Deterministic transformations between unitary operations. Exponential advantage with adaptive quantum circuits and the power of indefinite causality

Funding

We thank Qingxiuxiong Dong, Mio Murao, Atsushi Shimbo, Akihito Soeda, Michal Studzinski for fruitful discussions and Tomasz Mlynik for noting a typo in an earlier version of the manuscript. We acknowledge Q-leap (MEXT Q-leap JPMXS0118069605) and the JSPS Kakenhi 18H04286. M.T.Q. acknowledges the Austrian Science Fund (FWF) through the SFB project BeyondC (subproject F7103), a grant from the Foundational Questions Institute (FQXi) as part of the Quantum Information Structure of Spacetime (QISS) Project (qiss.fr). The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 801110. It reflects only the authors' view, the EU Agency is not responsible for any use that may be made of the information it contains. ESQ has received funding from the Austrian Federal Ministry of Education, Science and Research (BMBWF)