一维量子系统自由能的快速算法

IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Samuel O. Scalet
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引用次数: 0

摘要

我们考虑的问题是逼近具有有限范围的平移不变一维量子自旋系统的自由能密度。由于与已知硬度结果的问题密切相关,这个问题的复杂性并不复杂,但最近有人提出了一种经典的亚对数时间算法[Fawzi 等人,2022]。结合之前用于相关问题的几种算法技术,我们提出了一种渐近优于这一结果的算法,并给出了严格的运行时间界限。我们的主要技术是使用相变不存在结果中已知的荒木扩展和矩阵积算子构造。我们还回顾了一种使用量子信念传播的相关方法[Kuwahara et al., 2018],结合我们的发现,可以得到等效的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A faster algorithm for the free energy in one-dimensional quantum systems
We consider the problem of approximating the free energy density of a translation-invariant, one-dimensional quantum spin system with finite range. While the complexity of this problem is nontrivial due to its close connection to problems with known hardness results, a classical subpolynomial-time algorithm has recently been proposed [Fawzi et al., 2022]. Combining several algorithmic techniques previously used for related problems, we propose an algorithm outperforming this result asymptotically and give rigorous bounds on its runtime. Our main techniques are the use of Araki expansionals, known from results on the nonexistence of phase transitions, and a matrix product operator construction. We also review a related approach using the Quantum Belief Propagation [Kuwahara et al., 2018], which in combination with our findings yields an equivalent result.
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来源期刊
Journal of Mathematical Physics
Journal of Mathematical Physics 物理-物理:数学物理
CiteScore
2.20
自引率
15.40%
发文量
396
审稿时长
4.3 months
期刊介绍: Since 1960, the Journal of Mathematical Physics (JMP) has published some of the best papers from outstanding mathematicians and physicists. JMP was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. The Journal of Mathematical Physics (JMP) features content in all areas of mathematical physics. Specifically, the articles focus on areas of research that illustrate the application of mathematics to problems in physics, the development of mathematical methods for such applications, and for the formulation of physical theories. The mathematics featured in the articles are written so that theoretical physicists can understand them. JMP also publishes review articles on mathematical subjects relevant to physics as well as special issues that combine manuscripts on a topic of current interest to the mathematical physics community. JMP welcomes original research of the highest quality in all active areas of mathematical physics, including the following: Partial Differential Equations Representation Theory and Algebraic Methods Many Body and Condensed Matter Physics Quantum Mechanics - General and Nonrelativistic Quantum Information and Computation Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory General Relativity and Gravitation Dynamical Systems Classical Mechanics and Classical Fields Fluids Statistical Physics Methods of Mathematical Physics.
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