Researchers have developed Tomography-NMR, an open-source Python package designed to reconstruct quantum density matrices from spectroscopic measurement data. This tool addresses a gap in the documentation and availability of software for quantum state tomography (QST), a crucial process for characterizing the state of a quantum system. The package offers a transparent and reproducible implementation of the entire analysis pipeline, from spectral signal preprocessing to density matrix visualization, thereby facilitating reproducibility and standardization in quantum computing and condensed matter physics research.

The software implements a complete analysis pipeline for two-qubit quantum state tomography, utilizing the product operator formalism. It begins by Fourier-transforming time-domain signals into frequency-domain spectra. Subsequently, spectral peak intensities are mapped to expansion coefficients of the density matrix, enabling the full quantum state reconstruction. Tomography-NMR provides three integration methods tailored for different scenarios: direct peak height measurement and fixed-parameter numerical integration, which require no theoretical reference and are suitable for unknown states, and a systematic parameter optimization method against a known target state.

The software was validated using experimentally prepared two-qubit states measured via nuclear magnetic resonance (NMR) spectroscopy of coupled ³¹P nuclei. For a benchmark set of known states, the software achieved reconstruction fidelities of approximately 98% with the reference-free methods, and exceeded 99% with parameter optimization. Across a benchmark set of 20 two-qubit states, including computational basis states, Bell states, and the outputs of three fundamental quantum gates (CNOT, H, and T), average reconstruction fidelities ranged from 0.975 to 0.995. Although specifically developed for NMR, the package's modular architecture allows for adaptation to other spectroscopic platforms and measurement protocols, broadening its potential applications.