Scaling spectroscopic quantum state tomography beyond two qubits

Extend the Tomography-NMR software to three or more qubits by developing spectral deconvolution methods for overlapping multiplet peaks, constructing the enlarged tomography lookup tables, and validating the resulting reconstruction algorithms experimentally.

Background

Tomography-NMR currently reconstructs two-qubit density matrices from NMR spectra using product-operator coefficients extracted from resolved doublet peaks. For systems with three or more coupled qubits, the operator basis grows to 4N − 1 non-identity operators, and the number of required measurements increases exponentially.

Larger coupled-spin systems also produce increasingly crowded spectra in which multiplet peaks overlap. The present implementation relies on simple doublet integration and does not provide spectral deconvolution, so extending the package beyond two qubits requires both new algorithms for separating overlapping spectral contributions and experimental validation of the resulting higher-dimensional reconstructions.

References

The current implementation does not include such deconvolution, and extending the software to three or more qubits remains an open problem requiring both algorithmic development and careful experimental validation.

— Computational framework for quantum state tomography of spin ensembles  (2609.11868 - Seo et al., 10 Sep 2026) in Section Extensibility, subsection “Higher-dimensional systems”