相关论文: Finding Solutions to NP Problems: Philosophical Di…

Most research in the theory of evolutionary computation assumes that the problem at hand has a fixed problem size. This assumption does not always apply to real-world optimization challenges, where the length of an optimal solution may be…

Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points. A choice among these…

The question of whether all problems in NP class are also in P class is generally considered one of the most important open questions in mathematics and theoretical computer science as it has far-reaching consequences to other problems in…

This is the latest in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. In the previous papers, we have proved that the sat CNF problem is polynomially reduced to the problem of finding a…

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…

We present the partial evolutionary tensor neural networks (pETNNs), a novel framework for solving time-dependent partial differential equations with high accuracy and capable of handling high-dimensional problems. Our architecture…

In the last decade, public and industrial research funding has moved quantum computing from the early promises of Shor's algorithm through experiments to the era of noisy intermediate scale quantum devices (NISQ) for solving real-world…

Evolutionary algorithms are good general problem solver but suffer from a lack of domain specific knowledge. However, the problem specific knowledge can be added to evolutionary algorithms by hybridizing. Interestingly, all the elements of…

In the continuum limit (large number of qubits), adiabatic quantum algorithms display a remarkable similarity to sweeps through quantum phase transitions. We find that transitions of second or higher order are advantageous in comparison to…

In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…

The Traveling Salesman Problem (TSP) is a classical NP-hard problem that plays a crucial role in combinatorial optimization. In this paper, we are interested in the quantum search framework for the TSP because it has robust theoretical…

In order to formulate mathematical conjectures likely to be true, a number of base cases must be determined. However, many combinatorial problems are NP-hard and the computational complexity makes this research approach difficult using a…

This is a commentary on, and critique of, Latif Salum's paper titled "Tractability of One-in-three $\mathrm{3SAT}$: $\mathrm{P} = \mathrm{NP}$." Salum purports to give a polynomial-time algorithm that solves the $\mathrm{NP}$-complete…

Context: Evolutionary algorithms typically require a large number of evaluations (of solutions) to converge - which can be very slow and expensive to evaluate.Objective: To solve search-based software engineering (SE) problems, using fewer…

As of now, an optimal quantum algorithm solving partial differential equations eludes us. There are several different methods, each with their own strengths and weaknesses. In past years comparisons of these existing methods have been made,…

Finding a quantum computing method to solve nondeterministic polynomial time (NP)-complete problems is currently of paramount importance in quantum information science. Here an experiment is presented to demonstrate the use of Rydberg atoms…

The structure of satisfiability problems is used to improve search algorithms for quantum computers and reduce their required coherence times by using only a single coherent evaluation of problem properties. The structure of random k-SAT…

In this paper, we discussed CNF-SAT problem (NP-Complete problem) and analysis two solutions that can solve the problem, the PL-Resolution algorithm and the WalkSAT algorithm. PL-Resolution is a sound and complete algorithm that can be used…

Satisfiability (SAT) is a central problem in computer science, and advances in SAT-solving algorithms have a far-reaching impact across many fields. Recent works have proposed quantum SAT solvers based on Grover's algorithm, a quantum…

In this paper, we examine the claims made by the paper "A polynomial-time algorithm for 3-SAT" by Lizhi Du. The paper claims to provide a polynomial-time algorithm for solving the NP-complete problem 3-SAT. In examining the paper's…