[论文解读] Towards near-term quantum simulation of materials

Laura Clinton, Toby S. Cubitt+7 more|arXiv (Cornell University)|May 30, 2022

Quantum Computing Algorithms and Architecture参考文献 105被引用 11

一句话总结

本文提出了一种新颖的量子算法，用于近期内的材料量子模拟，通过利用材料哈密顿量在Wannier基下的局域性，实现了恒定深度的量子线路。通过采用定制的多层费米子编码，该方法确保泡利算符权重与系统尺寸无关，将SrVO₃（3×3×3晶格）的线路深度从7.5×10⁸降低至884，使无需容错错误纠正的NISQ设备上实现可行模拟成为可能。

ABSTRACT

<strong>Overview of data provided in support of <em>Towards near-term quantum simulation of materials</em></strong> Contents of this folder: `analyse_materials_results.py`: script used to generate the summary tables and figures presented in the manuscript. `towards_quantum_simulation_data`: raw data used and produced when studying various 3D materials. `towards_quantum_simulation_analysis`: tables (in `.tex` format) and figures (as PDFs) presented in the manuscript. The contents of `towards_quantum_simulation_analysis` were generated by `analyse_materials_results.py`, <br> i.e. the user need not run the script to produce the output files. <br> Users can generate these analyses directly by running ```python analyse_materials_results.py```, <br> though note the following packages will first need to be installed: `pandas &gt;= 1.2.3` `numpy &gt;= 1.23` `seaborn &gt;= 0.11.1` `lfig &gt;= 0.1.3` `matplotlib &gt; 3.7.0` <strong>Included data</strong><br> Within `towards_quantum_simulation_data`, there are subfolders <br> for each of the materials described in the manuscript, i.e. `SrVO3`, `GaAs`, `H3S`, `Si`, `Li2CuO2`. Within each material's folder are further subfolders for the `hamiltonian` and `encoding` used to represent the material, as well as subfolders for each of the `algorithms` studied. `hamiltonian`: files which specify the Hamiltonian for the material under study. There are a number of files `interactions.json` Hamiltonian terms in terms of Majorana monomials. `map_majorana_to_mode.json` keys are Majorana indices; values are the mode index to which they are associated. `map_mode_to_group.json` keys are mode indices; values are the group (or site) index to which they are associated. `map_group_to_position.json` keys are group indices; values are the corresponding 3D Cartesian coordinates of the lattice used to represent the material. `stage_data.json` contains key/value pairs of any other fields of interest. `encoding` files which specify the fermionic encoding which is customised for the material under study. `encoding.json` which details the edges of the hybrid compact encoding described in Section VI of the supplementary material. `precompiler.json` contains all the information which permits the encoding construction, including the Hamiltonian terms (`_interactions`) which match those in `hamiltonian/interactions.json`. The same mappings as present in the Hamiltonian data(a.g. `map_group_to_position`). `stage_data.json` contains key/value pairs of any other fields of interest. `algorithms` contains subfolders for each of the algorithms desribed in the manuscript Those explored for circuits depths: `TDSSplitTermsPriorityCircuitDepth` (TDS in the manuscript) `TDSSplitTermsPriorityCircuitDepthNoSwapNetwork` (TDS\*) `VQESplitTerms` (VQE) `VQESplitTermsNoSwapNetwork` (VQE*) each of which contain the files, inside the `circuitry` folder: `circuit_terms.csv`, which lists each individual term, together with their Pauli string and rotation angle, required to construct the corresponding quantum circuit `circuit_layers_to_implement.csv` groups the same terms into layers to achieve parallelism in the circuit. `stage_data.json` contains key/value pairs of any other fields of interest. and those used to compose measurement layers, as outlined in Section VII D of the supplementary material: `MeasurementCommutativity` `MeasurementNaiveQubitwise` `MeasurementNonCrossing` each of which contain the files, inside the `compilation` folder: `layers.csv` lists the terms which may be measured simultaneously to achieve the measurement strategies shown in Table S14. `stage_data.json` contains key/value pairs of any other fields of interest. <strong>CSV files</strong> In `towards_quantum_simulation_data`, there are unified CSV files containing the results of applying the procedures described in the manuscript to the target materials. `circuit_costs.csv`: results of running the circuit compiler described in the manuscript. `measurements.csv`: results of running the measurement compiler described in the manuscript. These CSVs are used in the analysis script `analyse_materials_results.py` to produce the figures and tables presented in the manuscript.

研究动机与目标

• 解决近期内材料量子模拟中高线路深度这一关键瓶颈问题。
• 开发一种即使在系统尺寸增大时也能保持低线路深度的量子算法，从而实现在NISQ硬件上的实际模拟。
• 通过优化的、具备物理意识的编译器，弥合DFT获得的材料数据与可执行量子线路之间的差距。
• 通过将材料特异性物理结构融入算法设计，证明在近期内量子计算机上实现真实材料模拟是可行的。

提出的方法

• 该方法基于Wannier函数采用多层费米子编码，以保持局域性，并确保泡利算符权重与系统尺寸无关。
• 将哈密顿量变换至Wannier基，其中跃迁积分和库仑积分随距离迅速衰减，从而实现高效的线路分解。
• 开发专用编译器，将DFT数据转换为优化的量子线路指令，整合了线路级与物理驱动的优化。
• 采用针对Wannier基定制的约旦-维格纳变换，将费米子算符映射为权重有界的泡利字符串。
• 该算法应用于时间演化和变分量子本征求解器（VQE）工作流，每个Trotter或变分层均保持恒定深度。
• 该方法利用平移对称性和能带结构，以紧凑方式表示哈密顿量，从而减少门数。

实验结果

研究问题

• RQ1 能否通过智能编码使材料模拟的量子线路深度与系统尺寸无关？
• RQ2 如何利用Wannier函数的局域性来降低哈密顿量分解中泡利算符的权重？
• RQ3 具备物理意识的算法设计在多大程度上可减少近期内量子模拟的资源开销？
• RQ4 能否通过编译器流水线将DFT数据转化为适用于真实材料的优化、低深度量子线路？

主要发现

• 对于3×3×3晶格的SrVO₃，每Trotter或变分层的线路深度从7.5×10⁸降低至884，降幅超过80万倍。
• 相同系统的量子比特需求从864个减少至180个，展示了显著的资源节省。
• 由于局域化的Wannier函数和定制化编码，该方法实现了与系统尺寸无关的恒定线路深度。
• 编译器生成的优化线路整合了基于物理的对称性与局域性，同时降低了门数和测量成本。
• 在多种材料上的数值结果证实了该方法在真实材料模拟中的通用性与可扩展性。
• 结果表明，若算法设计中融入对材料特性的深刻理解，实现真实材料模拟可能无需容错量子计算。