相关论文: A Polynomial-Time Quantum Algorithm for Collision …

In recent years, quantum computing has drawn significant interest within the field of high-energy physics. We explore the potential of quantum algorithms to resolve the combinatorial problems in particle physics experiments. As a concrete…

In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs. The computational complexity is $O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is sufficient to prove…

We consider quantum algorithms for the unique sink orientation problem on cubes. This problem is widely considered to be of intermediate computational complexity. This is because there no known polynomial algorithm (classical or quantum)…

In this paper we propose a totally serious algorithm to solve NP problems in polynomial time provided one is willing to wager the fate of all observers in the universe on the many-world interpretation of quantum theory being correct.

We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…

Autonomous intersection management has the potential to reduce road traffic congestion and energy consumption. To realize this potential, efficient algorithms are needed. However, most existing studies locally optimize one intersection at a…

In this note, we polynomially reduce an instance of the partition problem to a dynamic lot sizing problem, and show that solving the latter problem solves the former problem. By solving the dynamic program formulation of the dynamic lot…

The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…

The problem of counting collisions or interactions is common in areas as computer graphics and scientific simulations. Since it is a major bottleneck in applications of these areas, a lot of research has been carried out on such subject,…

The maximum clique problem is a classical NP-complete problem in graph theory and has important applications in many domains. In this paper we show, in a partially non-constructive way, the existence of an exact polynomial-time algorithm…

We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs in polynomial time in the bit-size of the two edge vectors.…

In this article, we consider a collection of geometric problems involving points colored by two colors (red and blue), referred to as bichromatic problems. The motivation behind studying these problems is two fold; (i) these problems appear…

Triangulation of a three-dimensional point from at least two noisy 2-D images can be formulated as a quadratically constrained quadratic program. We propose an algorithm to extract candidate solutions to this problem from its semidefinite…

We consider the problem of planning a collision-free path of a robot in the presence of risk zones. The robot is allowed to travel in these zones but is penalized in a super-linear fashion for consecutive accumulative time spent there. We…

Many methods solve Poisson equations by using grid techniques which discretize the problem in each dimension. Most of these algorithms are subject to the curse of dimensionality, so that they need exponential runtime. In the paper "Quantum…

We devise a polynomial-time approximation scheme for the classical geometric problem of finding an approximate short path amid weighted regions. In this problem, a triangulated region P comprising of n vertices, a positive weight associated…

Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…

The aim of the paper is to answer a long-standing open problem on the relationship between NP and BQP. The paper shows that BQP contains NP by proposing a BQP quantum algorithm for the MAX-E3-SAT problem which is a fundamental NP-hard…

This paper presents a complete algorithmic study of the decision Boolean Satisfiability Problem under the classical computation and quantum computation theories. The paper depicts deterministic and probabilistic algorithms, propositions of…

We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…