We gratefully acknowledge discussions with R. Bousso, D. Harlow, F. Machado, I. Siddiqi, L. Susskind and Q. Zhuang. Additionally, we thank E. Edwards for the development of Fig. 1. This work is supported in part by the ARO through the IARPA LogiQ programme, the AFOSR MURI on Quantum Measurement and Verification, the ARO MURI on Modular Quantum Circuits, the DOE ASCR Program, and the NSF Physics Frontier Center at JQI. T.S. and N.Y.Y. acknowledge support from the Office of Science, Office of High Energy Physics of the US Department of Energy under contract number DE-AC02-05CH11231 through the COMPHEP pilot “Probing information scrambling via quantum teleportation” and the Office of Advanced Scientific Computing Research, Quantum Algorithm Teams Program. Research at the Perimeter Institute is supported by the Government of Canada through Innovation, Science and Economic Development Canada and by the province of Ontario through the Ministry of Economic Development, Job Creation and Trade. T.S. acknowledges support from the National Science Foundation Graduate Research Fellowship Program under grant number DGE 1752814.

Reviewer information

Nature thanks Daniel Harlow and the other anonymous reviewer(s) for their contribution to the peer review of this work.