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Generalized Probabilistic Approximate Optimization Algorithm.

Abdelrahman S Abdelrahman1, Shuvro Chowdhury2, Flaviano Morone3

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We introduce the generalized Probabilistic Approximate Optimization Algorithm (PAOA), a framework for fast sampling on probabilistic computers. PAOA outperforms QAOA and extends simulated annealing, showing improved performance on complex problems.

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Area of Science:

  • Quantum computing and optimization algorithms.
  • Development of novel computational frameworks for complex problem-solving.

Background:

  • Existing optimization algorithms face challenges with scalability and efficiency on current hardware.
  • Need for advanced variational Monte Carlo methods for probabilistic computing.

Purpose of the Study:

  • Introduce and formalize the generalized Probabilistic Approximate Optimization Algorithm (PAOA).
  • Enable parameterized and fast sampling on Ising machines and probabilistic computers.
  • Establish PAOA as a principled variational formulation.

Main Methods:

  • Iterative modification of network couplings guided by cost evaluations.
  • Establishing a correspondence between derivative-free updates and Markov flow gradients.
  • Implementing simulated annealing as a limiting case on FPGA-based probabilistic computers.

Main Results:

  • PAOA demonstrates superior performance compared to QAOA on the Sherrington-Kirkpatrick model.
  • Simulated annealing emerges as a limiting case of PAOA.
  • PAOA extends simulated annealing by optimizing multiple temperature profiles, enhancing performance on heavy-tailed problems.

Conclusions:

  • The generalized PAOA offers a powerful and flexible framework for optimization on probabilistic hardware.
  • PAOA provides a principled variational approach, extending existing methods like simulated annealing.
  • PAOA shows significant potential for solving large-scale, complex optimization problems efficiently.