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Ken N Okada1, Hirofumi Nishi2,3, Taichi Kosugi2,3

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Warm-start QAOA (Quantum Approximate Optimization Algorithm) improves performance on optimization problems. Higher accuracy of initial solutions leads to better results, especially for MAX-CUT problems on quantum computers.

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Area of Science:

  • Quantum Computing
  • Optimization Algorithms
  • Computational Complexity

Background:

  • The Quantum Approximate Optimization Algorithm (QAOA) is a leading hybrid quantum-classical approach for tackling complex optimization challenges on current noisy quantum hardware.
  • Warm-start strategies, which leverage pre-computed approximate solutions to initialize the quantum state or ansatz, have emerged as a method to enhance QAOA performance.

Purpose of the Study:

  • This research investigates the precise impact of approximate solution accuracy on the effectiveness of the warm-start QAOA (WS-QAOA).
  • The study aims to quantify the relationship between the quality of warm-start solutions and the performance gains observed in WS-QAOA.

Main Methods:

  • Numerical simulations were conducted to evaluate WS-QAOA performance on standard MAX-CUT problems.
  • The fidelity and approximation ratio were measured against the Hamming distance between approximate and exact solutions.

Main Results:

  • WS-QAOA demonstrates superior fidelity and approximation ratios compared to standard QAOA as the Hamming distance to exact solutions decreases.
  • Performance improvements are quantitatively linked to the initial state preparation within the quantum ansatz.
  • Applying WS-QAOA with solutions generated by QAOA itself yields enhanced results, particularly with shallower quantum circuits.

Conclusions:

  • The accuracy of approximate solutions is a critical factor in the success of WS-QAOA.
  • This study provides quantitative insights into the performance benefits of WS-QAOA and offers guidance on the required quality of warm-start solutions for practical applications.