Publisher Correction: Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution

Correction to: Nature Physics https://doi.org/10.1038/s41567-019-0704-4, published online 11 November 2019.

In the version of this Article originally published online, in the first equation in the sentence beginning “One popular approach is”, the term ‘$- \partial _\beta \left| {\it{\varPhi} \left( \beta \right)} \right\rangle =$’ was repeated; the equation should have read “$- \partial _\beta \left| {\it{\varPhi} \left( \beta \right)} \right\rangle = \left\{ {\left| \it{\varPhi} \right\rangle ,\;\hat H\left| \it{\varPhi} \right\rangle ,\hat H^2\left| \it{\varPhi} \right\rangle \ldots } \right\}\left| {\it{\varPhi} \left( \beta \right)} \right\rangle$”. In the same sentence, in the expression “〈Φ(0)|Ψ ≠ 0”, the right ket bracket was missing and should have read ‘〈Φ(0)|Ψ〉≠ 0’’. All versions of this Article have been amended.