arXiv subjects

Lexin Ding

Publications and source records attributed to Lexin Ding.

17 recordsLinked to original sources

arXiv2026

Propagating sparsely supported states with time-dependent neural quantum states

Neural quantum states (NQSs) have emerged as a powerful ansatz for quantum dynamics. Their high entanglement capacity promises to overcome the entanglement barrier. However, existing time-dependent NQS methods are ill-equipped to propagate sparsely supported initial states due to the inherent mismatch between the supports of such states and their time derivatives. To address this issue, we introduce the interpolation sampling method as a novel form of importance sampling, where samples are drawn from a distribution that interpolates between the wave function and its time derivative. Combined with a global-in-time variational principle, we demonstrate with the example of the two-dimensional transverse-field Ising model that interpolation sampling allows for accurate propagation of extremely peaked states that standard wave function sampling could not tackle. We further improve sampling efficiency by introducing (i) a configuration-time joint sampling scheme where spin configurations and time are both treated as random variables, and (ii) a hybrid strategy for sample proposal that incorporates the knowledge of a Krylov subspace. Our work extends the scope of time-dependent NQS methods to a wider range of physically relevant scenarios, while challenging the prevailing reliance on the Born distribution and its close variants as the default basis for sampling.

quant-ph↗

arXiv2026

Capturing electron correlation at mean-field cost: Assessment of i-DMFT and the underlying correlation conjecture

Accurately treating strong electron correlation in quantum chemistry typically requires multireference wave-function methods with steep computational scaling. The recently proposed i-DMFT method promises near configuration-interaction accuracy at mean-field cost by invoking an empirical linear relation between correlation energy and entropy (Collins' conjecture), whose validity remains unclear. We systematically assess this relation across a range of di- and polyatomic molecules, including diverse bond types, third-row elements, different types of geometric distortions, and excited states. We find that the conjectured linearity holds for bond-breaking processes dominated by electron redistribution within orbital pairs, but breaks down for heterolytic dissociation and excited states. In simple molecules, i-DMFT provides a reasonable description of total energies, but does not reliably reproduce reduced density matrices or individual energy components. It further degrades in more complex cases such as ethylene. Based on these results, we formulate criteria for the validity of the conjecture and outline implications for entropy-based reduced density matrix functionals.

physics.chem-ph↗

arXiv2026

Neural Quantum States Based on Selected Configurations

Neural quantum states (NQS) provide a flexible and highly expressive parameterization of wave functions for strongly correlated problems in quantum chemistry. Despite rapid advances in network architectures, the evaluation of electronic energies remains almost exclusively based on variational Monte Carlo (VMC). While VMC is effective for structured systems such as spin chains, its accuracy and efficiency for electronic Hamiltonians are hindered by sharply peaked distributions, stochastic gradient noise, and slow convergence with sample size. In this letter, we assess the capability of NQS-VMC to efficiently capture correlation in electronic ground states by comparing it to a recently developed NQS-based selected configuration (NQS-SC) approach. We set up a systematic comparison of the ground-state optimizations obtained with NQS-VMC and NQS-SC for molecular systems dominated by either static or dynamical correlation. The comparison demonstrates a clear advantage of NQS-SC over NQS-VMC in both energy accuracy and wave-function coefficients, particularly for statically correlated molecules. Moreover, NQS-SC exhibits robust systematic improvability, whereas NQS-VMC does not. These findings position NQS-SC as the new default approach over NQS-VMC for electronic structure calculations. We further observe that neither NQS-SC nor NQS-VMC can efficiently capture dynamical correlation, highlighting the need for future hybrid methods, such as multiconfigurational perturbation theories built on top of NQS solutions.

physics.chem-ph↗

arXiv2025

Modal Backflow Neural Quantum States for Anharmonic Vibrational Calculations

Neural quantum states (NQS) are a promising ansatz for solving many-body quantum problems due to their inherent expressiveness. Yet, this expressiveness can only be harnessed efficiently for treating identical particles if the suitable physical knowledge is hardwired into the neural network itself. For electronic structure, NQS based on backflow determinants has been shown to be a powerful ansatz for capturing strong correlation. By contrast, the analogue for bosons, backflow permanents, is unpractical due to the steep cost of computing the matrix permanent and due to the lack of particle conservation in common bosonic problems. To circumvent these obstacles, we introduce a modal backflow (MBF) NQS design and demonstrate its efficacy by solving the anharmonic vibrational problem. To accommodate the demand of high accuracy in spectroscopic calculations, we implement a selected-configuration scheme for evaluating physical observables and gradients, replacing the standard stochastic approach based on Monte Carlo sampling. A vibrational self-consistent field calculation is conveniently carried out within the MBF network, which serves as a pretraining step to accelerate and stabilize the optimization. In applications to both artificial and ab initio Hamiltonians, we find that the MBF network is capable of delivering spectroscopically accurate zero-point energies and vibrational transitions in all anharmonic regimes.

physics.chem-ph↗

arXiv2025

Chemical bonding concepts emerge naturally from maximally entangled atomic orbitals

Chemical bonding is a nonlocal phenomenon that binds atoms into molecules. Its ubiquitous presence in chemistry, however, stands in stark contrast to its ambiguous definition and the lack of a universal perspective for its understanding. In this work, we rationalize and characterize chemical bonding through the lens of an equally nonlocal concept from quantum information, the orbital entanglement. We introduce maximally entangled atomic orbitals (MEAOs) whose entanglement pattern is shown to recover both Lewis (two-center) and beyond-Lewis (multicenter) structures, with multipartite entanglement serving as a comprehensive index of bond strength. Our unifying framework for bonding analyses is effective not only for equilibrium geometries but also for transition states in chemical reactions and complex phenomena such as aromaticity. It also has the potential to elevate the Hilbert space atomic partitioning to match the prevalent real-space partitioning in the theory of atoms in molecules. Accordingly, our work provides a new framework for understanding fuzzy chemical concepts using rigorous, quantitative descriptors from quantum information.

quant-ph↗

arXiv2024

What Can Quantum Information Theory Offer to Quantum Chemistry?

It is the ultimate goal of this work to foster synergy between quantum chemistry and the flourishing field of quantum information theory. For this, we first translate quantum information concepts such as entanglement and correlation into the context of quantum chemical systems. In particular, we establish two conceptually distinct perspectives on `electron correlation' leading to a notion of orbital and particle correlation. We then demonstrate that particle correlation equals total orbital correlation minimized over all orbital bases. Accordingly, particle correlation resembles the minimal, thus intrinsic, complexity of many-electron wave functions while orbital correlation quantifies their complexity relative to a basis. We illustrate these concepts of intrinsic and extrinsic correlation complexity in molecular systems, which also manifests the crucial link between the two correlation pictures. Our results provide theoretical justification for the long-favored natural orbitals for simplifying electronic structures, and open new pathways for developing more efficient approaches towards the electron correlation problem.

quant-ph↗

arXiv2024

Unveiling Intrinsic Many-Body Complexity by Compressing Single-Body Triviality

The simultaneous treatment of static and dynamical correlations in strongly-correlated electron systems is a critical challenge. In particular, finding a universal scheme for identifying a single-particle orbital basis that minimizes the representational complexity of the many-body wavefunction is a formidable and longstanding problem. As a substantial contribution towards its solution, we show that the total orbital correlation actually reveals and quantifies the intrinsic complexity of the wavefunction,once it is minimized via orbital rotations. To demonstrate the power of this concept in practice, an iterative scheme is proposed to optimize the orbitals by minimizing the total orbital correlation calculated by the tailored coupled cluster singles and doubles (TCCSD) ansatz. The optimized orbitals enable the limited TCCSD ansatz to capture more non-trivial information of the many-body wavefunction, indicated by the improved wavefunction and energy. An initial application of this scheme shows great improvement of TCCSD in predicting the singlet ground state potential energy curves of the strongly correlated C$_{\rm 2}$ and Cr$_{\rm 2}$ molecule.

quant-ph↗

arXiv2024

Ground and Excited States from Ensemble Variational Principles

The extension of the Rayleigh-Ritz variational principle to ensemble states $\rho_{\mathbf{w}}\equiv\sum_k w_k |\Psi_k\rangle \langle\Psi_k|$ with fixed weights $w_k$ lies ultimately at the heart of several recent methodological developments for targeting excitation energies by variational means. Prominent examples are density and density matrix functional theory, Monte Carlo sampling, state-average complete active space self-consistent field methods and variational quantum eigensolvers. In order to provide a sound basis for all these methods and to improve their current implementations, we prove the validity of the underlying critical hypothesis: Whenever the ensemble energy is well-converged, the same holds true for the ensemble state $\rho_{\mathbf{w}}$ as well as the individual eigenstates $|\Psi_k\rangle$ and eigenenergies $E_k$. To be more specific, we derive linear bounds $d_-\Delta{E}_{\mathbf{w}} \leq \Delta Q \leq d_+ \Delta{E}_{\mathbf{w}}$ on the errors $\Delta Q $ of these sought-after quantities. A subsequent analytical analysis and numerical illustration proves the tightness of our universal inequalities. Our results and particularly the explicit form of $d_{\pm}\equiv d_{\pm}^{(Q)}(\mathbf{w},\mathbf{E})$ provide valuable insights into the optimal choice of the auxiliary weights $w_k$ in practical applications.

quant-ph↗

arXiv2023

Quantum Information-Assisted Complete Active Space Optimization (QICAS)

Automated active space selection is arguably one of the most challenging and essential aspects of multiconfigurational methods. In this work we propose an effective quantum information-assisted complete active space optimization (QICAS) scheme. What sets QICAS apart from other correlation-based selection schemes is (i) the use of unique measures from quantum information that assess the correlation in electronic structures in an unambiguous and predictive manner, and (ii) an orbital optimization step that minimizes the correlation discarded by the active space approximation. Equipped with these features QICAS yields for smaller correlated molecules sets of optimized orbitals with respect to which the CASCI energy reaches the corresponding CASSCF energy within chemical accuracy. For more challenging systems such as the Chromium dimer, QICAS offers an excellent starting point for CASSCF by greatly reducing the number of iterations required for numerical convergence. Accordingly, our study validates a profound empirical conjecture: the energetically optimal non-active spaces are predominantly those that contain the least entanglement.

quant-ph↗

arXiv2023

Refining the weighted subspace-search variational quantum eigensolver: compression of ans\"atze into a single pure state and optimization of weights

The weighted subspace-search variational quantum eigensolver (SSVQE) is a prominent algorithm for calculating excited-state properties of molecular quantum systems. In this work, we elaborate on some of its fundamental features with the aim of improving its practical realization. First, we demonstrate that the initial ans\"atze for various excited states could be prepared into a single pure state through a minimal number of ancilla qubits, followed by the optimization of a subsequent global unitary rotation in the targeted subspace. Since the ancillas' sole purpose is to purify an underlying ensemble $\rho_{\boldsymbol{w}}$ state with spectral weights $\boldsymbol{w}$, their measurement would just collapse $\rho_{\boldsymbol{w}}$ with probabilities $w_j$ to one of its eigenstates $|\Psi_j \rangle$. We thus observe that our realization of SSVQE is equivalent to the original SSVQE improved by importance sampling. Then, we elaborate by numerical means on the potential influence of the auxiliary weights $\boldsymbol{w}$ on the accuracy of the sought-after eigenstates and eigenenergies. Clear trends are discovered which are contrasted with some recent mathematical results concerning the ensemble variational principle that underlies SSVQE.

quant-ph↗

arXiv2023

Physical Entanglement Between Localized Orbitals

In [arXiv:2207.03377] the first closed formula of a faithful entanglement measure applicable to realistic electron systems has been derived. In the present work, we build on this key achievement with the ultimate goal of guiding the development of quantum technologies. For this, we first elucidate the process of entanglement swapping in electron systems such as atoms, molecules or solid bodies. This clearly demonstrates the necessity of both the reference to localized few-orbital subsystems and the implementation of the number-parity superselection rule. Accordingly, in virtue of Wick's theorem, we then provide a fully analytical study of the true physical entanglement between sites in free electron chains. In that sense, we break the common paradigm of restricting such analytical analyses to unitarily invariant settings, i.e. bipartitions of the chain into rather impractical, macroscopically large subsystems. We then upgrade this model to a hydrogen ring of interacting electrons and construct the sought-after localized orbitals. For both systems, we confirm the presence of long-distance entanglement, provided the filling fractions are sufficiently low/high.

quant-ph↗

arXiv2022

Fermionic Entanglement and Correlation

Entanglement plays a central role in numerous fields of quantum science. However, as one departs from the typical "Alice versus Bob" setting into the world of indistinguishable fermions, it is not immediately clear how the concept of entanglement is defined among these identical particles. Our endeavor to recover the notion of subsystems, or mathematically speaking, the tensor product structure of the Hilbert space, lead to two natural pictures of defining fermionic entanglement: the particle picture and the mode picture. In the particle picture, entanglement characterizes the deviation of a fermionic quantum state from the non-interacting ones, e.g., single Slater determinants. In the mode picture, we recover the notion of subsystems, by referring to the partitioning of the orbital/mode that the fermions occupy, which allows us to naturally adopt the formalism of entanglement between distinguishable constituents. Both pictures reveal essential and interconnected aspects of fermionic entanglement, and thus offer precise tools for studying electron entanglement in highly relevant systems such as atoms and molecules. We showcase here two applications: i) resolving the correlation paradox in the molecular dissociation limit, ii) quantitative electronic structure analysis with orbital entanglement.

quant-ph↗

arXiv2022

Quantifying Electron Entanglement Faithfully

Entanglement is one of the most fascinating concepts of modern physics. In striking contrast to its abstract, mathematical foundation, its practical side is, however, remarkably underdeveloped. Even for systems of just two orbitals or sites no faithful entanglement measure is known yet. By exploiting the spin symmetries of realistic many-electron systems, we succeed in deriving a closed formula for the relative entropy of entanglement between electron orbitals. Its broad applicability in the quantum sciences is demonstrated: (i) in light of the second quantum revolution, it quantifies the true physical entanglement by incorporating the crucial fermionic superselection rule (ii) an analytic description of the long-distance entanglement in free electron chains is found, refining Kohn's locality principle (iii) the bond-order wave phase in the extended Hubbard model can be confirmed, and (iv) the quantum complexity of common molecular bonding structures could be marginalized through orbital transformations, thus rationalizing zero-seniority wave function ansatzes.

quant-ph↗

arXiv2022

Quantum correlations in molecules: from quantum resourcing to chemical bonding

The second quantum revolution is all about exploiting the quantum nature of atoms and molecules to execute quantum information processing tasks. To support this growing endeavor and by anticipating the key role of quantum chemistry therein, our work establishes a toolbox for systematically exploring, quantifying and dissecting correlation effects in quantum chemical systems. By utilizing the geometric picture of quantum states we compare -- on a unified basis and in an operationally meaningful way -- total, quantum and classical correlation and entanglement in molecular ground states. To maximize the quantum informational resourcefulness of molecules an orbital optimization scheme is provided, leading to a paradigm-shifting insight: A single covalent bond equates to the entanglement $2\ln(2)$. This novel and more versatile perspective on electronic structure suggests a generalization of valence bond theory, overcoming deficiencies of modern chemical bonding theories.

quant-ph↗

arXiv2022

Comment on "Self-Consistent-Field Method for Correlated Many-Electron Systems with an Entropic Cumulant Energy"

In [Phys. Rev. Lett. 128, 013001 (2022)] a novel ground state method was proposed. It has been suggested that this $i$-DMFT would be a method within one-particle reduced density matrix functional theory (DMFT), capable of describing accurately molecules at various geometries with an information-theoretical nature. We reassess this work and its suggestions from a conceptual and practical point of view, leading to the following conclusions: i) A method which assigns to each molecule $\mathcal{M}$ its own functional $\mathcal{F}_{\!\mathcal{M}}$ is not a functional theory (striking violation of "universality") ii) even for the simplest systems $i$-DMFT yields incorrect one-particle reduced density matrices and iii) the use of an information-theoretical concept to describe molecular dissociation limits was not essential. The latter insight may help to fix the deficiency of $i$-DMFT to not reproduce correctly the smaller occupation numbers and thus to not recover the important dynamic correlations.

quant-ph↗

arXiv2020

Concept of orbital entanglement and correlation in quantum chemistry

A recent development in quantum chemistry has established the quantum mutual information between orbitals as a major descriptor of electronic structure. This has already facilitated remarkable improvements of numerical methods and may lead to a more comprehensive foundation for chemical bonding theory. Building on this promising development, our work provides a refined discussion of quantum information theoretical concepts by introducing the physical correlation and its separation into classical and quantum parts as distinctive quantifiers of electronic structure. In particular, we succeed in quantifying the entanglement. Intriguingly, our results for different molecules reveal that the total correlation between orbitals is mainly classical, raising questions about the general significance of entanglement in chemical bonding. Our work also shows that implementing the fundamental particle number superselection rule, so far not accounted for in quantum chemistry, removes a major part of correlation and entanglement previously seen. In that respect, realizing quantum information processing tasks with molecular systems might be more challenging than anticipated.

quant-ph↗

arXiv2020

Correlation paradox of the dissociation limit: A quantum information perspective

The interplay between electron interaction and geometry in a molecular system can lead to rather paradoxical situations. The prime example is the dissociation limit of the hydrogen molecule: While a significant increase of the distance $r$ between the two nuclei marginalizes the electron-electron interaction, the exact ground state does, however, not take the form of a single Slater determinant. By first reviewing and then employing concepts from quantum information theory, we resolve this paradox and its generalizations to more complex systems in a quantitative way. To be more specific, we illustrate and prove that thermal noise due to finite, possibly even just infinitesimally low, temperature $T$ will destroy the entanglement beyond a critical separation distance $r_{\mathrm{crit}}$($T$) entirely. Our analysis is comprehensive in the sense that we simultaneously discuss both total correlation and entanglement in the particle picture as well as in the orbital/mode picture. Our results reveal a conceptually new characterization of static and dynamical correlation in ground states by relating them to the (non)robustness of correlation with respect to thermal noise.

quant-ph↗