量子信息递归优化算法,PRX Quantum

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量子信息递归优化算法
PRX Quantum ( IF 9.3 ) Pub Date : 2024-05-03 , DOI: 10.1103/prxquantum.5.020327
Jernej Rudi Finžgar _{1,

2} , Aron Kerschbaumer _{1,

2} , Martin J.A. Schuetz _{3,

4} , Christian B. Mendl _{2,

5} , Helmut G. Katzgraber ₃

Affiliation

我们提出并实现了一系列用于组合优化问题的量子信息递归优化（QIRO）算法。我们的方法利用量子资源来获取用于特定问题的经典简化步骤的信息，从而递归地简化问题。这些简化步骤解决了量子分量（例如局部性）的限制，并确保了约束优化问题中解决方案的可行性。此外，我们使用回溯技术来进一步提高算法的性能，而不增加对量子硬件的要求。我们通过向 QIRO 提供量子近似优化算法浅层电路的经典模拟的相关性来展示我们方法的功能，解决具有数百个变量的最大独立集和最大可满足性问题的实例。我们还演示了如何将 QIRO 部署在中性原子量子处理器上以查找大型独立图集。总之，即使量子资源相对较弱，我们的方案也取得了与经典启发式相当的结果。此外，提高这些量子资源的质量可以提高算法的性能。值得注意的是，QIRO 的模块化性质提供了各种修改途径，将我们的工作定位为更广泛的组合优化混合量子经典算法的模板。

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Quantum-Informed Recursive Optimization Algorithms

We propose and implement a family of quantum-informed recursive optimization (QIRO) algorithms for combinatorial optimization problems. Our approach leverages quantum resources to obtain information that is used in problem-specific classical reduction steps that recursively simplify the problem. These reduction steps address the limitations of the quantum component (e.g., locality) and ensure solution feasibility in constrained optimization problems. Additionally, we use backtracking techniques to further improve the performance of the algorithm without increasing the requirements on the quantum hardware. We showcase the capabilities of our approach by informing QIRO with correlations from classical simulations of shallow circuits of the quantum approximate optimization algorithm, solving instances of maximum independent set and maximum satisfiability problems with hundreds of variables. We also demonstrate how QIRO can be deployed on a neutral atom quantum processor to find large independent sets of graphs. In summary, our scheme achieves results comparable to classical heuristics even with relatively weak quantum resources. Furthermore, enhancing the quality of these quantum resources improves the performance of the algorithms. Notably, the modular nature of QIRO offers various avenues for modifications, positioning our work as a template for a broader class of hybrid quantum-classical algorithms for combinatorial optimization.

更新日期：2024-05-04

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