We introduce a near-term algorithm for extracting the eigenvalues and eigenvalues of a density matrix, with application to error mitigation, entanglement spectroscopy, and principal component analysis (PCA).

PCA is an important primitive in big-data analysis. Previous quantum algorithms for PCA are difficult to implement on NISQ computers. Here, we propose an algorithm that minimizes both the qubit and circuit-depth requirements for this application. The makes large-scale PCA a more near-term application. In addition, our algorithm is useful error mitigation (see figure).

For details see "Variational Quantum State Eigensolver" by M. Cerezo, Kunal Sharma, Andrew Arrasmith, Patrick J. Coles. arXiv:2004.01372.