What is sample-based quantum diagonalization?

Sample-based quantum diagonalization is a quantum algorithm technique that estimates the eigenvalues and eigenvectors of matrices using measurements from quantum hardware, rather than requiring full quantum state tomography. This approach reduces the number of quantum measurements needed, making it more practical for near-term quantum devices with limited coherence times. IBM's method enables users to diagonalize matrices on their quantum processors by leveraging statistical sampling of quantum measurement outcomes.

Source: IBM Research | 2026-05-06