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arXiv 2005.14059quant-phcond-mat.stat-mech
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近期器件的量子采样算法

Quantum Sampling Algorithms for Near-Term Devices

Dominik S. Wild, Dries Sels, Hannes Pichler, Cristian Zanoci, Mikhail D. Lukin

摘要:

从经典吉布斯分布的有效采样是一个重要的计算问题,其应用范围从统计物理到蒙特卡罗和优化算法到机器学习。我们介绍了一个家庭的量子算法,通过准备一个状态编码整个吉布斯分布提供无偏的样本。我们表明,这种方法导致了一个经典的马尔可夫链算法的几个例子,包括伊辛模型和两个不同的图形的加权独立集的采样加速。我们的方法将计算复杂性与相变联系起来,提供了量子加速的物理解释。此外,它打开了一扇大门,探索潜在的有用的采样算法在近期的量子设备上的算法,从独立集的某些图形采样可以自然地实现使用里德伯原子阵列。

英文摘要:

Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of quantum algorithms that provide unbiased samples by preparing a state encoding the entire Gibbs distribution. We show that this approach leads to a speedup over a classical Markov chain algorithm for several examples including the Ising model and sampling from weighted independent sets of two different graphs. Our approach connects computational complexity with phase transitions, providing a physical interpretation of quantum speedup. Moreover, it opens the door to exploring potentially useful sampling algorithms on near-term quantum devices as the algorithm for sampling from independent sets on certain graphs can be naturally implemented using Rydberg atom arrays.

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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