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计算物理学

computational physics

© 2025 The Yuan Group

计算物理研究组

COMPUTATIONAL PHYSICS GROUP

中国武汉大学袁声军教授领导的计算物理研究团队

A group led by Prof. Shengjun Yuan at Wuhan University , Wuhan, China.

紧束缚传播法

TBPM

Tight-binding propagation method (TBPM) is an efficient method for solving ultra-large tight binding models with BILLIONS of orbitals. It maps the eigenvalue problem to the correlation functions determined by the time-dependent wave function, which propagates following the Schrödinger equation. Taking advantages of Chebyshev polynomials expansion of the propagation operator and the sparsity of tight-binding Hamiltonians, only sparse matrix-vector (spMv) operations are needed during the calculation, yielding linear scaling in both CPU time and RAM usage with respect to model size. TBPM is capable of evaluating many physical quantities, including DOS, local DOS, carrier density, optical (AC) conductivity, electrical (DC) conductivity, carrier velocity, mobility, elastic mean free path, Anderson localization length, polarization function, dielectric function, energy loss function, absorption spectrum, plasmon dispersion, plasmon lifetime and damping rate, quasi-eigenstate and real-space charge density, etc. For details of the numerical methods, please refer to TBPLaS: A tight-binding package for large-scale simulation, Computer Physics Communications 285, 108632 (2023).

紧束缚传播法是一种高效求解十亿轨道级别超大规模紧束缚模型的计算方法。该方法将本征值问题转换为随机波函数含时演化的问题，将演化算符展开为切比雪夫多项式，并充分利用紧束缚哈密顿量的稀疏性，在计算过程中只涉及稀疏矩阵-向量乘法，实现了线性标度的计算资源消耗。该方法可以计算态密度、局域态密度、载流子浓度、（光）电导率、载流子速率、迁移率、平均自由程、极化函数、介电函数、电子能量损失谱、吸收光谱、等离激元色散关系、寿命、准本征态等十几种物理性质。数值方法的详细内容可参见 TBPLaS: A tight-binding package for large-scale simulation, Computer Physics Communications 285, 108632 (2023).

密度泛函传播法

DFPM

密度泛函传播方法（DFPM）是一种基于密度泛函理论（DFT）的从头计算方法。与传统的对角化方法不同，DFPM利用随机态的含时传播基于哈密顿量直接获得电荷密度分布，自洽过程无需进行任何对角化。其内存开销和计算时间均与体系规模线性相关，可在中等硬件配置的计算机上对数百万原子体系进行自洽密度泛函理论计算。数值方法的详细内容可参见 A Time-Dependent Random State Approach for Large-scale Density Functional Calculations, Chin. Phys. Lett. 40, 027101 (2023) (Express Letter) 。

The density functional propagation method (DFPM) is an ab initio computational approach based on density functional theory (DFT). Unlike traditional diagonalization methods, DFPM utilizes the time propagation of stochastic states to directly obtain the electron charge density distribution from the Hamiltonian, achieving self-consistency without any diagonalization. Its memory usage and computational time both scale linearly with system size, enabling self-consistent density functional theory calculations for systems containing millions of atoms on computers with moderate hardware configurations. For details of the numerical methods, please refer to A Time-Dependent Random State Approach for Large-scale Density Functional Calculations, Chin. Phys. Lett. 40, 027101 (2023) (Express Letter) .

低维量子体系

Low-dimensional Quantum Systems

低维量子体系，例如二维材料（2D）、纳米管（1D）和量子点（0D）， 由于维度降低，与传统的三维（3D）材料不同。 它们具有许多有趣的物理性质，对未来新型 电子器件和 光子器件的发展至关重要。 我们结合了多种理论方法，包括第一性原理计算、紧束缚近似、 分子动力学模拟以及其他最先进的数值方法， 深入研究低维量子体系新颖性质，并与全球实验组保持紧密合作。

Low-dimensional Quantum Systems, such as two-dimensional materials (2D), nanotubes (1D) and quantum dots (0D), are different from conventional three-dimensional (3D) materials due to the reduced dimensionality. They have many interesting physical properties and are believed to be essential for the development of new electronic and photonic devices in the future. Combinations of different theoretical approaches, including first-principles calculations, tight-binding approximation, molecular dynamics simulations, and other state-of-the-art numerical methods, have been implemented in the study of these systems, in strong collaborations with experimental groups worldwide.

代表性论文：

Selected Publications:

Moiré 超晶格

Moire Superlattice

当两个周期性晶格以相对扭转角或 晶格常数不匹配的方式叠加时，会形成所谓的 Moiré 超晶格。在实验上，它已通过堆叠多种二维晶体而实现，包括 石墨烯等。Moiré 超晶格中涌现出一系列重要物理现象，如 平带态、Mott 绝缘体和 非常规超导性。然而，其超胞往往包含 海量原子，超出了常规方法的计算能力。我们的策略是构建 高精度紧束缚模型，并利用 TBPM 研究其性质，同时开发了软件包 TBPLaS 以处理大尺度体系。

When two periodic lattices are stacked with a relative twist angle or a lattice mismatch, a moiré superlattice can be formed. Experimentally, such structures have been realized by stacking graphene and other 2D crystals. Moiré superlattices host key phenomena such as flat bands, Mott insulators, and unconventional superconductivity. Their supercells often contain an enormous number of atoms, beyond conventional methods. Our strategy is to construct high-accuracy TB models and study them with TBPM, supported by our package TBPLaS for large-scale systems.

代表性论文：

Selected Publications:

分形

Fractals

近年来在纳米材料设计和制造方面的进展，使得实验上可以在复杂几何结构中实现电子调控，例如 分形结构。分形是一种具有 自相似性的层次结构，拥有 非整数维度。其研究价值不仅源于独特的美学特征，更因其能够探索 非整数维度的物理特性而备受关注。由于缺乏 空间平移对称性，分形结构与周期性晶体存在显著差异， 布洛赫定理在此类体系中不再适用。我们基于 TBPM 方法，从理论和数值上研究电子在 分数维空间中运动的量子力学性质。

The recent progress in the design and fabrication of nanoscale materials has enabled the experimental realization of electrons control in complex geometries such as fractals. Fractals are hierarchical structures characterized by self-similarity and non-integer dimensions. Their significance arises not only from their aesthetic properties but also from their potential to explore physical phenomena in non-integer dimensional spaces. Due to the absence of spatial translational symmetry, fractal structures differ significantly from periodic crystals, as Bloch's theorem is no longer applicable. Based on the TBPM method, we theoretically and numerically investigate the quantum mechanical properties of electrons roaming in fractional-dimensional spaces.

代表性论文：

Selected Publications:

准晶

Quasicrystals

准晶具有准周期结构，缺乏长程有序性。它缺乏 平移对称性，但具有旋转对称性。自 1982 年 Dan Shechtman 首次发现以来，已有数百种准晶被报道和确认，大多存在于铝合金中。我们最近对准晶的理论研究主要集中在 十二角准晶，这类准晶最近在 扭曲双层石墨烯中被成功制备。准晶中的 层间杂化产生了丰富的物理现象，这些现象在具有平移对称性的周期晶体中并不存在。

A quasicrystal has a quasiperiodic structure that is ordered but not periodic. It lacks translational symmetry but presents rotational symmetries. Since the original discovery by Dan Shechtman in 1982, hundreds of quasicrystals have been reported and confirmed, most often in aluminium alloys. Our recent theoretical investigation of quasicrystals mainly focuses on dodecagonal quasicrystals, which have been recently fabricated in twisted bilayer graphene. Interlayer hybridization in quasicrystals leads to rich physical phenomena not present in periodic crystals with translational symmetry.

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代表性论文：

Selected Publications:

量子自旋系统、中性原子系统与量子计算

Quantum Spin Systems, Neutral Atomic Systems, and Quantum Computation

量子系统有效地表现出经典行为的方式，对量子物理的基础理论至关重要。越来越明确的是，量子系统的经典性特征可由其环境诱导产生。过去几年中，我们使用了一个简化模型来研究量子自旋系统的退相干和热化过程。研究表明，诸如正则系综这样的经典态可以通过纯量子动力学途径达到。进一步地，我们将量子自旋系统的建模扩展至量子计算机模拟，其中逻辑操作通过具有特定哈密顿量的量子自旋系统构建。这是一种高效的模拟方法；尽管可模拟的量子比特数受限于计算机内存，但它仍提供理论工具，用于研究真实设备中量子计算机的特性，并考虑环境效应和内部或外部噪声。近来，我们将研究范围扩展至中性原子系统，关注其在量子计算和量子模拟中的应用。我们致力于利用中性原子系统中的退相干、热化以及纠缠动力学等基本过程，通过可控环境耦合诱导或抑制量子系统的经典行为，构造更高效的中性原子阵列。

The manner in which a quantum system becomes effectively classical is of great importance for the foundations of quantum physics. It has become increasingly clear that the symptoms of classicality of quantum systems can be induced by their environments. Over the past years, we used a toy model to explore decoherence and thermalization of quantum spin systems. We demonstrate that a classic state such as canonical ensemble is reachable via pure quantum dynamics. An extension of the modeling of quantum spin systems leads to the simulation of quantum computers, in which logical operations are constructed by a quantum spin system with a specified Hamiltonian. This is a very efficient way to simulate quantum computers; although the number of qubits that can be simulated is limited by machine memory, it still provides a theoretical tool to investigate the properties of quantum computers in real devices considering the effects of environments and/or internal or external noise. Recently, we have expanded the scope of our research to neutral atomic systems, focusing on applications in quantum computing and quantum simulation. We leverage fundamental processes—including decoherence, thermalization, and entanglement dynamics—to explore how to induce or suppress the classical behavior of quantum systems, aiming to construct more efficient neutral atomic arrays.

代表性论文：

Selected Publications:

量子计算与量子模拟云平台：构建面向中性原子体系的软件生态

Quantum Computation and Simulation Cloud Platform: Building a Software Ecosystem for Neutral Atom Systems

量子计算的发展，依赖于量子比特硬件性能的持续突破与软件生态系统的协同演进。硬件决定了量子计算能力的上限，而软件则定义了如何有效利用并最终将这种潜力转化为科研与产业价值。当前，多数研究集中于底层物理系统的构建，其控制系统往往与特定硬件高度绑定，依赖科研人员手动进行资源分配、调度与脉冲编译。随着量子比特规模的扩张与计算任务的日趋复杂，这种模式已成为制约量子计算发展的瓶颈。因此，发展一个层次清晰、接口标准、具备普适性的大规模量子比特操控软件体系，已成为本领域的迫切需求。

为应对这一挑战，我们构建了“量子计算与量子模拟云平台”（https://quantumclouds.cn）。该平台旨在建立连接用户与前沿量子计算资源的桥梁，将一系列独立的量子软件工具集成为一个功能完备、协同工作的在线环境，从而为科研、教学与开发人员提供一个高效、易用的量子计算软件生态。平台的核心功能覆盖了量子系统的模拟、编译与操控全流程。

1. 平台集成的多维度量子系统模拟引擎

  • 量子线路模拟器：包括支持高精度仿真的全振幅模拟器与适用于更大规模特定结构线路的张量网络模拟器。
  • 量子动力学模拟器：平台提供原子量子计算专用动力学模拟器，从系统哈密顿量出发，通过高阶时间演化算法精确还原原子比特的真实动力学过程，内置相位抖动、频率漂移等噪声模型。也提供通用动力学模拟器研究普适性二能级系统演化。
  • 大规模量子系统模拟器 (TBPLaS)：专用于大尺度凝聚态物理问题，可高效模拟数十亿原子规模的复杂量子体系，为新材料与量子物性研究提供独特计算支持。

2. 平台内嵌的全流程编译服务

  • 逻辑层编译：将用户输入的标准量子线路（如 OpenQASM）进行深度优化，通过线路重构压缩门数与深度，并映射为中性原子体系支持的原生逻辑门集合。
  • 脉冲层编译：基于优化后的逻辑线路，自动进行物理层编译，包括原子量子比特最优布局映射，并生成可在硬件上精确执行的脉冲波形序列。

3. 平台的远程自动化硬件操控接口

云平台提供标准化远程操控接口，编译器生成的脉冲时序文件可远程自动加载驱动原子量子计算原型机。用户无需操作复杂设备，即可完成算法提交、编译优化、真机执行与数据回传的全流程闭环，极大提升研发效率。

The advancement of quantum computing relies on the synergistic evolution of breakthroughs in quantum hardware and the development of a comprehensive software ecosystem. While hardware capabilities determine the upper limits of quantum computation, it is the software that dictates how effectively this potential can be harnessed and translated into scientific and industrial value. Currently, a significant portion of research focuses on the development of underlying physical systems, with control systems tightly coupled to specific hardware and reliant on manual resource allocation, scheduling, and pulse compilation by researchers. As the scale of quantum bits and the complexity of computational tasks increase, this paradigm has become a bottleneck, hindering progress, making the development of a standardized, hierarchical, and universally applicable software architecture for large-scale qubit manipulation an urgent priority.

To address this challenge, we have developed the Quantum Computation and Simulation Cloud Platform (https://quantumclouds.cn). The platform integrates independent quantum software tools into a fully functional, collaborative online environment, bridging users with cutting-edge quantum computing resources. It provides a robust and user-friendly software ecosystem for quantum computing, covering the full workflow of quantum system simulation, compilation, and control.

1. Integrated Multi-Faceted Quantum System Simulation Engines

  • Quantum Circuit Simulators: Full-amplitude simulator for high-precision medium-scale systems and tensor network simulator for large-scale structured circuits.
  • Quantum Dynamics Simulators: Dedicated dynamics simulator for neutral atom quantum computing, reproducing atomic qubit dynamics from the Hamiltonian with high-order time-evolution algorithms, including phase jitter and frequency drift noise models. Also offers a general-purpose simulator for universal two-level systems.
  • Large-Scale Quantum System Simulator (TBPLaS): Specialized for large-scale condensed matter problems, efficiently simulating up to several billion atoms, supporting research on Moiré superlattices, fractals, and advanced materials.

2. Embedded End-to-End Compilation Service

  • Logical Layer Compilation: Optimizes standard quantum circuits (e.g., OpenQASM), reducing gate count and depth, mapping to the native gate set of neutral atom systems.
  • Pulse Layer Compilation: Converts optimized logical circuits into physical pulses, performing optimal qubit layout mapping and generating executable waveform sequences.

3. Remote and Automated Hardware Control Interface

Provides a standardized remote control interface allowing pulse sequences to be loaded and executed automatically on neutral atom quantum prototypes, enabling a full closed-loop workflow entirely in the cloud, greatly enhancing R&D efficiency.

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