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arXiv 2408.03026quant-phcond-mat.dis-nn
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深度展开的局部量子退火

Deep Unfolded Local Quantum Annealing

Shunta Arai, Satoshi Takabe

AI总结:

本文提出将深度展开方案与局部量子退火相结合,通过反向传播从训练数据中学习参数,并在Sherrington-Kirkpatrick模型上验证其收敛速度和性能优于原始LQA,且参数可推广到未知实例和不同系统规模。

摘要:

局部量子退火(LQA)是一种迭代算法,旨在求解组合优化问题。其灵感来源于量子退火(QA),后者利用绝热时间演化来确定给定目标函数的全局最小值。在最初的LQA中,经典哈密顿量通过梯度下降进行最小化。LQA的性能依赖于参数的选择。由于原始代价函数的非凸性质,LQA常常陷入局部极小值,从而限制了其有效性。为应对这一挑战,我们将LQA与深度展开方案相结合,从而能够通过反向传播从训练数据中调节参数。作为演示,我们将深度展开的LQA应用于Sherrington-Kirkpatrick模型,该模型是统计物理学中的一个基本模型。我们的研究结果表明,深度展开的LQA优于原始LQA,展现出显著的收敛速度提升和性能改进。由于训练得到的参数可以推广到未知实例和不同的系统规模,我们的结果具有重要的实际意义,并为现实世界应用提供了有价值的见解。

英文摘要:

Local quantum annealing (LQA), an iterative algorithm, is designed to solve combinatorial optimization problems. It draws inspiration from QA, which utilizes adiabatic time evolution to determine the global minimum of a given objective function. In the original LQA, the classical Hamiltonian is minimized via gradient descent. The performance of LQA depends on the choice of the parameters. Owing to the non-convex nature of the original cost function, LQA often becomes trapped in local minima, limiting its effectiveness. To address this challenge, we combine LQA with a deep unfolding scheme, which enables us to tune the parameters from the training data via back-propagation. {As a demonstration, we apply the deep unfolded LQA to the Sherrington-Kirkpatrick model, which is a fundamental {model} in statistical physics.} Our findings exhibit that deep unfolded LQA outperforms the original LQA, exhibiting remarkable convergence speed and performance improvement. As the trained parameters can be generalized to unknown instances and different system sizes, our results have significant practical implications and provide valuable insights for real-world applications.

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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