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arXiv 2302.00429quant-ph
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纠缠在基于量子松弛的优化算法中的作用

The Role of Entanglement in Quantum-Relaxation Based Optimization Algorithms

Kosei Teramoto, Rudy Raymond, Hiroshi Imai

AI总结:

本研究探讨了量子纠缠在基于量子松弛的优化算法(QRAO)中的作用,发现量子性虽不总能提升性能,但在部分实例中能帮助找到最优解,表明QRAO不仅能扩展可解问题规模,还能从纠缠中获益。

摘要:

量子随机存取优化器(QRAO)是Fuller等人提出的一种基于量子松弛的优化算法,它利用量子随机存取码(QRAC)将二进制优化的多个变量编码在单个量子比特中。与QAOA等标准量子优化器不同,它利用的是在计算基下非对角的局部量子哈密顿量的本征态。有迹象表明,用量子纠缠可能不需要用标准量子优化器求解二进制优化问题,因为对角哈密顿量的最大本征态包含经典态。在本研究中,虽然量子性并不总能提升量子松弛的性能,但我们观察到存在一些实例,量子松弛在量子性的帮助下成功找到了最优解。我们的结果表明,QRAO不仅能扩展在有限量子计算机上可解的二进制优化问题实例规模,还能从量子纠缠中获益。

英文摘要:

Quantum Random Access Optimizer (QRAO) is a quantum-relaxation based optimization algorithm proposed by Fuller et al. that utilizes Quantum Random Access Code (QRAC) to encode multiple variables of binary optimization in a single qubit. Differing from standard quantum optimizers such as QAOA, it utilizes the eigenstates of local quantum Hamiltonians that are not diagonal in the computational basis. There are indications that quantum entanglement may not be needed to solve binary optimization problems with standard quantum optimizers because their maximal eigenstates of diagonal Hamiltonians include classical states. In this study, while quantumness does not always improve the performance of quantum relaxations, we observed that there exist some instances in which quantum relaxation succeeds to find optimal solutions with the help of quantumness. Our results suggest that QRAO not only can scale the instances of binary optimization problems solvable with limited quantum computers but also can benefit from quantum entanglement.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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