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The quantum approximate optimization algorithm creates thermal-like states in Ising models that are hard for classical computers to simulate. A hidden correlation determines the effective temperature, linking energy, covariance, and Hamming distance.

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Area of Science:

  • Quantum computing
  • Quantum algorithms
  • Statistical mechanics

Background:

  • The Quantum Approximate Optimization Algorithm (QAOA) is a leading candidate for demonstrating quantum advantage.
  • Understanding the properties of states produced by QAOA is crucial for its practical application.
  • Ising spin models are fundamental to condensed matter physics and quantum computation.

Purpose of the Study:

  • To investigate the nature of states generated by a single-layer QAOA on universal Ising spin models.
  • To determine the classical simulation complexity of these QAOA-generated states.
  • To identify the factors influencing the effective temperature of these states.

Main Methods:

  • Analytical derivations to characterize the quantum states.
  • Numerical simulations to verify theoretical predictions.
  • Analysis of state properties including energy, covariance, and Hamming distances.

Main Results:

  • Single-layer QAOA on universal Ising models produces pseudo-Boltzmann (thermal-like) states.
  • These states exhibit classical simulation difficulties, failing the rapid mixing condition for Ising models.
  • A universal correlation was discovered, linking state energy, energy level covariance, and Hamming distances to determine the effective temperature.

Conclusions:

  • QAOA states on Ising models may not offer a direct path to quantum advantage via simulation speedup.
  • The identified correlation provides a new perspective on the relationship between quantum states and their classical simulation properties.
  • Further research is needed to explore multi-layer QAOA and different quantum models.