相关论文: Computation of Atomic Fibers of Z-Linear Maps
The calculation time for the energy of atoms and molecules scales exponentially with system size on a classical computer but polynomially using quantum algorithms. We demonstrate that such algorithms can be applied to problems of chemical…
We describe recent progress in developing practical ab initio methods for which the computer effort is proportional to the number of atoms: linear scaling or O(N) methods. It is shown that the locality property of the density matrix gives a…
How, in principle, could one solve the atomic structure of a quasicrystal, modeled as a random tiling decorated by atoms, and what techniques are available to do it? One path is to solve the phase problem first, obtaining the density in a…
Let $X$ be a finite set in $Z^d$. We consider the problem of optimizing linear function $f(x) = c^T x$ on $X$, where $c\in Z^d$ is an input vector. We call it a problem $X$. A problem $X$ is related with linear program $\max\limits_{x \in…
Numerical calculations of excitonic properties of novel nanostructures, such as nanowire and crystal phase quantum dots, must combine atomistic accuracy with an approachable computational complexity. The key difficulty comes from the fact…
We present a purely combinatorial solution of the problem of enumerating planar bicubic maps with hard particles. This is done by use of a bijection with a particular class of blossom trees with particles, obtained by an appropriate cutting…
Atomistic simulations have become a powerful tool in materials research due to the extremely fine spatial and temporal resolution provided by such techniques. In order to understand the fundamental principles which govern material behavior…
Let $G=(V(G),E(G))$ be a molecular graph, where $V(G)$ and $E(G)$ are the sets of vertices (atoms) and edges (bonds). A topological index of a molecular graph is a numerical quantity which helps to predict the chemical/physical properties…
Linear optical circuits of growing complexity are playing an increasing role in emerging photonic quantum technologies. Individual photonic devices are typically described by a unitary matrix containing amplitude and phase information, the…
Pipelined algorithms implemented in field programmable gate arrays are being extensively used for hardware triggers in the modern experimental high energy physics field and the complexity of such algorithms are increases rapidly. For…
Given a collection $\{Z_1,Z_2,\ldots,Z_m\}$ of $n$-sided polygons in the plane and a query polygon $W$ we give algorithms to find all $Z_\ell$ such that $W=f(Z_\ell)$ with $f$ an unknown similarity transformation in time independent of the…
In algebra, atomicity is the study of divisibility by and factorizations into atoms (also called irreducibles). In one side of the spectrum of atomicity we find the antimatter algebraic structures, inside which there are no atoms and,…
We present an efficient procedure to filter out from an optical lattice, having inhomogeneous site occupation number, only preselected number of bosonic atoms per site and place them into another internal atomic state, creating thereby a…
In this paper, we present a dynamic programming approach for identifying extremal polyomino chains with respect to degree-based topological indices. This approach provides an explicit recurrence and constructive algorithm that enables both…
Vladimir Shpilrain and Jie-Tai Yu have asked for an effective algorithm to decide if two elements of C[x,y] are related by an automorphism of C[x,y]. We describe here an efficient algorithm that decides this question and finds the…
Knowledge of appropriate local fiber architecture is necessary to simulate patient-specific electromechanics in the human heart. However, it is not yet possible to reliably measure in-vivo fiber directions, especially in human atria. Thus,…
We establish a formal bridge between qubit-based and photonic quantum computing. We do this by defining a functor from the ZX calculus to linear optical circuits. In the process we provide a compositional theory of quantum linear optics…
We study the general integer programming problem where the number of variables $n$ is a variable part of the input. We consider two natural parameters of the constraint matrix $A$: its numeric measure $a$ and its sparsity measure $d$. We…
The braid group appears in many scientific fields and its representations are instrumental in understanding topological quantum algorithms, topological entropy, classification of manifolds and so on. In this work, we study planer diagrams…
Integer programming (IP), as the name suggests is an integer-variable-based approach commonly used to formulate real-world optimization problems with constraints. Currently, quantum algorithms reformulate the IP into an unconstrained form…