Related papers: Unitary transformations within density matrix embe…
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…
One of the most used approaches in simulating materials is the tight-binding approximation. When using this method in a material simulation, it is necessary to compute the eigenvalues and eigenvectors of the Hamiltonian describing the…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
We present an analytical study of the spatial decay rate $\gamma$ of the one-particle density matrix $\rho(\vec r,\vec r')\sim\exp(-\gamma|\vec r-\vec r'|)$ for systems described by single particle orbitals in periodic potentials in…
We demonstrate the power of a first principle-based and practicable method that allows for the perturbative computation of reduced density matrix elements of an open quantum system without making use of any master equations. The approach is…
We study the matrix completion problem when the observation pattern is deterministic and possibly non-uniform. We propose a simple and efficient debiased projection scheme for recovery from noisy observations and analyze the error under a…
This research presents a novel depth estimation algorithm based on a Transformer-encoder architecture, tailored for the NYU and KITTI Depth Dataset. This research adopts a transformer model, initially renowned for its success in natural…
Robust point-set registration in the presence of noise and outliers is challenging because the matched points (inliers) must be identified before reliable alignment can be performed. Existing robust registration methods typically optimize…
The self-consistent evaluation of Hubbard parameters using linear-response theory is crucial for quantitatively predictive calculations based on Hubbard-corrected density-functional theory. Here, we extend a recently-introduced approach…
The last decade has seen a large increase in the number of electronic-structure calculations that involve adding a Hubbard term to the local density approximation band-structure Hamiltonian. The Hubbard term is then solved either at the…
An approximation for the exchange-correlation energy of reduced-density-matrix-functional theory was recently derived from a study of the homogeneous electron gas (N.N. Lathiotakis, N. Helbig, E.K.U. Gross, Phys. Rev. B 75, 195120 (2007)).…
Reduced basis methods are popular for approximately solving large and complex systems of differential equations. However, conventional reduced basis methods do not generally preserve conservation laws and symmetries of the full order model.…
The accurate determination of magnetic phase transitions in electronic systems is an important task of solid state theory. While numerically exact results are readily available for model systems such as the half-filled 3D Hubbard model, the…
Based on the standard many-fermion field theory, the authors construct models describing ultracold fermions in a 1D optical lattices by implementing a mode expansion of the fermionic field operator where modes, in addition to space…
We present a new paradigm for speeding up randomized computations of several frequently used functions in machine learning. In particular, our paradigm can be applied for improving computations of kernels based on random embeddings. Above…
We present a new and efficient optimization method to determine the structure of disordered systems in agreement with available experimental data. Our approach permits the application of accurate electronic structure calculations within the…
During the noisy intermediate-scale quantum (NISQ) era, it is important to optimize the quantum circuits in circuit depth and gate count, especially entanglement gates, including the CNOT gate. Among all the unitary operators, diagonal…
This work focuses on optimizing the gates of a quantum circuit with a given topology to approximate the unitary time evolution governed by a Hamiltonian. Recognizing that unitary matrices form a mathematical manifold, we employ Riemannian…
In this work we develop and analyze an adaptive finite element method for efficiently solving electrical impedance tomography -- a severely ill-posed nonlinear inverse problem for recovering the conductivity from boundary voltage…
For any torsion-free hyperbolic group $\Gamma$ and any group $G$ that is fully residually $\Gamma$, we construct algorithmically a finite collection of homomorphisms from $G$ to groups obtained from $\Gamma$ by extensions of centralizers,…