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This summary is machine-generated.

This study explores the traveling salesman problem (TSP) using the quantum approximate optimization algorithm (QAOA) on quantum simulators. A balanced QAOA mixer design shows promise for solving complex optimization problems on quantum computers.

Keywords:
noisy simulationquantum approximate optimization algorithmquantum computingquantum simulationtraveling salesman problem

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Area of Science:

  • Quantum Computing
  • Computational Complexity
  • Optimization Algorithms

Background:

  • The traveling salesman problem (TSP) is a benchmark NP-hard problem frequently used to assess quantum computing paradigms.
  • Studying TSP on quantum computers is crucial for understanding the potential of quantum algorithms for complex optimization tasks.

Purpose of the Study:

  • To investigate the application of the quantum approximate optimization algorithm (QAOA) for solving the traveling salesman problem (TSP).
  • To evaluate different QAOA mixer designs and optimization strategies on gate-based quantum simulators.
  • To assess the feasibility of digital quantum simulation for finding optimal TSP solutions.

Main Methods:

  • Formulated the traveling salesman problem (TSP) as an optimization problem for quantum computation.
  • Employed an improved qubit encoding strategy and a layer-wise learning optimization protocol within the QAOA framework.
  • Conducted numerical simulations on a gate-based digital quantum simulator for TSP instances with 3, 4, and 5 cities.

Main Results:

  • Evaluated the performance of three distinct QAOA mixer designs based on numerical accuracy and optimization cost.
  • Identified that a well-balanced QAOA mixer design demonstrates superior potential for gate-based simulators and future quantum devices.
  • Observed that noise model simulations support the effectiveness of the balanced mixer design.

Conclusions:

  • Digital quantum simulation using problem-inspired ansatz is a viable approach for solving the traveling salesman problem (TSP).
  • The choice of QAOA mixer design significantly impacts simulation performance and accuracy.
  • A balanced QAOA mixer design is recommended for practical applications on quantum hardware.