Improving Quantum Approximate Optimization by Noise-Directed Adaptive Remapping

TL;DR

This paper introduces Noise-Directed Adaptive Remapping (NDAR), a heuristic that leverages noise in quantum processors to improve the performance of quantum optimization algorithms by transforming noise into a beneficial factor.

Contribution

The paper proposes NDAR, a novel noise-aware heuristic that enhances quantum approximate optimization by turning noise into a constructive element, demonstrated on Rigetti's quantum device.

Findings

Achieved approximation ratios of 0.9-0.96 with NDAR on 82-qubit graphs.

NDAR significantly outperforms standard QAOA at the same depth.

Noise can be exploited to improve quantum optimization performance.

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.