Related papers: SymPT: a comprehensive tool for automating effecti…
In this work we present a new basis set for electronic structures (Density Functional Theory (DFT)) calculations. This basis set extends Soler Williams Linearized Augmented Plane Wave (SLAPW) basis sets by allowing variable Muffin Tin (MT)…
Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer…
Dynamics of a charged particle in the canonical coordinates is a Hamiltonian system, and the well-known symplectic algorithm has been regarded as the de facto method for numerical integration of Hamiltonian systems due to its long-term…
In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive…
We present SWift (SignWriting improved fast transcriber), an advanced editor for computer-aided writing and transcribing using SignWriting (SW). SW is devised to allow deaf people and linguists alike to exploit an easy-to-grasp written form…
Graph Signal Processing has become a very useful framework for signal operations and representations defined on irregular domains. Exploiting transformations that are defined on graph models can be highly beneficial when the graph encodes…
Quantum computing promises transformative impacts in simulating Hamiltonian dynamics, essential for studying physical systems inaccessible by classical computing. However, existing compilation techniques for Hamiltonian simulation, in…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
The connection between ghost-free formulations of RG-invariant perturbation theory in the both Euclidean and Minkowskian regions is studied. Our basic tool is the "double spectral representation", similar to definition of Adler function,…
Quantum walks (QWs) are of interest as examples of uniquely quantum behavior and are applicable in a variety of quantum search and simulation models. Implementing QWs on quantum devices is useful from both points of view. We describe a…
We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of…
We present a \emph{new} formulation of perturbation theory for quantum systems, designated here as: `mean field perturbation theory'(MFPT), which is free from power-series-expansion in any physical parameter, including the coupling…
Recently the synchrosqueezed transform (SST) was developed as an empirical mode decomposition (EMD)-like tool to enhance the time-frequency resolution and energy concentration of a multi-component non-stationary signal and provides more…
Predicting the behaviors of Hamiltonian systems has been drawing increasing attention in scientific machine learning. However, the vast majority of the literature was focused on predicting separable Hamiltonian systems with their kinematic…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
We present a quantum algorithm for simulating rovibrational Hamiltonians on fault-tolerant quantum computers. The method integrates exact curvilinear kinetic energy operators and general-form potential energy surfaces expressed in a hybrid…
The strong-coupling perturbation theory (SCPT) for correlated electron systems is extended to the case of full Coulomb interaction. The Coulomb mechanism of the orbital polarization is discussed and attention is paid to the importance of…
We revisit the Schrieffer-Wolff transformation and present a path integral version of this important canonical transformation. The equivalence between the low-energy sector of the Anderson model in the so-called local moment regime and the…
Symbolic computation is an important approach in automated program analysis. Most state-of-the-art tools perform symbolic computation as interpreters and directly maintain symbolic data. In this paper, we show that it is feasible, and in…
Schrieffer-Wolff transformation is one of the very important transformations in the study of quantum many body physics. It is used to arrive at the low energy effective hamiltonian of Quantum many-body hamiltonians, which are not generally…