QAOA-GPT: Efficient Generation of Adaptive and Regular Quantum Approximate Optimization Algorithm Circuits

--Quantum computing has the potential to improve our ability to solve certain optimization problems that are computationally difficult for classical computers, by offering new algorithmic approaches that may provide speedups under specific conditions. In this work, we introduce QAOA-GPT, a generative framework that leverages Generative Pretrained Transformers (GPT) to directly synthesize quantum circuits for solving quadratic unconstrained binary optimization problems, and demonstrate it on the MaxCut problem on graphs. T o diversify the training circuits and ensure their quality, we have generated a synthetic dataset using the adaptive QAOA approach, a method that incrementally builds and optimizes problem-specific circuits. The experiments conducted on a curated set of graph instances demonstrate that QAOA-GPT, generates high quality quantum circuits for new problem instances unseen in the training as well as successfully parametrizes QAOA. Our results show that using QAOA-GPT to generate quantum circuits will significantly decrease both the computational overhead of classical QAOA and adaptive approaches that often use gradient evaluation to generate the circuit and the classical optimization of the circuit parameters. Our work shows that generative AI could be a promising avenue to generate compact quantum circuits in a scalable way. Quantum computing is rapidly emerging technology with significant potential across various domains, including finance [1], chemical simulations [2], material science [3], combinatorial optimization [4], and machine learning [5], among others. V ariational quantum-classical algorithms represent one of the most promising classes of quantum algorithms in different domains, showing potential for both fault-tolerant quantum computers and near-term noisy intermediate-scale quantum (NISQ) devices. The Quantum Approximate Optimization Algorithm (QAOA) [6] and many of its subsequent versions and customizations [7] belong to this class and demonstrate great potential due to their problem/application flexibility and compatibility with various quantum architectures. The original QAOA framework employs a fixed ansatz structure, which can limit expressibility and hinder performance, particularly on near-term quantum devices where circuit depth is limited. This rigid design may not capture the problem-specific features needed for efficient optimization. Such methods as ADAPT -QAOA [8] address this challenge by iteratively constructing the ansatz in a problem-informed manner. At each step, ADAPT -QAOA selects operators from a predefined pool based on their gradient with respect to the cost function, incorporating only those that contribute most significantly to improving the objective.