Related papers: A Quantum Approach to the Discretizable Molecular …
Molecular docking is a crucial phase in drug discovery, involving the precise determination of the optimal spatial arrangement between two molecules when they bind. The such analysis, the 3D structure of molecules is a fundamental…
In this paper, we study differentially private (DP) algorithms for computing the geometric median (GM) of a dataset: Given $n$ points, $x_1,\dots,x_n$ in $\mathbb{R}^d$, the goal is to find a point $\theta$ that minimizes the sum of the…
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum…
A semidefinite program (SDP) is a particular kind of convex optimization problem with applications in operations research, combinatorial optimization, quantum information science, and beyond. In this work, we propose variational quantum…
Diophantine equations are multivariate equations, usually polynomial, in which only integer solutions are admitted. A brute force method for finding solutions would be to systematically substitute possible integer solutions and check for…
A new approach to large-scale nuclear structure calculations, based on the Density Matrix Renormalization Group (DMRG), is described. The method is tested in the context of a problem involving many identical nucleons constrained to move in…
Distributed computing seems to be a natural approach to overcome size limitations of quantum computers in terms of number of qubits. But one lacks an efficient distribution approach to deal systematically with potential algorithms. This…
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…
We study a fundamental problem in computational chemistry known as molecular conformation generation, trying to predict stable 3D structures from 2D molecular graphs. Existing machine learning approaches usually first predict distances…
New manufacturing techniques such as 3D printing have recently enabled the creation of previously infeasible chemical reactor designs. Optimizing the geometry of the next generation of chemical reactors is important to understand the…
Molecular conformation generation (MCG) is a fundamental and important problem in drug discovery. Many traditional methods have been developed to solve the MCG problem, such as systematic searching, model-building, random searching,…
In this work we apply the Deep Galerkin Method (DGM) described in Sirignano and Spiliopoulos (2018) to solve a number of partial differential equations that arise in quantitative finance applications including option pricing, optimal…
Graph matching is a fundamental tool in computer vision and pattern recognition. In this paper, we introduce an algorithm for graph matching based on the proximal operator, referred to as differentiable proximal graph matching (DPGM).…
It is suggested that the individual outcomes of a measurement process can be understood within standard quantum mechanics in terms of the measuring apparatus, treated as a quantum computer, executing Grover's search algorithm.
The density-matrix renormalization group (DMRG) is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. This…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
Computing intrinsic distances on discrete surfaces is at the heart of many minimization problems in geometry processing and beyond. Solving these problems is extremely challenging as it demands the computation of on-surface distances along…
We introduce the use of high order automatic differentiation, implemented via the algebra of truncated Taylor polynomials, in genetic programming. Using the Cartesian Genetic Programming encoding we obtain a high-order Taylor representation…
Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here, we demonstrate a method for solving a particular system of equations by using the concept…
Solving linear ordinary differential equations (ODE) is one of the most promising applications for quantum computers to demonstrate exponential advantages. The challenge of designing a quantum ODE algorithm is how to embed non-unitary…