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The one-particle reduced density-matrix (1-RDM) functional theory is a promising alternative to density-functional theory (DFT) that uses the 1-RDM rather than the electronic density as a basic variable. However, long-standing challenges…
We develop a representability-aware and interpolable neural network (NN) framework for predicting two-particle reduced density matrices (2-RDMs). The NN incorporates a subset of representability conditions through its architecture and loss…
Excited-state properties of highly correlated systems are key to understanding photosynthesis, luminescence, and the development of novel optical materials, but accurately capturing their interactions is computationally costly. We present…
The accurate description of the non-linear response of many-electron systems to strong-laser fields remains a major challenge. Methods that bypass the unfavorable exponential scaling with particle number are required to address larger…
Machine learning is rapidly accelerating materials and chemical discovery, but most current models target energies, forces, or selected molecular properties rather than the underlying many-body electronic structure. Learning…
The N-representability problem for reduced density matrices remains a fundamental challenge in electronic structure theory. Following our previous work that employs a unitary-evolution algorithm based on an adaptive derivative-assembled…
Classical shadow tomography provides a randomized scheme for approximating the quantum state and its properties at reduced computational cost with applications in quantum computing. In this Letter we present an algorithm for realizing fewer…
For many-electron systems, the second-order reduced density matrix (2-RDM) provides sufficient information for characterizing their properties of interests in physics and chemistry, ranging from total energy, magnetism, quantum correlation…
The ground state energy of a many-electron system can be approximated by an variational approach in which the total energy of the system is minimized with respect to one and two-body reduced density matrices (RDM) instead of many-electron…
The last several decades have seen significant advances in the theoretical modeling of materials within the fields of solid-state physics and materials science, but many methods commonly applied to this problem struggle to capture strong…
Quantum algorithms for molecular electronic structure have been developed with lower computational scaling than their classical counterparts, but emerging quantum hardware is far from being capable of the coherence,connectivity and gate…
Minimizing the energy of an $N$-electron system as a functional of a two-electron reduced density matrix (2-RDM), constrained by necessary $N$-representability conditions (conditions for the 2-RDM to represent an ensemble $N$-electron…
The second-order reduced density matrix method (the RDM method) has performed well in determining energies and properties of atomic and molecular systems, achieving coupled-cluster singles and doubles with perturbative triples (CC SD(T))…
We introduce the Nuclear Electronic All-Particle Density Matrix Renormalization Group (NEAP-DMRG) method for solving the time-independent Schr\"odinger equation simultaneously for electrons and other quantum species. In contrast to already…
Parametric two-electron reduced-density-matrix (p-2RDM) methods have enjoyed much success in recent years; the methods have been shown to exhibit accuracies greater than coupled cluster with single and double substitutions (CCSD) for both…
Conventional matrix completion methods approximate the missing values by assuming the matrix to be low-rank, which leads to a linear approximation of missing values. It has been shown that enhanced performance could be attained by using…
The simulation of strongly correlated many-electron systems is one of the most promising applications for near-term quantum devices. Here we use a class of eigenvalue solvers (presented in Phys. Rev. Lett. 126, 070504 (2021)) in which a…
Two-body reduced density matrices (2RDMs) encode the essential two-electron physics of electronic states, but their quartic storage cost poses a major limitation in practical workflows. We investigate a simple protocol to compress both…
One of the major computational bottlenecks in one-body reduced density matrix (1RDM) functional theory is the evaluation of approximate 1RDM functionals and their derivatives. The reason is that more advanced approximate functionals are…
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…