自旋系综量子态层析的计算框架
Computational framework for quantum state tomography of spin ensembles
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- Brown University（布朗大学）
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中文总结 AI 辅助
提出开源的Tomography-NMR Python包，基于乘积算子形式体系实现双量子比特自旋系综的量子态层析，提供三种积分方法，在20个基准态上平均保真度达0.975-0.995，填补了实验谱提取密度矩阵的文档空白。
中文摘要 AI 辅助
我们提出了Tomography-NMR，一个开源的Python包，用于从光谱测量数据重建量子密度矩阵。该包实现了基于乘积算子形式体系的双量子比特量子态层析的完整分析流程：原始时域信号经傅里叶变换转换为频域谱，谱峰强度映射为密度矩阵的展开系数，从而重建完整的量子态。针对不同使用场景提供了三种积分方法：直接峰高测量和固定参数数值积分无需理论参考，适用于未知态，在已知态的基准集上保真度约为98%；而针对已知目标态的系统参数优化方法，在相同基准态上重建保真度超过99%。尽管量子态层析的详细理论框架已很成熟，但从实验谱中提取密度矩阵的实际操作流程在文献中往往记录不足，并被专有软件所掩盖。本包通过提供从谱预处理到密度矩阵可视化的每一步分析的完全透明、可复现的实现，填补了这一空白。该软件已在通过耦合$^{31}$P核的核磁共振（NMR）谱学测量的实验制备双量子比特态上得到验证。在包含20个双量子比特态的基准集上，平均重建保真度范围为0.975至0.995，这些态包括计算基态、贝尔态以及三个基本量子门（CNOT、H和T）的输出。尽管是为NMR开发的，其模块化架构便于适应其他光谱平台和替代测量协议。
英文摘要
We present Tomography-NMR, an open-source Python package that reconstructs quantum density matrices from spectroscopic measurement data. The package implements a complete analysis pipeline for two-qubit quantum state tomography based on the product operator formalism: raw time-domain signals are Fourier-transformed into frequency-domain spectra, spectral peak intensities are mapped to expansion coefficients of the density matrix, and the full quantum state is reconstructed. Three integration methods are provided for different use cases: direct peak height measurement and fixed-parameter numerical integration require no theoretical reference and are suited to unknown states, achieving fidelities of approximately 98\% on a benchmark set of known states, while a systematic parameter optimization against a known target state achieves reconstruction fidelities exceeding 99\% for the same benchmark states. While the detailed theoretical framework for quantum state tomography is well established, the practical procedures for extracting density matrices from experimental spectra are often inadequately documented in the literature and obscured within proprietary software. This package addresses that gap by providing a fully transparent, reproducible implementation of every analysis step, from spectral preprocessing to density matrix visualization. The software has been validated on experimentally prepared two-qubit states measured via nuclear magnetic resonance (NMR) spectroscopy of coupled $^{31}$P nuclei. Average reconstruction fidelities range from 0.975 to 0.995 across a benchmark set of 20 two-qubit states, including the computational basis states, Bell states, and the outputs of three fundamental quantum gates (CNOT, H, and T). Although developed for NMR, the modular architecture facilitates adaptation to other spectroscopic platforms and alternative measurement protocols.
