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arXiv:2207.13030

Efficient protocol for solving combinatorial graph problems on neutral-atom quantum processors

Wesley da Silva Coelho, Mauro D'Arcangelo, Louis-Paul Henry

Published Jul 26, 2022• 3 citations
arXivHTMLPDF

Abstract

On neutral atom platforms, preparing specific quantum states is usually achieved by pulse shaping, i.e., by optimizing the time-dependence of the Hamiltonian related to the system. This process can be extremely costly, as it requires sampling of the final state in the quantum processor many times. Hence, determining a good pulse, as well as a good embedding, to solve specific combinatorial graph problems is one of the most important bottlenecks of the analog approach. In this work, we propose a novel protocol for solving hard combinatorial graph problems that combines variational analog quantum computing and machine learning. Our numerical simulations show that the proposed protocol can reduce dramatically the number of iterations to be run on the quantum device. Finally, we assess the quality of the proposed approach by estimating the related Q-score, a recently proposed metric aimed at benchmarking QPUs.

DOI
10.48550/arxiv.2207.13030

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On neutral atom platforms, preparing specific quantum states is usually achieved by pulse shaping, i.e., by optimizing the time-dependence of the Hamiltonian related to the system. This process can be extremely costly, as it requires sampling of the final state in the quantum processor many times. Hence, determining a good pulse, as well as a good embedding, to solve specific combinatorial graph problems is one of the most important bottlenecks of the analog approach. In this work, we propose a novel protocol for solving hard combinatorial graph problems that combines variational analog quantum computing and machine learning. Our numerical simulations show that the proposed protocol can reduce dramatically the number of iterations to be run on the quantum device. Finally, we assess the quality of the proposed approach by estimating the related Q-score, a recently proposed metric aimed at benchmarking QPUs.
Analog quantum processors based on Rydberg atom arrays are a powerful platform for many-body quantum simulation, combinatorial optimization, and graph machine learning. As these devices become increasingly accessible, establishing confidence in their outputs requires predictive models that quantitatively connect microscopic hardware imperfections to empirical results. Here, we present a noise-aware emulation framework that propagates the dominant noise mechanisms throughout the full computation cycle to predict device behavior. We validate the framework by benchmarking two representative protocols, quantum annealing and post-quench dynamics, on three Pasqal quantum processors where classical simulations still provide ground truth. Across all three devices, the measured observables fall within the uncertainty envelopes predicted by the emulator. Beyond reproducing the data, the framework isolates which physical mechanism dominates in each operating regime, provides quantitative guidance for algorithm design and hardware improvements, and establishes a foundation for verifying analog processors in regimes beyond classical reach.
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Neutral atom platforms are analogue quantum simulators that offer the possibility to map graphs onto a 2D qubit register using programmable Rubidium atoms arrays, whose valence electrons' energy state is used as qubits, using optical tweezers. This makes it possible to implement algorithms for solving graph combinatorial optimization and Quantum Machine Learning (QML) tasks, such as graph classification. However, the restrictions of real hardware, as well as the very low number of publicly available machines, make such implementation non-trivial. In this work, we manage to compute the Quantum Evolution Kernel (QEK) to extract the features from graphs of the PROTEINS dataset using the 256-qubits Aquila platform (available through AWS) and then we apply classical Machine Learning (ML) techniques for the final classification. The method is benchmarked against classical kernels, resulting in slightly better performance, proving the effectiveness of the method, even in the case of a noisy quantum simulator.
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We propose a numerical approach to design highly efficient adiabatic schedules for analog quantum computing, focusing on the maximum-independent-set problem and neutral atom platforms. On the basis of a representative dataset of small graphs, we present numerical evidence that the optimum schedules depend principally on the hardness of the problem rather than on its size. These schedules perform better than the benchmark protocols and admit a straightforward implementation in the hardware. This allows us to extrapolate the results to larger graphs and to successfully solve moderately hard problems using QuEra’s 256-qubit Aquila computer. We believe that extending our approach to hybrid algorithms could be the key to solving the hardest instances with the current technology, making yet another step toward real-world applications.