Related papers: An O(N) quasi-Ewald splitting method for nanoconfi…
We present a quasipolynomial-time algorithm for solving the weak membership problem for the convex set of separable, i.e. non-entangled, bipartite density matrices. The algorithm decides whether a density matrix is separable or whether it…
Recently, the fabrication of CdSe nanoplatelets became an important research topic. Nanoplatelets are often described as having a similar electronic structure as 2D dimensional quantum wells and are promoted as colloidal quantum wells with…
The study of out-of-equilibrium quantum many-body dynamics remains one of the most exciting research frontiers of physics, standing at the crossroads of our understanding of complex quantum phenomena and the realization of quantum…
While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number…
We present an O(\sqrt{N}) discrete query quantum algorithm for evaluating balanced binary NAND formulas and an O(N^{{1/2}+O(\frac{1}{\sqrt{\log N}})}) discrete query quantum algorithm for evaluating arbitrary binary NAND formulas.
Graph partitioning schedules parallel calculations like sparse matrix-vector multiply (SpMV). We consider contiguous partitions, where the $m$ rows (or columns) of a sparse matrix with $N$ nonzeros are split into $K$ parts without…
The ENUF method, i.e., Ewald summation based on the Non-Uniform FFT technique (NFFT), is implemented in Dissipative Particle Dynamics (DPD) simulation scheme to fast and accurately calculate the electrostatic interactions at mesoscopic…
A novel splitting algorithm is proposed for the numerical simulation of neuromorphic circuits. The algorithm is grounded in the operator-theoretic concept of monotonicity, which bears both physical and algorithmic significance. The…
The particle-particle random phase approximation (pp-RPA) has been shown to be capable of describing double, Rydberg, and charge transfer excitations, for which the conventional time-dependent density functional theory (TDDFT) might not be…
In this paper, we propose a numerical scheme for structured population models defined on a separable and complete metric space. In particular, we consider a generalized version of a transport equation with additional growth and non-local…
We construct quantum circuits which exactly encode the spectra of correlated electron models up to errors from rotation synthesis. By invoking these circuits as oracles within the recently introduced "qubitization" framework, one can use…
We build and study a recursive algorithm based on the occupation measure of an Euler scheme with decreasing step for the numerical approximation of the quasistationary distribution (QSD) of an elliptic diffusion in a bounded domain. We…
We present a Gutzwiller von Neumann dynamics (GvND) method for simulating equilibrium and nonequilibrium phenomena in strongly correlated electron systems. Our approach is a real-space formulation of the time-dependent Gutzwiller…
An $n$-qubit quantum circuit is said to be peaked if it has an output probability that is at least inverse-polynomially large as a function of $n$. We describe a classical algorithm with quasipolynomial runtime $n^{O(\log{n})}$ that…
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…
We introduce a Monte-Carlo algorithm for the simulation of charged particles moving in the continuum. Electrostatic interactions are not instantaneous as in conventional approaches, but are mediated by a constrained, diffusing electric…
We present a technique to efficiently compute long-range interactions in systems with periodic boundary conditions. We extend the well-known Ewald method by using a linear combination of screening Gaussian charge distributions instead of…
We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…
The projection-based quantum embedding method is applied to electronically excited states of valence, Rydberg, and charge-transfer character, valence- and core-ionized states, as well as bound and temporary radical anions. We embed…
In this paper, we study the mathematical structure and numerical approximation of elliptic problems posed in a (3D) domain $\Omega$ when the right-hand side is a (1D) line source $\Lambda$. The analysis and approximation of such problems is…