Two-body Terms Research Articles

Towards determining the presence of barren plateaus in some chemically inspired variational quantum algorithms

In quantum chemistry, the variational quantum eigensolver (VQE) is a promising algorithm for molecular simulations on near-term quantum computers. However, VQEs using hardware-efficient circuits face scaling challenges due to the barren plateau problem. This raises the question of whether chemically inspired circuits from unitary coupled cluster (UCC) methods can avoid this issue. Here we provide theoretical evidence indicating they may not. By examining alternated dUCC ansätzes and relaxed Trotterized UCC ansätzes, we find that in the infinite depth limit, a separation occurs between particle-hole one- and two-body unitary operators. While one-body terms yield a polynomially concentrated energy landscape, adding two-body terms leads to exponential concentration. Numerical simulations support these findings, suggesting that popular 1-step Trotterized unitary coupled-cluster with singles and doubles (UCCSD) ansätze may not scale. Our results emphasize the link between trainability and circuit expressiveness, raising doubts about VQEs’ ability to surpass classical methods.

Microsolvation of a Proton by Ar Atoms: Structures and Energetics of ArnH+ Clusters.

We present a computational investigation on the structural arrangements and energetic stabilities of small-size protonated argon clusters, Ar nH +. Using high-level ab initio electronic structure computations, we determined that the linear symmetric triatomic ArH +Ar ion serves as the molecular core for all larger clusters studied. Through harmonic normal-mode analysis for clusters containing up to seven argon atoms, we observed that the proton-shared vibration shifts to lower frequencies, consistent with measurements in gas-phase IRPD and solid Ar-matrix isolation experiments. We explored the sum-of-potentials approach by employing kernel-based machine-learning potential models trained on CCSD(T)-F12 data. These models included expansions of up to two-body, three-body, and four-body terms to represent the underlying interactions as the number of Ar atoms increases. Our results indicate that the four-body contributions are crucial for accurately describing the potential surfaces in clusters with n> 3. Using these potential models and an evolutionary programming method, we analyzed the structural stability of clusters with up to 24 Ar atoms. The most energetically favored Ar nH + structures were identified for magic size clusters at n = 7, 13, and 19, corresponding to the formation of Ar-pentagon rings perpendicular to the ArH +Ar core ion axis. The sequential formation of such regular shell structures is compared to ion yield data from high-resolution mass spectrometry measurements. Our results demonstrate the effectiveness of the developed sum-of-potentials model in describing trends in the nature of bonding during the single proton microsolvation by Ar atoms, encouraging further quantum nuclear studies.

On the backreaction of Dirac matter in JT gravity and SYK model

We model backreaction in AdS2 JT gravity via a proposed boundary dual Sachdev-Ye-Kitaev quantum dot coupled to Dirac fermion matter and study it from the perspective of quantum entanglement and chaos. The boundary effective action accounts for the backreaction through a linear coupling of the Dirac fermions to the Gaussian-random two-body Majorana interaction term in the low-energy limit. We calculate the time evolution of the entanglement entropy between graviton and Dirac fermion fields for a separable initial state and find that it initially increases and then saturates to a finite value. Moreover, in the limit of a large number of fermions, we find a maximally entangled state between the Majorana and Dirac fields in the saturation region, implying a transition of the von Neumann algebra of observables from type I to type II. This transition in turn indicates a loss of information in the holographically dual emergent spacetime. We corroborate these observations with a detailed numerical computation of the averaged nearest-neighbor gap ratio of the boundary spectrum and provide a useful complement to quantum entanglement studies of holography.

Unveiling order from chaos by approximate 2-localization of random matrices

Quantum many-body systems are typically endowed with a tensor product structure. A structure they inherited from probability theory, where the probability of two independent events is the product of the probabilities. The tensor product structure of a Hamiltonian thus gives a natural decomposition of the system into independent smaller subsystems. It is interesting to understand whether a given Hamiltonian is compatible with some particular tensor product structure. In particular, we ask, is there a basis in which an arbitrary Hamiltonian has a 2-local form, i.e., it contains only pairwise interactions? Here we show, using analytical and numerical calculations, that a generic Hamiltonian (e.g., a large random matrix) can be approximately written as a linear combination of two-body interaction terms with high precision; that is, the Hamiltonian is 2-local in a carefully chosen basis. Moreover, we show that these Hamiltonians are not fine-tuned, meaning that the spectrum is robust against perturbations of the coupling constants. Finally, by analyzing the adjacency structure of the couplings [Formula: see text], we suggest a possible mechanism for the emergence of geometric locality from quantum chaos.

The fastest generation of multipartite entanglement with natural interactions

Natural interactions among multiple quantum objects are fundamentally composed of two-body terms only. In contradistinction, single global unitaries that generate highly entangled states typically arise from Hamiltonians that couple multiple individual subsystems simultaneously. Here, we study the time to produce strongly nonclassical multipartite correlations with a single unitary generated by the natural interactions. We restrict the symmetry of two-body interactions to match the symmetry of the target states and focus on the fastest generation of multipartite entangled Greenberger–Horne–Zeilinger, W, Dicke and absolutely maximally entangled states for up to seven qubits. These results are obtained by constraining the energy in the system and accordingly can be seen as state-dependent quantum speed limits for symmetry-adjusted natural interactions. They give rise to a counter-intuitive effect where the creation of particular entangled states with an increasing number of particles does not require more time. The methods used rely on extensive numerical simulations and analytical estimations.

Structural phases of classical 2D clusters with competing two-body and three-body interactions

In modeling systems of interacting particles, many-body terms beyond pairwise interactions are often overlooked. Nevertheless, in certain scenarios, even small contributions from three-body or higher-order terms can disrupt significant changes in their collective behavior. Here we investigate the effects of three-body interactions on the structure and stability of 2D, harmonically confined clusters. We consider clusters with three distinct pairwise interactions: , , and , thus covering a wide range of condensed and soft matter systems, such as vortices in mesoscopic superconductors, charged colloids, and dusty plasma. In each case, we evaluate the energetics and normal mode spectra of equilibrium and metastable configurations as the intensity of an attractive, Gaussian three-body potential is varied. We demonstrate that, above a threshold value of the three-body energy strength, the cluster shrinks and eventually becomes self-sustained, that is, it remains cohesive after the confinement potential is shut down. Depending on the strengths of the two-body and three-body interaction terms, this compaction can be continuous or abrupt. The latter case is characterized by a discontinuous jump in the particle density and coexsitence of the compact and non-compact phases as metastable states, as in a first-order phase transition. For some values of the particle number, the compaction is preceded by one or more structural changes, resulting in configurations not usually seen in purely pairwise-additive clusters.

Towards the understanding of the genuine three-body interaction for p–p–p and p–p–Lambda

Three-body nuclear forces play an important role in the structure of nuclei and hypernuclei and are also incorporated in models to describe the dynamics of dense baryonic matter, such as in neutron stars. So far, only indirect measurements anchored to the binding energies of nuclei can be used to constrain the three-nucleon force, and if hyperons are considered, the scarce data on hypernuclei impose only weak constraints on the three-body forces. In this work, we present the first direct measurement of the p–p–p and p–p–Lambda systems in terms of three-particle correlation functions carried out for pp collisions at sqrt{s} = 13 TeV. Three-particle cumulants are extracted from the correlation functions by applying the Kubo formalism, where the three-particle interaction contribution to these correlations can be isolated after subtracting the known two-body interaction terms. A negative cumulant is found for the p–p–p system, hinting to the presence of a residual three-body effect while for p–p–Lambda the cumulant is consistent with zero. This measurement demonstrates the accessibility of three-baryon correlations at the LHC.

Many-Body Effects in Aqueous Systems: Synergies Between Interaction Analysis Techniques and Force Field Development

Interaction analysis techniques, including the many-body expansion (MBE), symmetry-adapted perturbation theory, and energy decomposition analysis, allow for an intuitive understanding of complex molecular interactions. We review these methods by first providing a historical context for the study of many-body interactions and discussing how nonadditivities emerge from Hamiltonians containing strictly pairwise-additive interactions. We then elaborate on the synergy between these interaction analysis techniques and the development of advanced force fields aimed at accurately reproducing the Born-Oppenheimer potential energy surface. In particular, we focus on ab initio-based force fields that aim to explicitly reproduce many-body terms and are fitted to high-level electronic structure results. These force fields generally incorporate many-body effects through (a) parameterization of distributed multipoles, (b) explicit fitting of the MBE, (c) inclusion of many-atom features in a neural network, and (d) coarse-graining of many-body terms into an effective two-body term. We also discuss the emerging use of the MBE to improve the accuracy and speed of ab initio molecular dynamics.

Fast and accurate prediction of material properties with three-body tight-binding model for the periodic table.

Parametrized tight-binding models fit to first-principles calculations can provide an efficient and accurate quantum mechanical method for predicting properties of molecules and solids. However, well-tested parameter sets are generally only available for a limited number of atom combinations, making routine use of this method difficult. Furthermore, many previous models consider only simple two-body interactions, which limits accuracy. To tackle these challenges, we develop a density functional theory database of nearly 1 000 000 materials, which we use to fit a universal set of tight-binding parameters for 65 elements and their binary combinations. We include both two-body and three-body effective interaction terms in our model, plus self-consistent charge transfer, enabling our model to work for metallic, covalent, and ionic bonds with the same parameter set. To ensure predictive power, we adopt a learning framework where we repeatedly test the model on new low-energy crystal structures and then add them to the fitting data set, iterating until predictions improve. We distribute the materials database and tools developed in this paper publicly.

Quantum-geometric contribution to the Bogoliubov modes in a two-band Bose-Einstein condensate

We consider a weakly interacting Bose-Einstein condensate that is loaded into an optical lattice with a two-point basis and described by a two-band Bose-Hubbard model with generic one-body and two-body terms. By first projecting the system onto the lower Bloch band and then applying the Bogoliubov approximation to the resultant Hamiltonian, we show that the inverse effective-mass tensor of the superfluid carriers in the Bogoliubov spectrum has two physically distinct contributions. In addition to the usual inverse band-mass tensor that is originating from the intraband processes within the lower Bloch band, there is also a quantum-geometric contribution that is induced by the two-body interactions through the interband processes. We also discuss the conditions under which the latter contribution is expressed in terms of the quantum-metric tensor of the Bloch states, i.e., the natural Fubini-Study metric on the Bloch sphere.

Subleading contributions to N -boson systems inside the universal window

We study bosonic systems in the regime in which the two-body system has a shallow bound state or, equivalently, a large value of the two-body scattering length. Using the effective field theory framework as a guide, we construct a series of potential terms which have decreasing importance in the description of the binding energy of the systems. The leading order potential terms consist of a two-body term, usually attractive, plus a three-body term, usually repulsive; this last term is required to prevent the collapse of systems with more than two particles. At this order, the parametrization of the two-body potential is done to obtain a correct description of the scattering length, which governs the dynamics in this regime, whereas the three-body term fixes a three-body datum. We investigate the role of the cut-off in the leading order description and we extend the exploration beyond the leading order by including the next-to-leading order terms in both, the two- and three-body potentials. We use the requirement of the stability of the N-body system, whose energy is variationally estimated, to introduce the three-body forces. The potential parametrization, as a function of the cut-off, is fixed to describe the energy of 4 He clusters up to seven particles within the expected accuracy. Finally, we also explore the possibility to describe at the same time the atom-dimer scattering length.

Bond order via cavity-mediated interactions

We numerically study the phase diagram of bosons tightly trapped in the lowest band of an optical lattice and dispersively coupled to a single-mode cavity field. The dynamics is encompassed by an extended Bose-Hubbard model. Here, the cavity-mediated interactions are described by a two-body potential term with a global range and by a correlated tunneling term where the hopping amplitude depends on a global observable. We determine the ground state properties in one dimension by means of the density matrix renormalization group algorithm, focusing on the effects due to the correlated tunneling. The latter is responsible for the onset of bond orders, manifesting in one insulating and two gapless bond ordered phases. We discuss the resulting phases for different geometries that correspond to different relative strengths of the correlated tunneling coefficient. We finally analyze the scaling of the entanglement entropy in the gapless bond ordered phases that appear entirely due to global interactions and determine the corresponding central charges.

Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits.

Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron-electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. The transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.

Quasi-deuteron model at low renormalization group resolution

Background: The quasi-deuteron model introduced by Levinger is used to explain cross sections for knocking out high-momentum protons in photoabsorption on nuclei. This is within a framework we characterize as exhibiting high renormalization group (RG) resolution. Assuming a one-body reaction operator, the nuclear wave function must include two-body short-range correlations (SRCs) with deuteronlike quantum numbers. In Phys. Rev. C 104, 034311 (2021), we showed that SRC physics can be naturally accounted for at low RG resolution.Purpose: Here we describe the quasi-deuteron model at low RG resolution and determine the Levinger constant, which is proportional to the ratio of nuclear photoabsorption to that for photodisintegration of a deuteron.Method: We extract the Levinger constant based on the ratio of momentum distributions at high relative momentum. We compute momentum distributions evolved under similarity RG (SRG) transformations where the SRC physics is shifted into the operator as a universal two-body term. The short-range nature of this operator motivates using local-density approximations with uncorrelated wave functions in evaluating nuclear matrix elements, which greatly simplifies the analysis. The operator must be consistently matched to the RG scale and scheme of the interaction for a reliable extraction. We apply SRG transformations to different nucleon-nucleon (NN) interactions and use the deuteron wave functions and Weinberg eigenvalues to determine approximate matching scales.Results: We predict the Levinger constant for several NN interactions and a wide range of nuclei comparing to experimental extractions.Conclusions: The predictions at low RG resolution are in good agreement with experiment when starting with a hard NN interaction and the initial operator. Similar agreement is found using soft NN interactions when the additional two-body operator induced by evolution from hard to soft is included.

Fragmentation-Based Decomposition of a Metalloenzyme-Substrate Interaction: A Case Study for a Lytic Polysaccharide Monooxygenase.

We present a novel decomposition scheme for electronic interaction energies based on the flexible formulation of fragmentation schemes through fragment combination ranges (FCRs; J. Chem. Phys., 2021, 155, 164105). We devise a clear additive decomposition with contribution of nondisjoint fragments and correction terms for overlapping fragments and apply this scheme to the metalloenzyme-substrate complex of a lytic polysaccharide monooxygenase (LPMO) with an oligosaccharide. By this, we further illustrate the straightforward adaptability of the FCR-based schemes to novel systems. Our calculations suggest that the description of the electronic structure is a larger error source than the fragmentation scheme. In particular, we find a large impact of the basis set size on the interaction energies. Still, the introduction of three-body interaction terms in the fragmentation setup improves the agreement to the supermolecular reference. Yet, the qualitative results for the decomposition scheme with two-body terms only largely agree within the investigated electronic-structure approaches and basis sets, which are B97-3c, DFT (TPSS and B3LYP), and MP2 methods. The overlap contributions are found to be small, allowing analysis of the interaction energy into individual amino acid residues: We find a particularly strong interaction between the substrate and the LPMO copper active site.

Application of Computer-Aided Precious Metal Materials in Electrochemistry of Ceramic Jewelry Design

In order to solve the electrochemical application of precious metal materials in ceramic jewelry design, a computer-aided design method of precious metal materials in ceramic jewelry was proposed. First, the potential energy surface analyzed in this paper is composed of the sum of disomy and trisomy, with different proportions of disomy and trisomy. Therefore, in the fitting process, the above two relations can be used to measure the contribution of the two-body term and the three-body term, respectively; secondly, from the viewpoint of lattice dynamics, precious metals are of special significance, because they are simple fcc lattice and large and pure single crystals can be obtained. Therefore, their accurate phonon dispersion curves can be obtained experimentally; finally, the phonon dispersion curves along the highly symmetric vector direction are given, and the calculated results are in good agreement with the experimental data. This shows that the new analytical potential energy surface accurately reproduces the interactions inside these crystals. The new analytical potential energy surfaces of the three noble metals correctly reproduce the macroscopic properties of the system, including elastic modulus, cohesive energy, and phonon dispersion curve, as well as important surface features. For all three systems, the order of the surface energies of the unreconstituted surfaces is (110) > (100) > (111), which is also correct. At the same time, the new potential energy surface gives the correct relaxation behavior of the unreconstituted surface.

Efficient Monte Carlo Sampling for Molecular Systems Using Continuous Normalizing Flow

Monte Carlo molecular simulation is a powerful computational method for simulating molecular behavior. It generates samples of the possible states of molecular systems. To generate a sample efficiently, it is advantageous to avoid suggesting extremely high-energy states that would never become possible states. In this study, we propose a new sampling method for Monte Carlo molecular simulation, that is, a continuous normalizing molecular flow (CNMF) method, which can create various probabilistic distributions of molecular states from some initial distribution. The CNMF method generates samples by solving a first-order differential equation with two-body intermolecular interaction terms. We also develop specific probabilistic distributions using CNMF called inverse square flow, which yields distributions with zero probability density when molecule pairs are in close proximity, whereas probability densities are compressed uniformly from the initial distribution in all other cases. Using inverse square flow, we demonstrate that Monte Carlo molecular simulation is more efficient than the standard simulation. Although the increased computational costs of the CNMF method are non-negligible, this method is feasible for parallel computation and has the potential for expansion.

Thermalization of randomly coupled SYK models

We investigate the thermalization of Sachdev–Ye–Kitaev (SYK) models coupled via random interactions following quenches from the perspective of entanglement. Previous studies have shown that when a system of two SYK models coupled by random two-body terms is quenched from the thermofield double state with sufficiently low effective temperature, the Rényi entropies do not saturate to the expected thermal values in the large-N limit. Using numerical large-N methods, we first show that the Rényi entropies in a pair SYK models coupled by two-body terms can thermalize, if quenched from a state with sufficiently high effective temperature, and hence exhibit state-dependent thermalization. In contrast, SYK models coupled by single-body terms appear to always thermalize. We provide evidence that the subthermal behavior in the former system is likely a large-N artifact by repeating the quench for finite N and finding that the saturation value of the Rényi entropy extrapolates to the expected thermal value in the N → ∞ limit. Finally, as a finer grained measure of thermalization, we compute the late-time spectral form factor of the reduced density matrix after the quench. While a single SYK dot exhibits perfect agreement with random matrix theory, both the quadratically and quartically coupled SYK models exhibit slight deviations.

Fragment-Based Excited-State Calculations Using the GW Approximation and the Bethe-Salpeter Equation.

Herein, we present a fragment-based approach for calculating the charged and neutral excited states in molecular systems, based on the many-body Green's function method within the GW approximation and the Bethe-Salpeter equation (BSE). The implementation relies on the many-body expansion of the total irreducible polarizability on the basis of fragment molecular orbitals. The GW quasi-particle energies in complex molecular environments are obtained by the GW calculation for the target fragment plus induced polarization contributions of the surrounding fragments at the static Coulomb-hole plus screened exchange level. In addition, we develop a large-scale GW/BSE method for calculating the delocalized excited states of molecular aggregates, based on the fragment molecular orbital method and the exciton model. The accuracy of fragment-based GW and GW/BSE methods was evaluated on molecular clusters and molecular crystals. We found that the accuracy of the total irreducible polarizability can be improved systematically by including two-body correction terms, and the fragment-based calculations can reasonably reproduce the results of the corresponding unfragmented calculations with a relative error of less than 100 meV. The proposed approach enables efficient excited-state calculations for large molecular systems with reasonable accuracy.

Beyond-Mean-Field Effects in Rabi-Coupled Two-Component Bose-Einstein Condensate.

We theoretically calculate and experimentally measure the beyond-mean-field (BMF) equation of state in a coherently coupled two-component Bose-Einstein condensate (BEC) in the regime where averaging of the interspecies and intraspecies coupling constants over the hyperfine composition of the single-particle dressed state predicts the exact cancellation of the two-body interaction. We show that with increasing the Rabi-coupling frequency Ω, the BMF energy density crosses over from the nonanalytic Lee-Huang-Yang scaling ∝n^{5/2} to an expansion in integer powers of density, where, in addition to a two-body BMF term ∝n^{2}sqrt[Ω], there emerges a repulsive three-body contribution ∝n^{3}/sqrt[Ω]. We experimentally evidence these two contributions, thanks to their different scaling with Ω, in the expansion of a Rabi-coupled two-component ^{39}K condensate in a waveguide. By studying the expansion with and without Rabi coupling, we reveal an important feature relevant for observing BMF effects and associated phenomena in mixtures with spin-asymmetric losses: Rabi coupling helps preserve the spin composition and thus prevents the system from drifting away from the point of the vanishing mean field.