Correction to: npj Quantum Information https://doi.org/10.1038/s41534-022-00522-6, published online 03 February 2022

The original version of this Article contained errors in the fourth sentence of the second paragraph in the subsection “Overview of the algorithm” and fourth sentence of the first paragraph in the subsection “Photon emission ordering” under Results and Discussion, first sentence and seventh sentence in the subsection “Complexity of finding optimal photon emission orderings” under Methods, in which wrong terminology ‘NP-complete’ were used. The correct version states ‘NP-hard’ in place of ‘NP-complete’ for all four above locations.

This has now been corrected in both the PDF and HTML versions of the Article.

The original version of the Supplementary Information associated with this Article contained an error in the in-line equation of the second last sentence of Supplementary Note 2, which incorrectly read \(\left| \varphi \right\rangle _L = e^{i\frac{\varphi }{2}X_L}\left| + \right\rangle _L,\). The correct version reads \(\left| \varphi \right\rangle _L = e^{i\frac{\varphi }{2}Z_L}\left| + \right\rangle _L,\) with the ‘XL’ operator replaced by ‘ZL’.

The HTML has been updated to include a corrected version of the Supplementary Information.