies quantum phase transitions and crossovers in many-body systems., Comment: 19 pages, 9 figures

The relationship between the thermodynamic and computational characteristics of dynamical physical systems has been a major theoretical interest since at least the 19th century, and has been of increasing practical importance as the energetic cost of digital devices has exploded over the last half century. One of the most important thermodynamic features of real-world computers is that they operate very far from thermal equilibrium, in finite time, with many quickly (co-)evolving degrees of freedom. Such computers also must almost always obey multiple physical constraints on how they work. For example, all modern digital computers are periodic processes, governed by a global clock. Another example is that many computers are modular, hierarchical systems, with strong restrictions on the connectivity of their subsystems. This properties hold both for naturally occurring computers, like brains or Eukaryotic cells, as well as digital systems. These features of real-world computers are absent in 20th century analyses of the thermodynamics of computational processes, which focused on quasi-statically slow processes. However, the field of stochastic thermodynamics has been developed in the last few decades - and it provides the formal tools for analyzing systems that have exactly these features of real-world computers. We argue here that these tools, together with other tools currently being developed in stochastic thermodynamics, may help us understand at a far deeper level just how the fundamental physical properties of dynamic systems are related to the computation that they perform., Comment: Updated version

The ability to manipulate electronic spin channels in 2D materials is crucial for realizing next-generation spintronics. Spin filters are spintronic components that polarize spins using external fields or material properties like magnetism. Recently, topological protection from backscattering has emerged as an enticing feature through which to enhance the robustness of 2D spin filters. In this work, we propose and then characterize one of the first 2D topological spin filters: bilayer CrI3/1T'-WTe2 (BLCW). To do so, we use a combination of DFT, maximally localized Wannier functions, and quantum transport simulations to demonstrate that the BLCW satisfies the principal criteria for being a topological spin filter; namely that it is gapless, exhibits spin-polarized charge transfer (SPCT) from WTe2 to CrI3 that renders the BLCW metallic, and has a topological boundary which retains the edge conductance of monolayer (ML) 1T'-WTe2. We observe that the atomic magnetic moments on Cr from DFT are approximately 3.2 mB/Cr in the BL compared to 2.9 mB/Cr with small negative ferromagnetic (FM) moments induced on the W atoms in freestanding ML CrI3. Subtracting the charge/spin densities of the constituent ML's from those of the BLCW further reveals SOC-enhanced SPCT from WTe2 to CrI3. We find that the BLCW is topologically trivial by showing that its Chern number is zero. Lastly, we show that interfacial scattering at the boundary between the terraced materials does not remove WTe2's edge conductance. This evidence indicates that BLCW is gapless, magnetic, and topologically trivial, meaning that a terraced WTe2/CrI3 BL heterostructure in which only a portion of a WTe2 ML is topped with CrI3 is a promising candidate for a 2D topological spin filter. Our results further suggest that 1D chiral edge states may be realized by stacking FM ML's, like CrI3, atop 2D nonmagnetic Weyl semimetals like 1T'-WTe2.

The exchange-correlation (XC) functional in density functional theory is used to approximate multi-electron interactions. A plethora of different functionals is available, but nearly all are based on the hierarchy of inputs commonly referred to as "Jacob's ladder." This paper introduces an approach to construct XC functionals with inputs from convolutions of arbitrary kernels with the electron density, providing a route to move beyond Jacob's ladder. We derive the variational derivative of these functionals, showing consistency with the generalized gradient approximation (GGA), and provide equations for variational derivatives based on multipole features from convolutional kernels. A proof-of-concept functional, PBEq, which generalizes the PBE$\alpha$ framework where $\alpha$ is a spatially-resolved function of the monopole of the electron density, is presented and implemented. It allows a single functional to use different GGAs at different spatial points in a system, while obeying PBE constraints. Analysis of the results underlines the importance of error cancellation and the XC potential in data-driven functional design. After testing on small molecules, bulk metals, and surface catalysts, the results indicate that this approach is a promising route to simultaneously optimize multiple properties of interest.

This paper presents a novel approach for predicting the relative populations of protein conformations using AlphaFold 2, an AI-powered method that has revolutionized biology by enabling the accurate prediction of protein structures. While AlphaFold 2 has shown exceptional accuracy and speed, it is designed to predict proteins' single ground state conformations and is limited in its ability to predict fold switching and the effects of mutations on conformational landscapes. Here, we demonstrate how AlphaFold 2 can directly predict the relative populations of different conformations of proteins and even accurately predict changes in those populations induced by mutations by subsampling multiple sequence alignments. We tested our method against NMR experiments on two proteins with drastically different amounts of available sequence data, Abl1 kinase and the granulocyte-macrophage colony-stimulating factor, and predicted changes in their relative state populations with accuracies in excess of 80%. Our method offers a fast and cost-effective way to predict protein conformations and their relative populations at even single point mutation resolution, making it a useful tool for pharmacology, analyzing NMR data, and studying the effects of evolution., Comment: 26 pages, 9 figures

Many experimentally-accessible, finite-sized interacting quantum systems are most appropriately described by the canonical ensemble of statistical mechanics. Conventional numerical simulation methods either approximate them as being coupled to a particle bath, or use projective algorithms which may suffer from non-optimal scaling with system size or large algorithmic prefactors. In this paper, we introduce a highly stable, recursive Auxiliary Field Quantum Monte Carlo approach that can directly simulate systems in the canonical ensemble. We apply the method to the fermion Hubbard model in one and two spatial dimensions in a regime known to exhibit a significant "sign" problem and find improved performance over existing approaches including rapid convergence to ground state expectation values. The effects of excitations above the ground state are quantified using an estimator-agnostic approach including studying the temperature dependence of the purity and overlap fidelity of the canonical and grand canonical density matrices. As an important application, we show that thermometry approaches often exploited in ultra-cold atoms that employ an analysis of the velocity distribution in the grand canonical ensemble may be subject to errors leading to an under-estimation of extracted temperatures with respect to the Fermi temperature., Comment: 14 pages, 7 figures, and Supplemental Information with key derivations. For associated data and code repository see: https://github.com/DelMaestroGroup/papers-code-CanEnsAFQMC

Diffusion Monte Carlo (DMC) is one of the most accurate techniques available for calculating the electronic properties of molecules and materials, yet it often remains a challenge to economically compute forces using this technique. As a result, ab initio molecular dynamics simulations and geometry optimizations that employ Diffusion Monte Carlo forces are often out of reach. One potential approach for accelerating the computation of "DMC forces" is to machine learn these forces from DMC energy calculations. In this work, we employ Behler-Parrinello Neural Networks to learn DMC forces from DMC energy calculations for geometry optimization and molecular dynamics simulations of small molecules. We illustrate the unique challenges that stem from learning forces without explicit force data and from noisy energy data by making rigorous comparisons of potential energy surface, dynamics, and optimization predictions among ab initio Density Functional Theory (DFT) simulations and machine learning models trained on DFT energies with forces, DFT energies without forces, and DMC energies without forces. We show for three small molecules - C2, H2O, and CH3Cl - that machine learned DMC dynamics can reproduce average bond lengths and angles within a few percent of known experimental results at a 100th of the typical cost. Our work describes a much-needed means of performing dynamics simulations on high-accuracy, DMC PESs and for generating DMC-quality molecular geometries given current algorithmic constraints.

Diffusion Monte Carlo (DMC) is being recognized as a higher-accuracy, albeit more computationally expensive, alternative to Density Functional Theory (DFT) for energy predictions of catalytic systems. A major computational bottleneck in the use of DMC for catalysis is the need to perform finite-size extrapolations by simulating increasingly large periodic cells (supercells) to eliminate many-body finite-size effects and obtain energies in the thermodynamic limit. Here, we show that this computational cost can be significantly reduced by leveraging the cancellation of many-body finite-size errors that accompanies the evaluation of energy differences when calculating quantities like binding energies and mapping potential energy surfaces. We test the error cancellation and convergence in two well-known adsorbate/slab systems, H2O/LiH(001) and CO/Pt(111). Based on this, we identify strategies for obtaining binding energies in the thermodynamic limit that optimize error cancellation to balance accuracy and computational efficiency. We then predict the correct order of adsorption site preference on CO/Pt(111), a challenging problem for DFT. Our accurate, inexpensive DMC calculations recover the top > bridge > hollow site order, in agreement with experimental observations. We proceed to map the potential energy surface of CO hopping between Pt(111) adsorption sites. This reveals the existence of an L-shaped top-bridge-hollow diffusion trajectory characterized by energy barriers that provide an additional kinetic justification for experimental observations of CO/Pt(111) adsorption. Overall, this work demonstrates that it is routinely possible to achieve order-of-magnitude speedups and memory savings in DMC calculations by taking advantage of error cancellation in the calculation of energy differences that are ubiquitous in heterogeneous catalysis and surface chemistry more broadly.

Key to being able to accurately model the properties of realistic materials is being able to predict their properties in the thermodynamic limit. Nevertheless, because most many-body electronic structure methods scale as a high-order polynomial, or even exponentially, with system size, directly simulating large systems in their thermodynamic limit rapidly becomes computationally intractable. As a result, researchers typically estimate the properties of large systems that approach the thermodynamic limit by extrapolating the properties of smaller, computationally-accessible systems based on relatively simple scaling expressions. In this work, we employ Gaussian processes to more accurately and efficiently extrapolate many-body simulations to their thermodynamic limit. We train our Gaussian processes on Smooth Overlap of Atomic Positions (SOAP) descriptors to extrapolate the energies of one-dimensional hydrogen chains obtained using two high-accuracy many-body methods: Coupled Cluster theory and Auxiliary Field Quantum Monte Carlo (AFQMC). In so doing, we show that Gaussian processes trained on relatively short, 10-30-atom chains can predict the energies of both homogeneous and inhomogeneous hydrogen chains in their thermodynamic limit with sub-milliHartree accuracy. Unlike standard scaling expressions, our GPR-based approach is highly generalizable given representative training data and is not dependent on systems' geometries or dimensionality. This work highlights the potential for machine learning to correct for the finite size effects that routinely complicate the interpretation of finite size many-body simulations., Comment: 14 pages, 8 figures

The first magnetic 2D material discovered, monolayer (ML) CrI$_3$, is particularly fascinating due to its ground state ferromagnetism. Yet, because monolayer materials are difficult to probe experimentally, much remains unresolved about ML CrI$_{3}$'s structural, electronic, and magnetic properties. Here, we leverage Density Functional Theory (DFT) and high-accuracy Diffusion Monte Carlo (DMC) simulations to predict lattice parameters, magnetic moments, and spin-phonon and spin-lattice coupling of ML CrI$_{3}$. We exploit a recently developed surrogate Hessian DMC line search technique to determine CrI$_{3}$'s monolayer geometry with DMC accuracy, yielding lattice parameters in good agreement with recently-published STM measurements - an accomplishment given the $\sim 10$% variability in previous DFT-derived estimates depending upon the functional. Strikingly, we find previous DFT predictions of ML CrI$_3$'s magnetic spin moments are correct on average across a unit cell, but miss critical local spatial fluctuations in the spin density revealed by more accurate DMC. DMC predicts magnetic moments in ML CrI$_3$ are 3.62 $\mu_B$ per chromium and -0.145 $\mu_B$ per iodine; both larger than previous DFT predictions. The large disparate moments together with the large spin-orbit coupling of CrI$_3$'s I-$\textit{p}$ orbital suggests a ligand superexchange-dominated magnetic anisotropy in ML CrI$_3$, corroborating recent observations of magnons in its 2D limit. We also find ML CrI$_3$ exhibits a substantial spin-phonon coupling of $\sim$3.32 cm$^{-1}$. Our work thus establishes many of ML CrI$_{3}$'s key properties, while also continuing to demonstrate the pivotal role DMC can assume in the study of magnetic and other 2D materials., Comment: 16 pages, 13 figures

Ion traps are promising architectures for implementing scalable quantum computing, but they suffer from excessive "anomalous" heating that prevents their full potential from being realized. This heating, which is orders of magnitude larger than that expected from Johnson-Nyquist noise, results in ion motion that leads to decoherence and reduced fidelity in quantum logic gates. The exact origin of anomalous heating is an open question, but experiments point to adsorbates on trap electrodes as a likely source. Many different models of anomalous heating have been proposed, but these models have yet to pinpoint the atomistic origin of the experimentally-observed $1/\omega$ electric field noise scaling observed in ion traps at frequencies between 0.1-10 MHz. In this work, we perform the first computational study of the ion trap electric field noise produced by the motions of multiple monolayers of adsorbates described by first principles potentials. In so doing, we show that correlated adsorbate motions play a definitive role in producing $1/\omega$ noise and identify candidate collective adsorbate motions, including translational and rotational motions of adsorbate patches and multilayer exchanges, that give rise to $1/\omega$ scaling at the MHz frequencies typically employed in ion traps. These results demonstrate that multi-adsorbate systems, even simple ones, can give rise to a set of activated motions that can produce the $1/\omega$ noise observed in ion traps and that collective, rather than individual, adsorbate motions are much more likely to give rise to low-frequency heating.

Finite temperature auxiliary field-based Quantum Monte Carlo methods, including Determinant Quantum Monte Carlo (DQMC) and Auxiliary Field Quantum Monte Carlo (AFQMC), have historically assumed pivotal roles in the investigation of the finite temperature phase diagrams of a wide variety of multidimensional lattice models and materials. Despite their utility, however, these techniques are typically formulated in the grand canonical ensemble, which makes them difficult to apply to condensates like superfluids and difficult to benchmark against alternative methods that are formulated in the canonical ensemble. Working in the grand canonical ensemble is furthermore accompanied by the increased overhead associated with having to determine the chemical potentials that produce desired fillings. Given this backdrop, in this work, we present a new recursive approach for performing AFQMC simulations in the canonical ensemble that does not require knowledge of chemical potentials. To derive this approach, we exploit the convenient fact that AFQMC solves the many-body problem by decoupling many-body propagators into integrals over one-body problems to which non-interacting theories can be applied. We benchmark the accuracy of our technique on illustrative Bose and Fermi Hubbard models and demonstrate that it can converge more quickly to the ground state than grand canonical AFQMC simulations. We believe that our novel use of HS-transformed operators to implement algorithms originally derived for non-interacting systems will motivate the development of a variety of other methods and anticipate that our technique will enable direct performance comparisons against other many-body approaches formulated in the canonical ensemble., Comment: 15 pages, 4 figures

The ability to accurately predict the finite temperature properties of realistic quantum solids is central to uncovering new phases and engineering materials with novel properties. Nonetheless, there remain comparatively few many-body techniques capable of elucidating the finite temperature physics of solids from first principles. In this work, we take a significant step towards developing such a technique by generalizing our previous, fully ab initio finite temperature Auxiliary Field Quantum Monte Carlo (FT-AFQMC) method to model periodic solids and employing it to uncover the finite temperature physics of periodic hydrogen chains. Based upon our calculations of these chains' many-body thermodynamic quantities and correlation functions, we outline their metal-insulator and magnetic ordering as a function of both H-H bond distance and temperature. At low temperatures approaching the ground state, we observe both metal-insulator and ferromagnetic-antiferromagnetic crossovers at bond lengths between 0.5 and 0.75 {\AA}. We then demonstrate how this low-temperature ordering evolves into a metallic phase with decreasing magnetic order at higher temperatures. By comparing the features we observe to those previously seen in one-dimensional, half-filled Hubbard models at finite temperature and in ground state hydrogen chains, interestingly, we identify signatures of the Pomeranchuk effect in hydrogen chains for the first time and show that spin and charge excitations that typically arise at distinct temperatures in the Hubbard model are indistinguishably coupled in these systems. Beyond qualitatively revealing the many-body phase behavior of hydrogen chains, our efforts shed light on the further theoretical developments that will be required to construct the phase diagrams of the more complex transition metal, lanthanide, and actinide solids of longstanding interest to physicists., Comment: 52 pages, 12 figures

We review recent advances in the capabilities of the open source ab initio Quantum Monte Carlo (QMC) package QMCPACK and the workflow tool Nexus used for greater efficiency and reproducibility. The auxiliary field QMC (AFQMC) implementation has been greatly expanded to include k-point symmetries, tensor-hypercontraction, and accelerated graphical processing unit (GPU) support. These scaling and memory reductions greatly increase the number of orbitals that can practically be included in AFQMC calculations, increasing accuracy. Advances in real space methods include techniques for accurate computation of band gaps and for systematically improving the nodal surface of ground state wavefunctions. Results of these calculations can be used to validate application of more approximate electronic structure methods including GW and density functional based techniques. To provide an improved foundation for these calculations we utilize a new set of correlation-consistent effective core potentials (pseudopotentials) that are more accurate than previous sets; these can also be applied in quantum-chemical and other many-body applications, not only QMC. These advances increase the efficiency, accuracy, and range of properties that can be studied in both molecules and materials with QMC and QMCPACK.

We present first principles calculations of the magnetic and orbital properties of Ba$_2$NaOsO$_6$ (BNOO), a 5$d^1$ Mott insulator with strong spin orbit coupling (SOC) in its low temperature emergent quantum phases. Our computational method takes into direct consideration recent NMR results that established that BNOO develops a local octahedral distortion preceding the formation of long range magnetic order. We found that the two-sublattice canted ferromagnetic ground state identified in Lu \etal, Nature Comm. {\bf 8}, 14407 (2017) is accompanied by a two-sublattice staggered orbital ordering pattern in which the $t_{2g}$ orbitals are selectively occupied as a result of strong spin orbit coupling. The staggered orbital order found here using first principles calculations asserts the previous proposal of Chen \etal, Phys. Rev. B {\bf 82}, 174440 (2010) and Lu \etal, Nature Comm. {\bf 8}, 14407 (2017), that two-sublattice magnetic structure is the very manifestation of staggered quadrupolar order. Therefore, our results affirm the essential role of multipolar spin interactions in the microscopic description of magnetism in systems with locally entangled spin and orbital degrees of freedom., Comment: 6 pages, 4 Figures, accepted for publication in PRB

Layered perovskite ruthenium oxides exhibit a striking series of metal-insulator and magnetic-nonmagnetic phase transitions easily tuned by temperature, pressure, epitaxy, and nonlinear drive. In this work, we combine results from two complementary state of the art many-body methods, Auxiliary Field Quantum Monte Carlo and Dynamical Mean Field Theory, to determine the low-temperature phase diagram of Ca$_2$RuO$_4$. Both methods predict a low temperature, pressure-driven metal-insulator transition accompanied by a ferromagnetic-antiferromagnetic transition. The properties of the ferromagnetic state vary non-monotonically with pressure and are dominated by the ruthenium $d_{xy}$ orbital, while the properties of the antiferromagnetic state are dominated by the $d_{xz}$ and $d_{yz}$ orbitals. Differences of detail in the predictions of the two methods are analyzed. This work is theoretically important as it presents the first application of the Auxiliary Field Quantum Monte Carlo method to an orbitally-degenerate system with both Mott and Hunds physics, and provides an important comparison of the Dynamical Mean Field and Auxiliary Field Quantum Monte Carlo methods., Comment: 6 pages, 4 figures

We present first principles calculations of the electrostatic properties of Ba$_2$NaOsO$_6$ (BNOO), a 5$d^1$ Mott insulator with strong spin orbit coupling (SOC) in its low temperature quantum phases. In light of recent NMR experiments showing that BNOO develops a local octahedral distortion that is accompanied by the emergence of an electric field gradient (EFG) and precedes the formation of long range magnetic order [Lu et al., Nature Comm. 8, 14407 (2017), Liu et al., Phys. Rev. B. 97, 224103 (2018), Liu et al., Physica B. 536, 863 (2018)], we calculated BNOO's EFG tensor for several different model distortions. The local orthorhombic distortion that we identified as mostly strongly agreeing with experiment corresponds to a Q2 distortion mode of the Na-O octahedra, in agreement with conclusions given in [Liu et al., Phys. Rev. B. 97, 224103 (2018)]. Furthermore, we found that the EFG is insensitive to the type of underlying magnetic order. By combining NMR results with first principles modeling, we have thus forged a more complete understanding of BNOO's structural and magnetic properties, which could not be achieved based upon experiment or theory alone., Comment: 11 pages, Submitted to Physical Review B

Molecular data systems have the potential to store information at dramatically higher density than existing electronic media. Some of the first experimental demonstrations of this idea have used DNA, but nature also uses a wide diversity of smaller non-polymeric molecules to preserve, process, and transmit information. In this paper, we present a general framework for quantifying chemical memory, which is not limited to polymers and extends to mixtures of molecules of all types. We show that the theoretical limit for molecular information is two orders of magnitude denser by mass than DNA, although this comes with different practical constraints on total capacity. We experimentally demonstrate kilobyte-scale information storage in mixtures of small synthetic molecules, and we consider some of the new perspectives that will be necessary to harness the information capacity available from the vast non-genomic chemical space.

In the study of strongly-correlated, many-electron systems, the Hubbard Kanamori (HK) model has emerged as one of the prototypes for transition metal oxide physics. The model is multi-band in nature and contains Hund's coupling terms, which have pronounced effects on metal-insulator transitions, high-temperature superconductivity, and other physical properties. In the following, we present a complete theoretical framework for treating the HK model using the ground state Auxiliary Field Quantum Monte Carlo (AFQMC) method and analyze its performance on few-band models whose parameters approximate those observed in ruthenate, rhodates, and other materials exhibiting Hund's physics. Unlike previous studies, the constrained path and phaseless approximations are used to respectively control the sign and phase problems, which enables high accuracy modeling of the HK model's ground state properties within parameter regimes of experimental interest. We demonstrate that, after careful consideration of the Hubbard-Stratonovich transformations and trial wave functions employed, relative errors in the energy of less than 1% can routinely be achieved for moderate to large values of the Hund's coupling constant. Crucially, our methodology also accurately predicts magnetic ordering and phase transitions. The results presented open the door to more predictive modeling of Hund's physics within a wide range of strongly-correlated materials using AFQMC., Comment: 14 pages, 7 figures, 2 tables

In order to realize the full potential of ion trap quantum computers, an improved understanding is required of the motional heating that trapped ions experience. Experimental studies of the temperature-, frequency-, and ion--electrode distance-dependence of the electric field noise responsible for motional heating, as well as the noise before and after ion bombardment cleaning of trap electrodes, suggest that fluctuations of adsorbate dipoles are a likely source of so-called `anomalous heating,' or motional heating of the trapped ions at a rate much higher than the Johnson noise limit. Previous computational studies have investigated how the fluctuation of model adsorbate dipoles affects anomalous heating. However, the way in which specific adsorbates affect the electric field noise has not yet been examined, and an electric dipole model employed in previous studies is only accurate for a small subset of possible adsorbates. Here, we analyze the behavior of both in-plane and out-of-plane vibrational modes of fifteen adsorbate--electrode combinations within the independent fluctuating dipole model, utilizing accurate first principles computational methods to determine the surface-induced dipole moments. We find the chemical specificity of the adsorbate can change the electric field noise by seven orders of magnitude and specifically that soft in-plane modes of weakly-adsorbed hydrocarbons produce the greatest noise and ion heating. We discuss the dynamics captured by the fluctuating dipole model, namely the adsorbate dependent turn-on temperature and electric field noise magnitude, and also discuss the model's failure to reproduce the measured 1/$\omega$ noise frequency scaling with a single adsorbate species. We suggest future research directions for improved, quantitatively predictive models based on extensions of the present framework to multiple interacting adsorbates.

In this work, we introduce a new type of linear classifier that is implemented in a chemical form. We propose a novel encoding technique which simultaneously represents multiple datasets in an array of microliter-scale chemical mixtures. Parallel computations on these datasets are performed as robotic liquid handling sequences, whose outputs are analyzed by high-performance liquid chromatography. As a proof of concept, we chemically encode several MNIST images of handwritten digits and demonstrate successful chemical-domain classification of the digits using volumetric perceptrons. We additionally quantify the performance of our method with a larger dataset of binary vectors and compare the experimental measurements against predicted results. Paired with appropriate chemical analysis tools, our approach can work on increasingly parallel datasets. We anticipate that related approaches will be scalable to multilayer neural networks and other more complex algorithms. Much like recent demonstrations of archival data storage in DNA, this work blurs the line between chemical and electrical information systems, and offers early insight into the computational efficiency and massive parallelism which may come with computing in chemical domains., Comment: Accepted to 2018 IEEE International Conference on Rebooting Computing

Neutral molecules with sufficiently large dipole moments can bind electrons in diffuse nonvalence orbitals with most of their charge density far from the nuclei, forming so-called dipole-bound anions. Because long-range correlation effects play an important role in the binding of an excess electron and overall binding energies are often only of the order of 10-100s of wave numbers, predictively modeling dipole-bound anions remains a challenge. Here, we demonstrate that quantum Monte Carlo methods can accurately characterize molecular dipole-bound anions with near threshold dipole moments. We also show that correlated sampling Auxiliary Field Quantum Monte Carlo is particularly well-suited for resolving the fine energy differences between the neutral and anionic species. These results shed light on the fundamental limitations of quantum Monte Carlo methods and pave the way toward using them for the study of weakly-bound species that are too large to model using traditional electron structure methods.

We present an \textit{ab initio} auxiliary field quantum Monte Carlo method for studying the electronic structure of molecules, solids, and model Hamiltonians at finite temperature. The algorithm marries the \textit{ab initio} phaseless auxiliary field quantum Monte Carlo algorithm known to produce high accuracy ground state energies of molecules and solids with its finite temperature variant, long used by condensed matter physicists for studying model Hamiltonian phase diagrams, to yield a phaseless, \textit{ab initio} finite temperature method. We demonstrate that the method produces internal energies within chemical accuracy of exact diagonalization results across a wide range of temperatures for H$_{2}$O (STO-3G), C$_{2}$ (STO-6G), the one-dimensional hydrogen chain (STO-6G), and the multi-orbital Hubbard model. Our method effectively controls the phase problem through importance sampling, \textit{often even without invoking the phaseless approximation}, down to temperatures at which the systems studied approach their ground states and may therefore be viewed as exact over wide temperature ranges. This technique embodies a versatile tool for studying the finite temperature phase diagrams of a plethora of systems whose properties cannot be captured by a Hubbard U term alone. Our results moreover illustrate that the severity of the phase problem for model Hamiltonians far exceeds that for many molecules at all of the temperatures studied.

QMCPACK is an open source quantum Monte Carlo package for ab-initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wave functions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit (CPU) and graphical processing unit (GPU) systems. We detail the program's capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://www.qmcpack.org .

Fractional derivatives are nonlocal differential operators of real order that often appear in models of anomalous diffusion and a variety of nonlocal phenomena. Recently, a version of the Schr\"odinger Equation containing a fractional Laplacian has been proposed. In this work, we develop a Fractional Path Integral Monte Carlo algorithm that can be used to study the finite temperature behavior of the time-independent Fractional Schr\"odinger Equation for a variety of potentials. In so doing, we derive an analytic form for the finite temperature fractional free particle density matrix and demonstrate how it can be sampled to acquire new sets of particle positions. We employ this algorithm to simulate both the free particle and $^{4}$He (Aziz) Hamiltonians. We find that the fractional Laplacian strongly encourages particle delocalization, even in the presence of interactions, suggesting that fractional Hamiltonians may manifest atypical forms of condensation. Our work opens the door to studying fractional Hamiltonians with arbitrarily complex potentials that escape analytical solutions., Comment: 18 pages, 14 figures

Quantum Monte Carlo (QMC) algorithms have long relied on Jastrow factors to incorporate dynamic correlation into trial wave functions. While Jastrow-type wave functions have been widely employed in real-space algorithms, they have seen limited use in second-quantized QMC methods, particularly in projection methods that involve a stochastic evolution of the wave function in imaginary time. Here we propose a scheme for generating Jastrow-type correlated trial wave functions for auxiliary-field QMC methods. The method is based on decoupling the two-body Jastrow into one-body projectors coupled to auxiliary fields, which then operate on a single determinant to produce a multi-determinant trial wave function. We demonstrate that intelligent sampling of the most significant determinants in this expansion can produce compact trial wave functions that reduce errors in the calculated energies. Our technique may be readily generalized to accommodate a wide range of two-body Jastrow factors and applied to a variety of model and chemical systems., Comment: Revised version with 7 pages, 6 figures, 2 tables

We present a quantum Monte Carlo (QMC) technique for calculating the exact finite-temperature properties of Bose-Fermi mixtures. The Bose-Fermi Auxiliary-Field Quantum Monte Carlo (BF-AFQMC) algorithm combines two methods, a finite-temperature AFQMC algorithm for bosons and a variant of the standard AFQMC algorithm for fermions, into one algorithm for mixtures. We demonstrate the accuracy of our method by comparing its results for the Bose-Hubbard and Bose-Fermi-Hubbard models against those produced using exact diagonalization for small systems. Comparisons are also made with mean-field theory and the worm algorithm for larger systems. As is the case with most fermion Hamiltonians, a sign or phase problem is present in BF-AFQMC. We discuss the nature of these problems in this framework and describe how they can be controlled with well-studied approximations to expand BF-AFQMC's reach. The new algorithm can serve as an essential tool for answering many unresolved questions about many-body physics in mixed Bose-Fermi systems., Comment: 19 pages, 6 figures

The extent of coupling between the folding of a protein and its binding to a substrate varies from protein to protein. Some proteins have highly structured native states in solution, while others are natively disordered and only fold fully upon binding. In this Letter, we use Monte Carlo simulations to investigate how disordered polymer chains grafted around a binding site affect the folding and binding of three model proteins. The protein that approaches the substrate fully folded is more hindered during the binding process than those whose folding and binding are cooperative. The polymer chains act as localized crowding agents and can select correctly folded and bound configurations in favor of non-specifically adsorbed states. The free energy change for forming all intra-protein and protein-substrate contacts can depend non-monotonically on the polymer length., Comment: 5 pages, 5 figures, 1 table