Many metaheuristic algorithms have been proposed to solve combinatorial and numerical optimization problems. Most optimization problems have high dependence, meaning that variables are strongly dependent on one another. If a method were to attempt to optimize each variable independently, its performance would suffer significantly. When traditional optimization techniques are applied to highdependence problems, they experience difficulty in finding the global optimum. To address this problem, this paper proposes a novel metaheuristic algorithm, the entanglement-enhanced quantum-inspired tabu search algorithm (Entanglement-QTS), which is based on the quantum-inspired tabu search (QTS) algorithm and the feature of quantum entanglement. Entanglement-QTS differs from other quantum-inspired evolutionary algorithms in that its Q-bits have entangled states, which can express a high degree of correlation, rendering the variables more intertwined. Entangled Q-bits represent a state-of-the-art idea that can significantly improve the treatment of multimodal and high-dependence problems. Entanglement-QTS can discover optimal solutions, balance diversification and intensification, escape numerous local optimal solutions by using the quantum not gate, reinforce the intensification effect by local search and entanglement local search, and manage strong-dependence problems and accelerate the optimization process by using entangled states. This paper uses nine benchmark functions to test the search ability of the entanglement-QTS algorithm. The results demonstrate that Entanglement-QTS outperforms QTS and other metaheuristic algorithms in both its effectiveness at finding the global optimum and its computational efficiency.Many metaheuristic algorithms have been proposed to solve combinatorial and numerical optimization problems. Most optimization problems have high dependence, meaning that variables are strongly dependent on one another. If a method were to attempt to optimize each variable independently, its performance would suffer significantly. When traditional optimization techniques are applied to highdependence problems, they experience difficulty in finding the global optimum. To address this problem, this paper proposes a novel metaheuristic algorithm, the entanglement-enhanced quantum-inspired tabu search algorithm (Entanglement-QTS), which is based on the quantum-inspired tabu search (QTS) algorithm and the feature of quantum entanglement. Entanglement-QTS differs from other quantum-inspired evolutionary algorithms in that its Q-bits have entangled states, which can express a high degree of correlation, rendering the variables more intertwined. Entangled Q-bits represent a state-of-the-art idea that can significantly improve the treatment of multimodal and high-dependence problems. Entanglement-QTS can discover optimal solutions, balance diversification and intensification, escape numerous local optimal solutions by using the quantum not gate, reinforce the intensification effect by local search and entanglement local search, and manage strong-dependence problems and accelerate the optimization process by using entangled states. This paper uses nine benchmark functions to test the search ability of the entanglement-QTS algorithm. The results demonstrate that Entanglement-QTS outperforms QTS and other metaheuristic algorithms in both its effectiveness at finding the global optimum and its computational efficiency.

IEEE AccessJan 1, 201764 citations

Spatial Search Algorithms

Renato Portugal

Springer eBooksJan 1, 20130 citations

Local Quantum Search Algorithm for Random $k$ -SAT with $Ω(n^{1+ε})$ ClausesLocal Quantum Search Algorithm for Random $k$-SAT with $Ω(n^{1+ε})$ Clauses

Mingyou Wu

The random k-SAT instances undergo a "phase transition" from being generally satisfiable to unsatisfiable as the clause number m passes a critical threshold, $r_k n$ . This causes a drastic reduction in the number of satisfying assignments, shifting the problem from being generally solvable on classical computers to typically insolvable. Beyond this threshold, it is challenging to comprehend the computational complexity of random k-SAT. In quantum computing, Grover's search still yields exponential time requirements due to the neglect of structural information. Leveraging the structure inherent in search problems, we propose the k-local quantum search algorithm, which extends quantum search to structured scenarios. Grover's search, by contrast, addresses the unstructured case where k=n. Given that the search algorithm necessitates the presence of a target, we specifically focus on the problem of searching the interpretation of satisfiable instances of k-SAT, denoted as max-k-SSAT. If this problem is solvable in polynomial time, then k-SAT can also be solved within the same complexity. We demonstrate that, for small $k \ge 3$ , any small $ε>0$ and sufficiently large n: $\cdot$ k-local quantum search achieves general efficiency on random instances of max-k-SSAT with $m=Ω(n^{2+δ+ε})$ using $\mathcal{O}(n)$ iterations, and $\cdot$ k-local adiabatic quantum search enhances the bound to $m=Ω(n^{1+δ+ε})$ within an evolution time of $\mathcal{O}(n^2)$ . In both cases, the circuit complexity of each iteration is $\mathcal{O}(n^k)$ , and the efficiency is assured with overwhelming probability $1 - \mathcal{O}(\mathrm{erfc}(n^{δ/2}))$ . By modifying this algorithm capable of solving all instances of max-k-SSAT, we further prove that max-k-SSAT is polynomial on average when $m=Ω(n^{2+ε})$ based on the average-case complexity theory.The random k-SAT instances undergo a "phase transition" from being generally satisfiable to unsatisfiable as the clause number m passes a critical threshold, $r_k n$. This causes a drastic reduction in the number of satisfying assignments, shifting the problem from being generally solvable on classical computers to typically insolvable. Beyond this threshold, it is challenging to comprehend the computational complexity of random k-SAT. In quantum computing, Grover's search still yields exponential time requirements due to the neglect of structural information. Leveraging the structure inherent in search problems, we propose the k-local quantum search algorithm, which extends quantum search to structured scenarios. Grover's search, by contrast, addresses the unstructured case where k=n. Given that the search algorithm necessitates the presence of a target, we specifically focus on the problem of searching the interpretation of satisfiable instances of k-SAT, denoted as max-k-SSAT. If this problem is solvable in polynomial time, then k-SAT can also be solved within the same complexity. We demonstrate that, for small $k \ge 3$, any small $ε>0$ and sufficiently large n: $\cdot$ k-local quantum search achieves general efficiency on random instances of max-k-SSAT with $m=Ω(n^{2+δ+ε})$ using $\mathcal{O}(n)$ iterations, and $\cdot$ k-local adiabatic quantum search enhances the bound to $m=Ω(n^{1+δ+ε})$ within an evolution time of $\mathcal{O}(n^2)$. In both cases, the circuit complexity of each iteration is $\mathcal{O}(n^k)$, and the efficiency is assured with overwhelming probability $1 - \mathcal{O}(\mathrm{erfc}(n^{δ/2}))$. By modifying this algorithm capable of solving all instances of max-k-SSAT, we further prove that max-k-SSAT is polynomial on average when $m=Ω(n^{2+ε})$ based on the average-case complexity theory.

arXiv:2403.03237Mar 5, 20241 citation

Quest for Fast Partial Search Algorithm

V. E. Korepin, Jinfeng Liao

arXiv:quant-ph/0510179Quantum Information ProcessingMay 9, 200619 citations

Quantum-Driven Constraint Optimization for Algorithmic Diversity

Jincheng Zhang

Quantum-driven constraint optimization presents a novel approach to algorithmic diversity by leveraging quantum annealing or quantum approximate optimization algorithms (QAOA) to systematically explore the space of possible algorithmic solutions. This paper introduces a framework where quantum computation is utilized to iteratively refine algorithmic designs, promoting the discovery of novel and diverse solutions that might be missed by classical optimization techniques. The core mechanism centers on the ability of quantum algorithms to escape local optima and navigate complex search spaces, ultimately leading to a more comprehensive exploration of algorithmic possibilities. This work addresses the limitations of conventional optimization methods by introducing a quantum-enhanced search strategy, ultimately aiming to significantly enhance the diversity of algorithmic designs.Quantum-driven constraint optimization presents a novel approach to algorithmic diversity by leveraging quantum annealing or quantum approximate optimization algorithms (QAOA) to systematically explore the space of possible algorithmic solutions. This paper introduces a framework where quantum computation is utilized to iteratively refine algorithmic designs, promoting the discovery of novel and diverse solutions that might be missed by classical optimization techniques. The core mechanism centers on the ability of quantum algorithms to escape local optima and navigate complex search spaces, ultimately leading to a more comprehensive exploration of algorithmic possibilities. This work addresses the limitations of conventional optimization methods by introducing a quantum-enhanced search strategy, ultimately aiming to significantly enhance the diversity of algorithmic designs.

Sep 6, 20260 citations

Local Quantum Search Algorithm for Random

k

-SAT with

Ω(n^{1+ε})

Clauses

The random k-SAT instances undergo a "phase transition" from being generally satisfiable to unsatisfiable as the clause number m passes a critical threshold,

r_k n

. This causes a drastic reduction in the number of satisfying assignments, shifting the problem from being generally solvable on classical computers to typically insolvable. Beyond this threshold, it is challenging to comprehend the computational complexity of random k-SAT. In quantum computing, Grover's search still yields exponential time requirements due to the neglect of structural information. Leveraging the structure inherent in search problems, we propose the k-local quantum search algorithm, which extends quantum search to structured scenarios. Grover's search, by contrast, addresses the unstructured case where k=n. Given that the search algorithm necessitates the presence of a target, we specifically focus on the problem of searching the interpretation of satisfiable instances of k-SAT, denoted as max-k-SSAT. If this problem is solvable in polynomial time, then k-SAT can also be solved within the same complexity. We demonstrate that, for small

k \ge 3

, any small

ε>0

and sufficiently large n:

\cdot

k-local quantum search achieves general efficiency on random instances of max-k-SSAT with

m=Ω(n^{2+δ+ε})

using

\mathcal{O}(n)

iterations, and

\cdot

k-local adiabatic quantum search enhances the bound to

m=Ω(n^{1+δ+ε})

within an evolution time of

\mathcal{O}(n^2)

. In both cases, the circuit complexity of each iteration is

\mathcal{O}(n^k)

, and the efficiency is assured with overwhelming probability

1 - \mathcal{O}(\mathrm{erfc}(n^{δ/2}))

. By modifying this algorithm capable of solving all instances of max-k-SSAT, we further prove that max-k-SSAT is polynomial on average when

m=Ω(n^{2+ε})

based on the average-case complexity theory.