True Ground State Research Articles

Quantum entanglement to extract a true ground state from an approximate ground state

Abstract We propose a procedure to extract a true ground state from an approximate ground state by using quantum entanglement. We use plural ancilla qubits with hierarchical structure, intending to gradually put up approximate precision. We demonstrate the procedure for quantum systems with a few qubits that derive from the (1+1)-dimensional Schwinger model by classically emulated digital quantum simulation. Although we use for simplicity an approximate ground state prepared by the adiabatic quantum computation, our procedure is applicable any approximate ground state that is a superposition of a true ground state and excited states. Our procedure is applicable for an N-qubits Hamiltonian with a non-degenerate ground state.

What is the true ground state of intermetallic compound Fe3Al?

We discuss recent doubts about the true ground-state (GS) structure of the intermetallic compound Fe3Al. It seems that it should be the D03 structure (observed experimentally), but there are some considerations that, perhaps, D03 might be a high-temperature (>400 K) structure and the GS at 0 K might be the L12 structure because there might be a high energy barrier between both structures and, when the temperature is lowered, the system is not able to transform into the (perhaps) lower-energy L12 structure. To elucidate this problem, we re-interpret our recent extended ab initio electronic structure calculations for Fe3Al performed with the help of the VASP code and using various exchange-correlation energies within the generalized gradient approximation (GGA). Regrettably, some calculations provide the L12 and some of them D03 as the GS structure.To resolve this question, we performed further calculations testing 9 frequently applied metaGGAs, such as TPSS, revTPSS, M06-L, SCAN(-L), rSCAN(-L) and r2SCAN(-L) representing a higher rung of the Jacob's ladder. It turns out that also here some meta-GGAs lead to L12 and some others to D03 GS structure and, again, we cannot decide.In this way, the present results represent the very first step on the way to understand the energetics of the Fe3Al compound and its ground state. We hope they may motivate future theoretical and experimental work in this direction.

Recent progresses in strange quark stars

According to the hypothesis that strange quark matter may be the true ground state of matter at extremely high densities, strange quark stars should be stable and could exist in the Universe. It is possible that pulsars may actually be strange stars, but not neutron stars. Here we present a short review on recent progresses in the field of strange quark stars. First, three popular phenomenological models widely used to describe strange quark matter are introduced, with special attention being paid on the corresponding equation of state in each model. Combining the equation of state with the Tolman-Oppenheimer-Volkov equations, the inner structure and mass-radius relation can be obtained for the whole sequence of strange stars. Tidal deformability and oscillations (both radial and non-radial oscillations), which are sensitive to the composition and the equations of state, are then described. Hybrid stars as a special kind of quark stars are discussed. Several other interesting aspects of strange stars are also included. For example, strong gravitational wave emissions may be generated by strange stars through various mechanisms, which may help identify strange stars via observations. Especially, close-in strange quark planets with respect to their hosts may provide a unique test for the existence of strange quark objects. Fierce electromagnetic bursts could also be generated by strange stars. The energy may come from the phase transition of neutron stars to strange stars, or from the merger of binary strange stars. The collapse of the strange star crust can also release a huge amount of energy. It is shown that strange quark stars may be involved in short gamma-ray bursts and fast radio bursts.

Probing Quantum Efficiency: Exploring System Hardness in Electronic Ground State Energy Estimation.

We consider the question of how correlated the system hardness is between classical algorithms of electronic structure theory in ground state estimation and quantum algorithms. To define the system hardness for classical algorithms, we employ empirical criterion based on the deviation of electronic energies produced by coupled cluster and configuration interaction methods from the exact ones along multiple bonds dissociation in a set of molecular systems. For quantum algorithms, we have selected the Variational Quantum Eigensolver (VQE) and Quantum Phase Estimation (QPE) methods. As characteristics of the system hardness for quantum methods, we analyzed circuit depths for the state preparation, the number of quantum measurements needed for the energy expectation value, and various cost characteristics for the Hamiltonian encodings via Trotter approximation and linear combination of unitaries (LCU). Our results show that the quantum resource requirements are mostly unaffected by classical hardness, with the only exception being the state preparation part, which contributes to both VQE and QPE algorithm costs. However, there are clear indications that constructing the initial state with a significant overlap with the true ground state is easier than obtaining the state with an energy expectation value within chemical precision. These results support optimism regarding the identification of a molecular system where a quantum algorithm excels over its classical counterpart, as quantum methods can maintain efficiency in classically challenging systems.

Sketching phase diagrams using low-depth variational quantum algorithms

Mapping out phase diagrams of quantum systems using classical simulations can be challenging or intractable due to the computational resources required to simulate even small quantum systems far away from the thermodynamic limit. We investigate using quantum computers and the variational quantum eigensolver (VQE) for this task. In contrast to the task of preparing the exact ground state using VQE, sketching phase diagrams might require less quantum resources and accuracy, because low fidelity approximations to the ground state may be enough to correctly identify different phases. We used classical numerical simulations of low-depth VQE circuits to compute order parameters for four well-studied spin and fermion models which represent a mix of 1D and 2D, and exactly-solvable and classically hard systems. We find that it is possible to predict the location of phase transitions up to reasonable accuracy using states produced by VQE even when their overlap with the true ground state is small. Further, we introduce a model-agnostic predictor of phase transitions based on the speed with which the VQE energy improves with respect to the circuit depth, and find that in some cases this is also able to predict phase transitions.

Two-flavor Color Superconducting Quark Stars May Not Exist

Large uncertainties in the determinations of the equation of state of dense stellar matter allow for the intriguing possibility that the bulk quark matter in beta equilibrium might be the true ground state of the matter at zero pressure. Also, quarks will form Cooper pairs very readily since the dominant interaction between quarks is attractive in some channels. As a result, quark matter will generically exhibit color superconductivity, with the favored pairing pattern at intermediately high densities being two-flavor pairing. In the light of several possible candidates for such self-bound quark stars, including the very low-mass central compact object in supernova remnant HESS J1731-347 reported recently, we carry out a one-field theoretic model, the Nambu–Jona–Lasinio model, to investigate the stability of the beta-stable two-flavor color superconducting (2SC) phase of quark matter, but find no physically allowed parameter space for the existence of 2SC quark stars.

Diffusion probabilistic models enhance variational autoencoder for crystal structure generative modeling

The crystal diffusion variational autoencoder (CDVAE) is a machine learning model that leverages score matching to generate realistic crystal structures that preserve crystal symmetry. In this study, we leverage novel diffusion probabilistic (DP) models to denoise atomic coordinates rather than adopting the standard score matching approach in CDVAE. Our proposed DP-CDVAE model can reconstruct and generate crystal structures whose qualities are statistically comparable to those of the original CDVAE. Furthermore, notably, when comparing the carbon structures generated by the DP-CDVAE model with relaxed structures obtained from density functional theory calculations, we find that the DP-CDVAE generated structures are remarkably closer to their respective ground states. The energy differences between these structures and the true ground states are, on average, 68.1 meV/atom lower than those generated by the original CDVAE. This significant improvement in the energy accuracy highlights the effectiveness of the DP-CDVAE model in generating crystal structures that better represent their ground-state configurations.

Real-time dynamics of false vacuum decay

We investigate false vacuum decay of a relativistic scalar field initialized in the metastable minimum of an asymmetric double-well potential. The transition to the true ground state is a well-defined initial-value problem in real time, which can be formulated in nonequilibrium quantum field theory on a closed time path. We employ the nonperturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion. We also compare to classical-statistical field theory simulations on a lattice in the high-temperature regime. By this, we demonstrate that the real-time decay rates are comparable to those obtained from the conventional Euclidean (bounce) approach. In general, we find that the decay rates are time dependent. For a more comprehensive description of the dynamics, we extract a time-dependent effective potential, which becomes convex during the nonequilibrium transition process. By solving the quantum evolution equations for the one- and two-point correlation functions for vacuum initial conditions, we demonstrate that quantum corrections can lead to transitions that are not captured by classical-statistical approximations. Published by the American Physical Society 2024

Wavefunction theory and density functional theory analysis of ground and excited electronic states of TaB and WB.

Several low-lying electronic states of TaB and WB molecules were studied using ab initio multireference configuration interaction (MRCI), Davidson corrected MRCI (MRCI+Q), and coupled cluster singles doubles and perturbative triples [CCSD(T)] methods. Their full potential energy curves (PECs), equilibrium electron configurations, equilibrium bond distances (res), dissociation energies (Des), excitation energies (Tes), harmonic vibrational frequencies (ωes), and anharmonicities (ωexes) are reported. The MRCI dipole moment curves (DMCs) of the first 5 electronic states of both TaB and WB are also reported and the equilibrium dipole moment (μ) values are compared with the CCSD(T) μ values. The most stable 13Π (1σ22σ23σ11π3) and 15Δ (1σ22σ23σ11π21δ1) electronic states of TaB lie close in energy with ∼62 kcal mol-1De with respect to the Ta(4F) + B(2P) asymptote. However, spin-orbit coupling effects make the 15Δ0+ state the true ground state of TaB. The ground electronic state of WB (16Π) has the 1σ22σ13σ11π31δ2 electron configuration and is followed by the excited 16Σ+ and 14Δ states. Finally, the MRCI De, re, ωe, and ωexe values of the 13Π state of TaB and 16Π and 14Δ states of WB are used to assess the density functional theory (DFT) errors on a series of exchange-correlation functionals that span multiple-rungs of the Jacob's ladder of density functional approximations (DFA).

A theoretical study of ferrocene based on combined configuration interaction singles (CIS) and time-dependent density functional theory (TDDFT) approach

The state-of-the art density functional theory (DFT) is used to clearly resolve the two parallel cyclopentadienyl rings of ferrocene, which are either staggered (D5d symmetry) or eclipsed (D5h symmetry), in their ground-state conformation. Present result revealed that the eclipsed conformer with D5h point group represents the true minimum ground state structure of ferrocene. Natural population analysis is used to determine how atomic charge is distributed across different atoms of ferrocene D5h conformer and also the distribution of electrons in the core, valence, and Rydberg sub-shells. It is further investigated in potential energy scan that the rotation of the dihedral angle δ from 0° to 3π/5 will reproduce three times D5h or D5d conformers periodically as the period of 2π/5 due to the pentagonal structure of the CP ring. Further to examine optical spectra in the ultraviolet-visible (UV–vis) range, configuration interaction single (CIS) and time-dependent density functional theory (TDDFT) have conducted which help in locating the significant electronic shifts between different energy levels. Absorption spectra for high spin states were also generated in order to comprehend the characteristics of low-lying spin excitation. According to our estimates, the greatest absorption intensity is restricted to an energy range of 4–6 eV. Knowledge of ferrocene conformers will improve the research on other metallocenes and their derivatives, which have applications in biotechnology, nanotechnology, and solar technology.

Magnetic Exchange Coupling in Macrocyclic Cobalt (II) Complexes: The Influence of Bridging Ligands and Choice of the Computational Methodologies

AbstractExchange‐coupled spin states of cobalt complexes represent the key to understanding the challenging nature of the magnetism of cobalt dimer. In this study, we introduce a comprehensive investigation of the nature of magnetic super‐exchange coupling interactions between two metallic centers in a macro ligand cobalt dimer. More importantly, we provide a detailed comparison between a series of bridging ligands and study their role in the magnetic exchange coupling constant in cobalt dimer with tetraaza macrocycle ligand scaffold. By varying the types of bridging and terminal ligands, we explored the nature of magnetic coupling in 24 species of cobalt dimers, which allowed us to draw a magneto‐structure relationship and monitor the effect of bridging/terminal ligands on the overall magnetism. We employed different density functional theory (DFT) methodologies and complete active space self‐consistent field (CASSCF) in our investigation. The results show that there are comprehensible functional dependencies, and the choice of exchange‐correlation functional is critical for calculating the magnetic properties. Using the experimental values of the exchange coupling, we found that hybrid functionals with 10–20 % Hartree‐Fock exchange integrals give acceptable accuracy. Furthermore, we adjusted the percentage of HF integrals to estimate the optimum value required to be included in the hybrid functionals. Finally, we used CASSCF to gain deeper understanding of the magnetic coupling for the valence magnetic electrons and to achieve the true ground state wavefunction, which is not feasible with conventional DFT calculations. However, the CASSCF calculations poorly underestimate the magnetic coupling, which can be significantly improved by including the dynamic correlations, as implemented in the NEVPT2 methodology.

Anisotropic quark stars in energy-momentum squared gravity

At super-saturation densities, quarks in the core of neutron stars (NSs) have been a subject of intense investigation for last few decades. In particular, an intriguing conjecture has emerged suggesting that the true ground state of hadronic matter may be strange quark matter (SQM). In the present manuscript, we study internal structure and the physical properties of quark stars (QSs) in energy-momentum squared gravity (EMSG) with MIT bag model equations of state (EoS). An important feature of this theory is the addition of the term f(TμνTμν) to the Einstein-Hilbert action. This modification in the action lead to changes in the right-hand side of Einstein's field equations (EFE). We obtain mass-radius relations for a spherically symmetric configuration supported by the anisotropic fluid matter distribution and solved the hydrostatic equilibrium equations numerically in the framework of EMSG. In addition, we present and discuss the stability of stellar structure depending on the model parameters.

(Third Place Poster Award) Computational Assessment of the Optoelectronic Structure and Biomolecular Complexation of Graphene Quantum Dots

With novel materials getting smaller and their size falling to the nanometer scale, it becomes harder to fully characterize them by only using the experimental apparatus at hand. Therefore, taking advantage of computational methods proves to be trustworthy in filling those gaps and in aiding our experimental data to get a better understanding of the nanomaterials’ structural and electronic properties. Graphene quantum dots (GQDs) have recently become one of the flagships of carbon nanotechnology due to their remarkable physical properties and, when functionalized, an ability to become water soluble, biocompatible and capable of fluorescence in the visible and near-infrared. This makes them perspective carriers for therapeutic delivery and image-tracking. In order to assess the advantages of their utilization for a variety of bioapplications, we have investigated optical properties of doped GQDs and their interactions with biomolecules using a variety of molecular simulation approaches. True atomic ground state of the N-GQD is achieved via performing first-principle calculations based on density functional theory (DFT). DFT calculations also unrevealed the contributions of each functional group within the structure to HOMO–LUMO band edges. The adsorption of biomolecules and genes on the GQD surface has been further investigated with regards of the GQD structure, complementing experimental results that verify gene and drug complexation. Figure 1

Exact and efficient Lanczos method on a quantum computer

We present an algorithm that uses block encoding on a quantum computer to exactly construct a Krylov space, which can be used as the basis for the Lanczos method to estimate extremal eigenvalues of Hamiltonians. While the classical Lanczos method has exponential cost in the system size to represent the Krylov states for quantum systems, our efficient quantum algorithm achieves this in polynomial time and memory. The construction presented is exact in the sense that the resulting Krylov space is identical to that of the Lanczos method, so the only approximation with respect to the exact method is due to finite sample noise. This is possible because, unlike previous quantum Krylov methods, our algorithm does not require simulating real or imaginary time evolution. We provide an explicit error bound for the resulting ground state energy estimate in the presence of noise. For our method to be successful efficiently, the only requirement on the input problem is that the overlap of the initial state with the true ground state must be Ω(1/poly(n)) for n qubits.

On Instabilities Caused by Magnetic Background Fields

We review instabilities that appear from the coupling of spin-one fields to a magnetic background in a non-Abelian theory. Such coupling results, due to asymptotic freedom in a negative quantum, contribute to the effective potential. In QCD, the Savvidy vacuum results. However, due to the tachyonic mode, such a state is not stable, and the question about the true ground state of QCD is still open. In the electroweak model, the corresponding instability is postponed to very large background fields and may be of relevance in the early universe, at best. We start with an introduction to the topic and display the necessary formulas and methods. Then, we consider the one-particle spectra of the fields in a magnetic background and the related Euler–Heisenberg Lagrangians. In addition, we discuss the potential instability connected with the anomalous moment of the electron. The main part is on the quantum correction to the energy in non-Abelian fields, including massive ones. Here, the focus is on so-called electroweak magnetism and the search for a classical solution of the field equations and their approximations by a lattice of flux tubes. Finally, we review approaches with non-homogeneous background fields and the background of an A0-field.

Operator solution of the light-front Thirring-Wess model

We present an operator solution of the Thirring-Wess model, formulated and quantized in terms of light-front (LF) variables. The model describes a system of massless fermions interacting with massive vector bosons in two space-time dimensions. An important ingredient of the solution is a consistent quantization of the two-dimensional massless LF fermion field. The field equations are solved exactly on an operator level and the quantum LF Hamiltonian is derived in terms of independent field variables. The axial anomaly and the interacting correlation functions are computed nonperturbatively from the operator solution. An analogous operator solution in the conventional field theory is briefly described for comparison. While in the LF case the ``empty'' Fock vacuum is the lowest-energy eigenstate of the full Hamiltonian, the corresponding Hamiltonian in the conventional theory has to be diagonalized in order to find the true physical ground state, which is a dynamical state with a complicated structure. A comment concerning a recently discussed equivalence between the LF and conventional form of field theory concludes the paper.

Confronting Strange Stars with Compact-Star Observations and New Physics

Strange stars ought to exist in the universe according to the strange quark matter hypothesis, which states that matter made of roughly equal numbers of up, down, and strange quarks could be the true ground state of baryonic matter rather than ordinary atomic nuclei. Theoretical models of strange quark matter, such as the standard MIT bag model, the density-dependent quark mass model, or the quasi-particle model, however, appear to be unable to reproduce some of the properties (masses, radii, and tidal deformabilities) of recently observed compact stars. This is different if alternative gravity theory (e.g., non-Newtonian gravity) or dark matter (e.g., mirror dark matter) are considered, which resolve these issues. The possible existence of strange stars could thus provide a clue to new physics, as discussed in this review.

An empirical study of quantum dynamics as a ground state problem with neural quantum states

We consider the Feynman–Kitaev formalism applied to a spin chain described by the transverse-field Ising model. This formalism consists of building a Hamiltonian whose ground state encodes the time evolution of the spin chain at discrete time steps. To find this ground state, variational wave functions parameterised by artificial neural networks—also known as neural quantum states (NQSs)—are used. Our work focuses on assessing, in the context of the Feynman–Kitaev formalism, two properties of NQSs: expressivity (the possibility that variational parameters can be set to values such that the NQS is faithful to the true ground state of the system) and trainability (the process of reaching said values). We find that the considered NQSs are capable of accurately approximating the true ground state of the system, i.e. they are expressive enough ansätze. However, extensive hyperparameter tuning experiments show that, empirically, reaching the set of values for the variational parameters that correctly describe the ground state becomes ever more difficult as the number of time steps increase because the true ground state becomes more entangled, and the probability distribution starts to spread across the Hilbert space canonical basis.

Variational quantum eigensolver for the Heisenberg antiferromagnet on the kagome lattice

Establishing the nature of the ground state of the Heisenberg antiferromagnet (HAFM) on the kagome lattice is well-known to be a prohibitively difficult problem for classical computers. Here, we give a detailed proposal for a variational quantum eigensolver (VQE) intending to solve this physical problem on a quantum computer. At the same time, this VQE constitutes an explicit experimental proposal for showing a useful quantum advantage on noisy intermediate-scale quantum devices because of its natural hardware compatibility. We classically emulate noiseless and noisy quantum computers with either 2D-grid or all-to-all connectivity and simulate patches of the kagome HAFM of up to 20 sites. In the noiseless case, the ground-state energy, as found by the VQE, approaches the true ground-state energy exponentially as a function of the circuit depth. Furthermore, VQEs for the HAFM on any graph can inherently perform their quantum computations in a decoherence-free subspace that protects against collective longitudinal and collective transversal noise, adding to the noise resilience of these algorithms. Nevertheless, the extent of the effects of other noise types suggests the need for error mitigation and performance targets alternative to high-fidelity ground-state preparation, even for essentially hardware-native VQEs.

Nuclear and magnetic spin structure of the antiferromagnetic triangular lattice compound LiCrTe2 investigated by mu ^+SR, neutron and X-ray diffraction

Two-dimensional (2D) triangular lattice antiferromagnets (2D-TLA) often manifest intriguing physical and technological properties, due to the strong interplay between lattice geometry and electronic properties. The recently synthesized 2-dimensional transition metal dichalcogenide LiCrTe_2, being a 2D-TLA, enriched the range of materials which can present such properties. In this work, muon spin rotation (mu ^+SR) and neutron powder diffraction (NPD) have been utilized to reveal the true magnetic nature and ground state of LiCrTe_2. From high-resolution NPD the magnetic spin order at base-temperature is not, as previously suggested, helical, but rather collinear antiferromagnetic (AFM) with ferromagnetic (FM) spin coupling within the ab-plane and AFM coupling along the c-axis. The value if the ordered magnetic Cr moment is established as mu _{textrm{Cr}}= 2.36~mu _{textrm{B}}. From detailed mu ^+SR measurements we observe an AFM ordering temperature T_{textrm{N}}approx 125 K. This value is remarkably higher than the one previously reported by magnetic bulk measurements. From mu ^+SR we are able to extract the magnetic order parameter, whose critical exponent allows us to categorize LiCrTe_2 in the 3D Heisenberg AFM universality class. Finally, by combining our magnetic studies with high-resolution synchrotron X-ray diffraction (XRD), we find a clear coupling between the nuclear and magnetic spin lattices. This suggests the possibility for a strong magnon–phonon coupling, similar to what has been previously observed in the closely related compound LiCrO_2.