In noisy quantum settings, Krylov subspace methods are limited by statistical fluctuations rather than ill-conditioning, and new imaginary and unitary filters can validate solutions without reference to the true eigenspectrum.
Ritz, ¨Uber eine neue methode zur l¨ osung gewisser variationsprobleme der mathematischen physik., Journal f¨ ur die reine und angewandte Mathematik (Crelles Journal) , 1 (1909)
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Tackling instabilities of quantum Krylov subspace methods: an analysis of the numerical and statistical errors
In noisy quantum settings, Krylov subspace methods are limited by statistical fluctuations rather than ill-conditioning, and new imaginary and unitary filters can validate solutions without reference to the true eigenspectrum.