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Solving independent set problems with photonic quantum circuits.

Xu-Fei Yin1,2,3, Xing-Can Yao1,2,3, Biao Wu4,5

  • 1Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China.

Proceedings of the National Academy of Sciences of the United States of America
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Summary
This summary is machine-generated.

Researchers digitally simulated non-Abelian adiabatic mixing (NAAM) to solve the independent set (IS) problem using a quantum network. This approach successfully identified maximum independent sets, demonstrating NAAM

Keywords:
adiabatic mixingindependent setsphotonic quantum computerquantum algorithm

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Area of Science:

  • Quantum Information Science
  • Computational Complexity
  • Graph Theory

Background:

  • The independent set (IS) problem is computationally challenging and equivalent to finding ground states of a mapped Hamiltonian.
  • Adiabatic quantum computation offers a framework for solving such problems.
  • Non-Abelian adiabatic mixing (NAAM) is a recent technique exploiting emergent gauge symmetry to address the IS problem.

Purpose of the Study:

  • To digitally simulate the non-Abelian adiabatic mixing (NAAM) protocol for solving a representative independent set (IS) problem.
  • To experimentally validate the effectiveness of NAAM using a linear optical quantum network.

Main Methods:

  • Digital simulation of NAAM using a linear optical quantum network.
  • Implementation involved three C-Phase gates, four deterministic two-qubit gate arrays (DGA), and ten single rotation gates.
  • Careful selection of the evolution path and sufficient Trotterization steps were employed.

Main Results:

  • Successfully identified the maximum independent set for the chosen graph.
  • Achieved a total probability of 0.875(16) for finding independent sets.
  • Nontrivial independent sets constituted approximately 31.4% of the total probability.

Conclusions:

  • The digital simulation successfully demonstrated the potential of NAAM for solving IS-equivalent problems.
  • The experimental setup validated the feasibility of using quantum networks for NAAM.
  • NAAM shows promise as an advantageous method for tackling complex computational problems.