Applying the quantum approximate optimization algorithm to the minimum vertex cover problem

Zhang, Yongqiang; Mu, Xiaodong; Liu, Xiao-Wen; Wang, Xingyu; Zhang, Xue; Li, Kai; Wu, Tianyi; Zhao, Dao; Chen, Dong

doi:10.1016/j.asoc.2022.108554

Cited by 18 publications

(5 citation statements)

References 28 publications

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“…Zhang et al. [ 12 ] propose quantum approximate optimization algorithm (QAOA), which uses a model for quantum computing different from quantum annealing, for the minimum vertex cover problem and apply it to graphs of ten vertices. However, the minimum vertex cover problem is simpler than set cover in the sense that its standard formulation involves a single equality constraint and no inequality ones.…”

Section: Previous Workmentioning

confidence: 99%

“…For the related problem of minimum vertex cover, Pelofske et al [11] design a quantum annealing algorithm that can deal with problems that are too large to fit onto the quantum hardware by decomposing them into smaller subproblems. Zhang et al [12] propose quantum approximate optimization algorithm (QAOA), which uses a model for quantum computing different from quantum annealing, for the minimum vertex cover problem and apply it to graphs of ten vertices. However, the minimum vertex cover problem is simpler than set cover in the sense that its standard formulation involves a single equality constraint and no inequality ones.…”

Section: Previous Workmentioning

confidence: 99%

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Quantum Annealing with Inequality Constraints: The Set Cover Problem

Djidjev

2023

Adv Quantum Tech

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Quantum annealing is a promising method for solving hard optimization problems by transforming them into quadratic unconstrained binary optimization (QUBO) problems. However, when constraints are involved, particularly multiple inequality constraints, incorporating them into the objective function poses challenges. In this paper, the authors present two novel approaches for solving problems with multiple inequality constraints on a quantum annealer and apply them to the set cover problem (SCP). The first approach uses the augmented Lagrangian method to represent the constraints, while the second approach employs a higher‐order binary optimization (HUBO) formulation. The experiments show that both approaches outperform the standard approach for solving the SCP on the D‐Wave Advantage quantum annealer. The HUBO formulation performs slightly better than the augmented Lagrangian method in solving the SCP, but its scalability in terms of embeddability in the quantum chip is worse. The results demonstrate that the proposed augmented Lagrangian and HUBO methods can successfully implement a large number of inequality constraints, making them applicable to a broad range of constrained problems beyond the SCP.

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Section: Previous Workmentioning

confidence: 99%

Section: Previous Workmentioning

confidence: 99%

Quantum Annealing with Inequality Constraints: The Set Cover Problem

Djidjev

2023

Adv Quantum Tech

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“…Quantum Approximate Optimization Algorithm (QAOA) [ 20–25 ] is a class of hybrid quantum‐classical algorithms, presented by Farhi et al. [ 26 ] to tackle combinatorial optimization problems such as

k

‐vertex cover [ 27 ] and exact cover. [ 28 ] In QAOA, the solution of the combinatorial optimization problem tends to be encoded as the ground state of the target Hamiltonian

H_{C}

.…”

Section: Introductionmentioning

confidence: 99%

Multilevel Leapfrogging Initialization Strategy for Quantum Approximate Optimization Algorithm

Ni,

Cai,

Liu

et al. 2024

Adv Quantum Tech

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Recently, Zhou et al. have proposed an Interpolation‐based (INTERP) strategy to generate the initial parameters for Quantum Approximate Optimization Algorithm (QAOA). INTERP guesses the initial parameters at level by applying interpolation to the optimized parameters at level , achieving better performance than random initialization (RI). Nevertheless, INTERP consumes extensive costs for deep QAOA because it necessitates optimization at each level depth. To address it, a Multilevel Leapfrogging Interpolation (MLI) strategy is proposed. MLI produces initial parameters from level to () at level , omitting the optimization rounds from level to . MLI executes optimization at few levels rather than each level, and this operation is called Multilevel Leapfrogging optimization (M‐Leap). The performance of MLI is investigated on the Maxcut problem. The simulation results demonstrate MLI achieves the same quasi‐optima as INTERP while consuming 1/2 of costs required by INTERP. Besides, for MLI, where there is no RI except for level 1, the greedy‐MLI strategy is presented. The simulation results suggest greedy‐MLI has better stability than INTERP and MLI beyond obtaining the quasi‐optima. According to the efficiency of finding the quasi‐optima, the idea of M‐Leap might be extended to other training tasks, especially those requiring numerous optimizations.

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“…Also, since MVCP is an NP-Complete optimization problem, research and development of possible solutions continue. Since MVCP is a problem that cannot be solved completely, different alternative approaches have been presented to solve this problem (Zhang et al, 2022). At the beginning of these are the heuristic and meta-heuristic methods.…”

Section: Introductionmentioning

confidence: 99%

“…Quantum is another optimization method proposed by Link et al to solve MVCP. The approximate optimization algorithm was used (Zhang et al, 2022). In this method, no linear time solution is developed for MVCP, but a probabilistic approach that can be performed on quantum computers is given.…”

Section: Introductionmentioning

confidence: 99%

A New Approach Based on Centrality Value in Solving the Minimum Vertex Cover Problem: Malatya Centrality Algorithm

Karcı

Yakut

Öztemiz

2022

AB-BBD

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The graph is a data structures and models that used to describe many real-world problems. Many engineering problems, such as safety and transportation, have a graph-like structure and are based on a similar model. Therefore, these problems can be solved using similar methods to the graph data model. Vertex cover problem that is used in modeling many problems is one of the important NP-complete problems in graph theory. Vertex-cover realization by using minimum number of vertex is called Minimum Vertex Cover Problem (MVCP). Since MVCP is an optimization problem, many algorithms and approaches have been proposed to solve this problem. In this article, Malatya algorithm, which offers an effective solution for the vertex-cover problem, is proposed. Malatya algorithm offers a polynomial approach to the vertex cover problem. In the proposed approach, MVCP consists of two steps, calculating the Malatya centrality value and selecting the covering nodes. In the first step, Malatya centrality values are calculated for the nodes in the graph. These values are calculated using Malatya algorithm. Malatya centrality value of each node in the graph consists of the sum of the ratios of the degree of the node to the degrees of the adjacent nodes. The second step is a node selection problem for the vertex cover. The node with the maximum Malatya centrality value is selected from the nodes in the graph and added to the solution set. Then this node and its coincident edges are removed from the graph. Malatya centrality values are calculated again for the new graph, and the node with the maximum Malatya centrality value is selected from these values, and the coincident edges to this node are removed from the graph. This process is continued until all the edges in the graph are covered. It is shown on the sample graph that the proposed Malatya algorithm provides an effective solution for MVCP. Successful test results and analyzes show the effectiveness of Malatya algorithm.

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Applying the quantum approximate optimization algorithm to the minimum vertex cover problem

Cited by 18 publications

References 28 publications

Quantum Annealing with Inequality Constraints: The Set Cover Problem

Quantum Annealing with Inequality Constraints: The Set Cover Problem

Multilevel Leapfrogging Initialization Strategy for Quantum Approximate Optimization Algorithm

A New Approach Based on Centrality Value in Solving the Minimum Vertex Cover Problem: Malatya Centrality Algorithm

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