Related papers: A Quantum Approach to the Discretizable Molecular …
Quantum advantage is the core of quantum computing. Grover's search algorithm is the only quantum algorithm with proven advantage to any possible classical search algorithm. However, realizing this quantum advantage in practice is quite…
We present a classical algorithm that, for any $D$-dimensional geometrically-local, quantum circuit $C$ of polylogarithmic-depth, and any bit string $x \in {0,1}^n$, can compute the quantity $|<x|C|0^{\otimes n}>|^2$ to within any…
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…
In this paper we present and analyse a discontinuous Galerkin finite element method (DGFEM) for the approximation of solutions to elliptic partial differential equations in nondivergence form, with oblique boundary conditions, on curved…
This paper introduces new methodology to triangulate dynamic Bayesian networks (DBNs) and dynamic graphical models (DGMs). While most methods to triangulate such networks use some form of constrained elimination scheme based on properties…
Molecular Docking (MD) is an important step of the drug discovery process which aims at calculating the preferred position and shape of one molecule to a second when they are bound to each other. During such analysis, 3D representations of…
We present a three-dimensional graph convolutional network (3DGCN), which predicts molecular properties and biochemical activities, based on 3D molecular graph. In the 3DGCN, graph convolution is unified with learning operations on the…
Designing multi-qubit quantum logic gates with experimental constraints is an important problem in quantum computing. Here, we develop a new quantum optimal control algorithm for finding unitary transformations with constraints on the…
We propose a different methodology towards approaching a Maze problem. We convert the problem into a Quantum Search Problem (QSP), and its solutions are sought for using the iterative Grover's Search Algorithm. Though the category of mazes…
Cellular scale decision making is modulated by the dynamics of signalling molecules and their diffusive trajectories from a source to small absorbing sites on the cellular surface. Diffusive capture problems are computationally challenging…
Molecular docking (MD) is a crucial task in drug design, which predicts the position, orientation, and conformation of the ligand when bound to a target protein. It can be interpreted as a combinatorial optimization problem, where quantum…
We explore quantum search from the geometric viewpoint of a complex projective space $CP$, a space of rays. First, we show that the optimal quantum search can be geometrically identified with the shortest path along the geodesic joining a…
The goal of Point Distance Solving Problems is to find 2D or 3D placements of points knowing distances between some pairs of points. The common guideline is to solve them by a numerical iterative method (\emph{e.g.} Newton-Raphson method).…
In the thesis, we use a recently developed tight characterisation of quantum query complexity, the adversary bound, to develop new quantum algorithms and lower bounds. Our results are as follows: * We develop a new technique for the…
Protein flexibility is crucial for understanding protein structures, functions, and dynamics, and it can be measured through experimental methods such as X-ray crystallography. Theoretical approaches have also been developed to predict…
Geometric programming (GP) provides a power tool for solving a variety of optimization problems. In the real world, many applications of geometric programming (GP) are engineering design problems in which some of the problem parameters are…
Deep learning methods have access to be employed for solving physical systems governed by parametric partial differential equations (PDEs) due to massive scientific data. It has been refined to operator learning that focuses on learning…
Density Matrix Renormalization Group (DMRG) algorithm has been extremely successful for computing the ground states of one-dimensional quantum many-body systems. For problems concerned with mixed quantum states, however, it is less…
We establish a lower bound concerning the computational complexity of Grover's algorithms on fractal networks. This bound provides general predictions for the quantum advantage gained for searching unstructured lists. It yields a…
Derandomization is the process of taking a randomized algorithm and turning it into a deterministic algorithm, which has attracted great attention in classical computing. In quantum computing, it is challenging and intriguing to derandomize…