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Gaussian boson sampling (GBS) enhances stochastic algorithms for identifying dense subgraphs. This quantum approach improves the NP-hard densest k-subgraph problem, offering a new computational tool.

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Area of Science:

  • Quantum Computing
  • Computational Complexity
  • Graph Theory

Background:

  • Boson sampling devices are key for demonstrating quantum supremacy.
  • The practical applications of boson sampling, particularly Gaussian boson sampling (GBS), for solving real-world problems remain underexplored.
  • Identifying dense subgraphs is a computationally challenging problem with significant practical implications.

Purpose of the Study:

  • To investigate the utility of Gaussian boson sampling (GBS) for solving practical computational problems.
  • To demonstrate that GBS can be effectively applied to the NP-hard densest k-subgraph problem.
  • To enhance existing stochastic algorithms using GBS for improved dense subgraph identification.

Main Methods:

  • Established a theoretical link between graph density and the number of perfect matchings (Hafnian).
  • Utilized the Hafnian as the key quantity determining sampling probabilities in GBS.
  • Developed GBS-enhanced versions of random search and simulated annealing algorithms.
  • Conducted numerical simulations of GBS on a 30-vertex graph to test the enhanced algorithms.

Main Results:

  • Gaussian boson sampling (GBS) significantly enhances stochastic algorithms for dense subgraph identification.
  • GBS demonstrates a high probability of selecting dense subgraphs, particularly for the densest k-subgraph problem.
  • Numerical simulations confirmed the effectiveness of GBS-enhanced algorithms in identifying dense subgraphs.

Conclusions:

  • Gaussian boson sampling (GBS) offers a powerful new approach for tackling the NP-hard densest k-subgraph problem.
  • The study validates the theoretical connection between graph density, Hafnians, and GBS sampling probabilities.
  • GBS-enhanced algorithms represent a promising advancement in computational graph analysis and quantum algorithm development.