Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0010021

Finding Solutions to NP Problems: Philosophical Difference Between Quantum and Evolutionary Search Algorithms

Greenwood, G. W.

Published Oct 5, 2000• 3 citations
arXivHTMLPDF

Abstract

There is no known polynomial-time algorithm that can solve an NP problem. Evolutionary search has been shown to be a viable method of finding acceptable solutions within a reasonable time period. Recently quantum computers have surfaced as another alternative method. But these two methods use radically different philosophies for solving NP problems even though both search methods are non-deterministic. This paper uses instances of {\bf SAT}, {\bf 3SAT} and {\bf TSP} to describe how these two methods differ in their approach to solving NP problems.

DOI
10.48550/arxiv.quant-ph/0010021

Related papers

Finding solutions to NP problems: philosophical differences between quantum and evolutionary search algorithms

G.W. Greenwood

This paper uses instances of SAT, 3SAT and TSP to describe how evolutionary search (running on a classical computer) differs from quantum search (running on a quantum computer) for solving NP problems.

IEEE Congress on Evolutionary Computation (CEC)•Nov 13, 2002•32 citations

A Review of Quantum-Inspired Genetic Algorithms

Rupali Mitra, Tamal Chakraborty, Romit S. Beed

By violating the extended Church-Turing thesis, the quantum computing (QC) paradigm has emerged as a serious contender to classical computing. We now know that certain classical exponential problems (NP (nondeterministic polynomial time)-complete) can be solved in polynomial time by QC. Shor’s integer factorization and Grover’s method for unstructured search are perhaps the most well-known quantum algorithms. QC has been successfully applied to a variety of domains including optimization problems. Optimization can be solved by using deterministic/numerical as well as stochastic methods. Genetic algorithms (GA) belong to the latter category. Incorporating quantum mechanical properties such as superposition, entanglement, interference into the structure of GA has resulted in a more efficient evolutionary computing method called the quantum-inspired genetic algorithm. This method has been successfully applied to image processing, signal processing, economic load dispatch, coalition formation, task scheduling, etc. This chapter presents an overview of the current trends and developments in the domain of quantum-inspired genetic algorithms with the aim of investigating areas of further research in this sphere.

Apple Academic Press eBooks•Feb 19, 2026•0 citations

Using an Evolutionary Algorithm to Create (MAX)-3SAT QUBOs

Sebastian Zielinski, Maximilian Zorn, Thomas Gabor +2 more

A common way of solving satisfiability instances with quantum methods is to transform these instances into instances of QUBO. State-of-the-art transformations from MAX-3SAT to QUBO work by mapping clauses of a 3SAT formula associated with the MAX-3SAT instance to an instance of QUBO and combining the resulting QUBOs into a single QUBO instance representing the whole MAX-3SAT instance. As creating these transformations is currently done manually or via exhaustive search methods and is, therefore, algorithmically inefficient, we see potential for including search-based optimization. In this paper, we propose two methods of using evolutionary algorithms to create QUBO representations of MAX-3SAT problems automatically. We evaluate our created QUBOs on 500 and 1000-clause 3SAT formulae and find competitive performance to state-of-the-art baselines when using both classical and quantum annealing solvers.

arXiv:2405.09272•Genetic and Evolutionary Computation Conference Companion (GECCO Companion)•Jul 14, 2024•1 citation

Quantum evolutionary algorithm for TSP combinatorial optimisation problem

Ma, Yijiang, Tan Chye Cheah

This paper implements a new way of solving a problem called the traveling salesman problem (TSP) using quantum genetic algorithm (QGA). We compared how well this new approach works to the traditional method known as a classical genetic algorithm (CGA). The TSP is a well-established challenge in combinatorial optimization where the objective is to find the most efficient path to visit a series of cities, minimizing the total distance, and returning to the starting point. We chose the TSP to test the performance of both algorithms because of its computational complexity and importance in practical applications. We choose the dataset from the international standard library TSPLIB for our experiments. By designing and implementing both algorithms and conducting experiments on various sizes and types of TSP instances, we provide an in-depth analysis of the accuracy of the optimal solution, the number of iterations, the execution time, and the stability of the algorithms for both. The empirical findings indicate that the CGA outperforms the QGA in terms of finding superior solutions more quickly in most of the test instances, especially when the problem size is large. This suggests that although the principle of quantum computing provides a new way to solve complex combinatorial optimisation problems, the implementation of quantum phenomena and the setting of parameters such as the optimal angle for a quantum revolving gate is challenging and need further optimisation to achieve the desired results. Additionally, it is important to note that the QGA has not been tested on real quantum hardware, so its true performance remains unverified. These limitations provide rich opportunities for further research in the future.

arXiv:2409.13788•Sep 20, 2024•0 citations

The Subset Sum Problem: Reducing Time Complexity of NP-Completeness with Quantum Search

Bo Moon

The Subset Sum Problem is a member of the NP-complete class, so no known polynomial time algorithm exists for it. Although there are polynomial time approximations and heuristics, these are not always acceptable, yet exact-solution algorithms are unfeasible for large input. Quantum computation offers new insights for not only the Subset Sum Problem but also the entire NP-complete class; most notably, Grover's quantum algorithm for an unstructured database search can be tailored to identify solutions to problems within mathematics and computer science. This paper discusses the physical and conceptual feasibility of quantum computation and demonstrates the utility of quantum search by analyzing the time complexities of the classical dynamic programming algorithm and Grover's algorithm in solving the Subset Sum Problem, evincing the implications this has on the NP-complete class in general.

Undergraduate Journal of Mathematical Modeling One + Two•May 1, 2013•3 citations

Continuous-time Quantum Algorithms: Searching and Adiabatic Computation

Lawrence M. Ioannou

One of the most important quantum algorithms is Grover's search algorithm [G96]. Quantum searching can be used to speed up the search for solutions to NP-complete problems e. g. 3SAT. Even so, the best known quantum algorithms for 3SAT are considered inefficient. \nSoon after Grover's discovery, Farhi and Gutmann [FG96] devised a "continuous-time analogue" of quantum searching. More recently Farhi et. al. [FGGS00] proposed a continuous-time 3SAT algorithm which invokes the adiabatic approximation [M76]. Their algorithm is difficult to analyze, hence we do not know whether it can solve typical 3SAT instances faster than Grover's search algorithm can. \nI begin with a review of the discrete- and continuous-time models of quantum computation. I then make precise the notion of "efficient quantum algorithms", motivating sufficient conditions for discrete- and continuous-time algorithms to be considered efficient via discussion of standard techniques for discrete-time simulation of continuous-time algorithms. After reviewing three quantum search algorithms [F00,FG96,G96], I develop the adiabatic 3SAT algorithm as a natural extension of Farhi and Gutmann's search algorithm. Along the way, I present the adiabatic search algorithm [vDMV01] and remark on its discrete-time simulation. Finally I devise a generalization of the adiabatic algorithm and prove some lower bounds for various cases of this general framework. \nUPDATE (February 2003): Please see article http://arxiv. org/abs/quant-ph/0302138 for a resolution to the problem of simulating the continuous-time adiabatic search algorithm with a quantum circuit using only O(sqrt(N)) resources.

•Jan 1, 2002•4 citations
There is no known polynomial-time algorithm that can solve an NP problem. Evolutionary search has been shown to be a viable method of finding acceptable solutions within a reasonable time period. Recently quantum computers have surfaced as another alternative method. But these two methods use radically different philosophies for solving NP problems even though both search methods are non-deterministic. This paper uses instances of {\bf SAT}, {\bf 3SAT} and {\bf TSP} to describe how these two methods differ in their approach to solving NP problems.
By violating the extended Church-Turing thesis, the quantum computing (QC) paradigm has emerged as a serious contender to classical computing. We now know that certain classical exponential problems (NP (nondeterministic polynomial time)-complete) can be solved in polynomial time by QC. Shor’s integer factorization and Grover’s method for unstructured search are perhaps the most well-known quantum algorithms. QC has been successfully applied to a variety of domains including optimization problems. Optimization can be solved by using deterministic/numerical as well as stochastic methods. Genetic algorithms (GA) belong to the latter category. Incorporating quantum mechanical properties such as superposition, entanglement, interference into the structure of GA has resulted in a more efficient evolutionary computing method called the quantum-inspired genetic algorithm. This method has been successfully applied to image processing, signal processing, economic load dispatch, coalition formation, task scheduling, etc. This chapter presents an overview of the current trends and developments in the domain of quantum-inspired genetic algorithms with the aim of investigating areas of further research in this sphere.
A common way of solving satisfiability instances with quantum methods is to transform these instances into instances of QUBO. State-of-the-art transformations from MAX-3SAT to QUBO work by mapping clauses of a 3SAT formula associated with the MAX-3SAT instance to an instance of QUBO and combining the resulting QUBOs into a single QUBO instance representing the whole MAX-3SAT instance. As creating these transformations is currently done manually or via exhaustive search methods and is, therefore, algorithmically inefficient, we see potential for including search-based optimization. In this paper, we propose two methods of using evolutionary algorithms to create QUBO representations of MAX-3SAT problems automatically. We evaluate our created QUBOs on 500 and 1000-clause 3SAT formulae and find competitive performance to state-of-the-art baselines when using both classical and quantum annealing solvers.
This paper implements a new way of solving a problem called the traveling salesman problem (TSP) using quantum genetic algorithm (QGA). We compared how well this new approach works to the traditional method known as a classical genetic algorithm (CGA). The TSP is a well-established challenge in combinatorial optimization where the objective is to find the most efficient path to visit a series of cities, minimizing the total distance, and returning to the starting point. We chose the TSP to test the performance of both algorithms because of its computational complexity and importance in practical applications. We choose the dataset from the international standard library TSPLIB for our experiments. By designing and implementing both algorithms and conducting experiments on various sizes and types of TSP instances, we provide an in-depth analysis of the accuracy of the optimal solution, the number of iterations, the execution time, and the stability of the algorithms for both. The empirical findings indicate that the CGA outperforms the QGA in terms of finding superior solutions more quickly in most of the test instances, especially when the problem size is large. This suggests that although the principle of quantum computing provides a new way to solve complex combinatorial optimisation problems, the implementation of quantum phenomena and the setting of parameters such as the optimal angle for a quantum revolving gate is challenging and need further optimisation to achieve the desired results. Additionally, it is important to note that the QGA has not been tested on real quantum hardware, so its true performance remains unverified. These limitations provide rich opportunities for further research in the future.
The Subset Sum Problem is a member of the NP-complete class, so no known polynomial time algorithm exists for it. Although there are polynomial time approximations and heuristics, these are not always acceptable, yet exact-solution algorithms are unfeasible for large input. Quantum computation offers new insights for not only the Subset Sum Problem but also the entire NP-complete class; most notably, Grover's quantum algorithm for an unstructured database search can be tailored to identify solutions to problems within mathematics and computer science. This paper discusses the physical and conceptual feasibility of quantum computation and demonstrates the utility of quantum search by analyzing the time complexities of the classical dynamic programming algorithm and Grover's algorithm in solving the Subset Sum Problem, evincing the implications this has on the NP-complete class in general.
One of the most important quantum algorithms is Grover's search algorithm [G96]. Quantum searching can be used to speed up the search for solutions to NP-complete problems e. g. 3SAT. Even so, the best known quantum algorithms for 3SAT are considered inefficient. \nSoon after Grover's discovery, Farhi and Gutmann [FG96] devised a "continuous-time analogue" of quantum searching. More recently Farhi et. al. [FGGS00] proposed a continuous-time 3SAT algorithm which invokes the adiabatic approximation [M76]. Their algorithm is difficult to analyze, hence we do not know whether it can solve typical 3SAT instances faster than Grover's search algorithm can. \nI begin with a review of the discrete- and continuous-time models of quantum computation. I then make precise the notion of "efficient quantum algorithms", motivating sufficient conditions for discrete- and continuous-time algorithms to be considered efficient via discussion of standard techniques for discrete-time simulation of continuous-time algorithms. After reviewing three quantum search algorithms [F00,FG96,G96], I develop the adiabatic 3SAT algorithm as a natural extension of Farhi and Gutmann's search algorithm. Along the way, I present the adiabatic search algorithm [vDMV01] and remark on its discrete-time simulation. Finally I devise a generalization of the adiabatic algorithm and prove some lower bounds for various cases of this general framework. \nUPDATE (February 2003): Please see article http://arxiv. org/abs/quant-ph/0302138 for a resolution to the problem of simulating the continuous-time adiabatic search algorithm with a quantum circuit using only O(sqrt(N)) resources.