随机量子控制的统计力学:d-adic Rényi 电路

IF 2.4 3区 物理与天体物理 Q1 Mathematics
Andrew A. Allocca, Conner LeMaire, Thomas Iadecola, Justin H. Wilson
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引用次数: 0

摘要

在具有较大现场希尔伯特空间维度的多体系统中,量子信息的动力学可以用有效统计力学模型进行启发性描述。受这一事实的启发,我们揭示了三个独立模型之间的联系:具有随机控制的经典混沌 d-adic 雷尼图谱、该图谱的量子类似物量子比特,以及随机图上的波茨模型。经典模型及其量子类似模型在随机应用的控制图的驱动下,在混沌阶段和受控阶段之间有一个共同的过渡,控制图试图使系统有序化。在量子模型中,控制图需要测量,同时驱动晚期稳态纠缠内容的相变。为了探索控制和纠缠转换的相互作用,我们从量子模型中推导出一个有效的波茨模型,并用它来探测见证这两种转换的信息理论量。我们发现,纠缠转换属于键珀尔帖普遍性类别,与其他测量诱导的相变一致,而控制转换则受经典随机漫步的支配。通过改变模型中的一个参数,可以使这两个相变相吻合,其结果与之前量子模型小规模数值研究中观察到的行为一致。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Statistical mechanics of stochastic quantum control: d-adic Rényi circuits

Statistical mechanics of stochastic quantum control: d-adic Rényi circuits
The dynamics of quantum information in many-body systems with large onsite Hilbert space dimension admits an enlightening description in terms of effective statistical mechanics models. Motivated by this fact, we reveal a connection between three separate models: the classically chaotic d-adic Rényi map with stochastic control, a quantum analog of this map for qudits, and a Potts model on a random graph. The classical model and its quantum analog share a transition between chaotic and controlled phases, driven by a randomly applied control map that attempts to order the system. In the quantum model, the control map necessitates measurements that concurrently drive a phase transition in the entanglement content of the late-time steady state. To explore the interplay of the control and entanglement transitions, we derive an effective Potts model from the quantum model and use it to probe information-theoretic quantities that witness both transitions. The entanglement transition is found to be in the bond-percolation universality class, consistent with other measurement-induced phase transitions, while the control transition is governed by a classical random walk. These two phase transitions can be made to coincide by varying a parameter in the model, producing a picture consistent with behavior observed in previous small-size numerical studies of the quantum model.
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来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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