Generalized Probabilistic Approximate Optimization Algorithm
Abdelrahman S Abdelrahman1, Shuvro Chowdhury2, Flaviano Morone3
1Department of Electrical and Computer Engineering, University of California, Santa Barbara, Santa Barbara, CA, USA. abdelrahman@ucsb.edu.
Nature Communications
|December 8, 2025
Summary
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.
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.
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