Improving Quantum Approximate Optimization by Noise-Directed Adaptive Remapping

We present Noise-Directed Adaptive Remapping (NDAR), a heuristic algorithm for approximately solving binary optimization problems by leveraging certain types of noise. Our algorithm bootstraps the noise attractor state by iteratively gauge-transforming the cost-function Hamiltonian in a way that transforms the noise attractor into higher-quality solutions. We present an improved Quantum Approximate Optimization Algorithm (QAOA) runs in experiments on Rigetti's quantum device. We report approximation ratios 0.9-0.96 for random, fully connected graphs on n=82 qubits, using only depth p=1 QAOA with NDAR. This compares to 0.34-0.51 for standard p=1 QAOA with the same number of function calls. The submission is based on preprint arXiv:2404.01412.