Improving Quantum Approximate Optimization by Noise-Directed Adaptive Remapping

• URL: http://arxiv.org/abs/2404.01412v2
• Date: Sat, 10 Aug 2024 03:14:31 GMT
• Title: Improving Quantum Approximate Optimization by Noise-Directed Adaptive Remapping
• Authors: Filip B. Maciejewski, Jacob Biamonte, Stuart Hadfield, Davide Venturelli,
• Abstract summary: Noise-Directed Remapping (NDAR) is a algorithm for approximately solving binary optimization problems by leveraging certain types of noise. We consider access to a noisy quantum processor with dynamics that features a global attractor state. 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.
• Score: 3.47862118034022
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present Noise-Directed Adaptive Remapping (NDAR), a heuristic algorithm for approximately solving binary optimization problems by leveraging certain types of noise. We consider access to a noisy quantum processor with dynamics that features a global attractor state. In a standard setting, such noise can be detrimental to the quantum optimization performance. 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. The transformation effectively changes the attractor into a higher-quality solution of the Hamiltonian based on the results of the previous step. The end result is that noise aids variational optimization, as opposed to hindering it. 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.

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