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Zhongguo kexue. Wulixue Lixue Tianwenxue

Frontiers of tensor networks and their applications in quantum many-body physics

Y. F. Guo, Shuo Yang

Published May 6, 2026• 0 citations
Publisher

Abstract

张量网络方法是研究量子多体物理的重要理论框架，其核心思想是利用量子态内部的纠缠结构，将具有指数复杂度的量子态拆解为由低维张量构成的网络，从而实现对多体系统的高效表达和模拟。近年来，张量网络的研究已由封闭系统拓展至非厄米及开放量子系统，在理论发展和实际应用等方面均取得显著进展。本文系统回顾了张量网络方法的发展历程，重点介绍其在量子多体物理中的代表性应用，包括强关联电子系统、量子计算与量子信息、拓扑物态等方向。研究表明，张量网络能够高效精确地模拟强关联量子多体系统，刻画各种有序态之间的竞争。混态张量网络可描述含噪声的量子态，为理解本征拓扑序和对称性保护拓扑序提供统一的理论框架。总之，张量网络已成为连接量子多体计算、量子计算、拓扑物态的通用语言，并将在量子物理的研究中发挥更关键的作用。

DOI
10.1360/sspma-2026-0184

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张量网络方法是研究量子多体物理的重要理论框架，其核心思想是利用量子态内部的纠缠结构，将具有指数复杂度的量子态拆解为由低维张量构成的网络，从而实现对多体系统的高效表达和模拟。近年来，张量网络的研究已由封闭系统拓展至非厄米及开放量子系统，在理论发展和实际应用等方面均取得显著进展。本文系统回顾了张量网络方法的发展历程，重点介绍其在量子多体物理中的代表性应用，包括强关联电子系统、量子计算与量子信息、拓扑物态等方向。研究表明，张量网络能够高效精确地模拟强关联量子多体系统，刻画各种有序态之间的竞争。混态张量网络可描述含噪声的量子态，为理解本征拓扑序和对称性保护拓扑序提供统一的理论框架。总之，张量网络已成为连接量子多体计算、量子计算、拓扑物态的通用语言，并将在量子物理的研究中发挥更关键的作用。
近年来，随着量子计算硬件设备的快速发展与逐步成熟，量子算法的实际应用场景日益丰富，量子信息处理的研究重心正逐步从基础理论探索转向更贴近现实需求的算法设计与系统实现。尤其是随着硬件技术路线的推进，量子计算在组合优化、量子模拟、密码学、机器学习等多个交叉领域展现出广阔的应用前景。在这一背景下，我国研究人员在量子算法、量子通信与量子信息理论等方面取得了一系列重要进展，推动了我国在该前沿科技领域的整体竞争力提升。借此契机，我们组织策划了“量子信息与量子计算中的前沿交叉问题”专题[1~5]，旨在集中展示科研人员在量子信息和量子计算前沿交叉领域的最新研究成果，促进本领域学者之间的深入交流与合作。本专题特别聚焦于量子技术与信息科学、物理学、数学等学科的交叉融合，围绕当前具有代表性和前瞻性的研究方向展开讨论。
Tensor networks are efficient representations of high-dimensional tensors with widespread applications in quantum many-body physics. Recently, they have been adapted to the field of machine learning, giving rise to an emergent research frontier that has attracted considerable attention. Here, we study the trainability of tensor-network based machine learning models by exploring the landscapes of different loss functions, with a focus on the matrix product states (also called tensor trains) architecture. In particular, we rigorously prove that barren plateaus (i.e., exponentially vanishing gradients) prevail in the training process of the machine learning algorithms with global loss functions. Whereas, for local loss functions the gradients with respect to variational parameters near the local observables do not vanish as the system size increases. Therefore, the barren plateaus are absent in this case and the corresponding models could be efficiently trainable. Our results reveal a crucial aspect of tensor-network based machine learning in a rigorous fashion, which provide a valuable guide for both practical applications and theoretical studies in the future.
金刚石氮-空位（nitrogen-vacancy，NV）色心量子体系因在室温条件下具有可实现单自旋寻址与操控、长量子相干时间等独特优势，在固态量子计算、量子精密测量等领域展现了巨大的应用潜力，其中单自旋的精确操控技术对于NV色心应用的发展尤为关键。NV色心量子体系中常用的自旋操控方法都是通过共振的交变磁场驱动和操控NV色心电子自旋。近年来，利用电场对量子自旋实现电调控的相关研究得到了广泛的关注。本文开展了利用交变电场对NV色心电子自旋进行调控的技术研究。通过电极所产生的交变电场成功驱动了NV色心自旋在∣ms=−1⟩|m_s=-1\rangle∣ms​=−1⟩与∣ms=+1⟩|m_s=+1\rangle∣ms​=+1⟩两个Δms=±2\Delta m_s =\pm2Δms​=±2的磁禁戒能级间的跃迁，并观测到受控自旋在相关能级的布居度周期性变化而展现出的Rabi振荡现象。进一步的研究表明电场驱动Rabi振荡的频率受驱动电场功率的调控，与驱动电场的共振频率无直接关系。将自旋电控制技术与磁控制技术方法相结合，能够实现对NV色心三个自旋能级间直接跃迁的全操控。自旋电控制技术的发展将进一步推动NV色心量子体系在量子模拟、量子计算、电磁场的精密测量等领域研究和应用的发展。
Large-scale tensor network simulations are crucial for developing robust complexity-theoretic bounds on classical quantum simulation, enabling circuit cutting approaches, and optimizing circuit compilation, all of which aid efficient quantum computation on limited quantum resources. Modern exascale high-performance computing platforms offer significant potential for advancing tensor network quantum circuit simulation capabilities. We implement TN-Sim, a tensor network simulator backend within the NWQ-Sim software package that utilizes the Tensor Algebra for Many-body Methods (TAMM) framework to support both distributed HPC-scale computations and local simulations with ITensor. To optimize the scale up in computation across multiple nodes we implement a task based parallelization scheme to demonstrate parallelized gate contraction for wide quantum circuits with many gates per layer. Through the integration of the TAMM framework with Matrix Product State (MPS) tensor network approaches, we deliver a simulation environment that can scale from local systems to HPC clusters. We demonstrate an MPS tensor network simulator running on the state-of-the-art Perlmutter (NVIDIA) supercomputer and discuss the potential portability of this software to HPC clusters such as Frontier (AMD) and Aurora (Intel). We also discuss future improvements including support for different tensor network topologies and enhanced computational efficiency.
摘 要:主流经济学因果认知先后经历决定论因果与概率因果两次革命,二者共享经典力学世界观的强本体论预设:因果关系客观先在、变量可独立分离、观测行为中立无扰、因果作用局域链式传递。这使得现代实证因果推断始终面临内生性无解、预期自实现、观测干预扭曲与非局部联动失效等底层困境。本文突破传统框架,原创性提出经济学意义上的量子因果论,将经济因果关系重构为因果叠加、因果纠缠与观测坍缩共同规定的量子态演化过程。文章严格证明:经典确定性因果是量子因果在“高频观测、大规模平均、强制度约束”条件下的统计近似;概率因果则是量子因果在“弱叠加、弱纠缠、弱观测干扰”情形下的退化特例。本文构建量子因果的公理体系、态空间表示、因果相干性判据与观测坍缩机制,首次提出经济退相干原理,有效化解量子叠加性与日常确定性因果的表观矛盾。研究表明,量子因果论能够统一解释从个体决策到宏观波动、从市场均衡到系统性风险的所有经济现象,为重新理解内生性、预期效应、政策传导与系统风险提供一般化基础,也为中国自主经济学知识体系构建提供具有范式革新意义的理论工具。 关键词:量子因果论;因果叠加;因果纠缠;观测坍缩;经济退相干
Aimed at introducing readers to the physics of strongly correlated many-body systems, these notes focus on numerical methods, with detailed discussions on implementing working code for exact diagonalization. A brief introduction to tensor network methods is also included. Prepared for the Summer School Quantumandu, held at Tribhuvan University (Kathmandu, Nepal) from 25 to 31 July 2024, as part of the ICTP's Physics Without Frontiers program, these notes are primarily intended for readers encountering this field for the first time.