Improving Quantum Approximate Optimization by Noise-Directed Adaptive Remapping
Quantum Artificial Intelligence Laboratory (QuAIL), NASA Ames Research Center, CA, USA
USRA Research Institute for Advanced Computer Science (RIACS), CA, USA
| Published: | 2025-11-06, volume 9, page 1906 |
| Editor: | Alessio Benavoli |
| Eprint: | arXiv:2404.01412v3 |
| Doi: | https://doi.org/10.22331/q-2025-11-06-1906 |
| Citation: | Quantum 9, 1906 (2025). |
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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.
Featured image: Visualization of NDAR's performance with real data for 82-qubit QPU optimization on Rigetti's hardware. For early iterations, you can see how the tail of the previous distribution becomes the approximate center of the new distribution. The improvement continues at a slowing rate until convergence.
For additional material see posts on X on this paper and Noise-Directed Adaptive Remapping.
Popular summary
In this work, we propose a simple heuristic algorithm (Noise-Directed Adaptive Remapping, or NDAR) to exploit the knowledge about the noise to iteratively align the quantum optimization with the noisy evolution. We assume that the noisy dynamics has some classical attractor state (let's call it $\left|0\dots0\right\rangle$) $-$ e.g., amplitude damping (the requirement is that the noise is asymmetric w.r.t. $\left|0\right\rangle$ and $\left|1\right\rangle$ basis states).
In NDAR, we run variational optimization in an outer loop. In each step, we take the best bitstring (candidate solution) from the previous step, and we remap the cost Hamiltonian to a new, logically equivalent encoding. The new encoding is such that $\left|0\dots0\right\rangle$ state has lower energy (in the vanilla, greedy version, it is the energy of the previous best solution). Hence, NDAR iteratively remaps the problem Hamiltonian in a way that makes the noise attractor a better and better candidate solution (see attached Figure).
We applied NDAR with p=1 QAOA on n=82-qubit fully-connected random graphs on Rigetti's new chip Ankaa-2. We got approximation ratios of 0.9-0.96 (spread across instances). This is compared to 0.34-0.51 for vanilla QAOA (without NDAR), given the same number of function calls.
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