Abstract
Given a quantum gate implementing a -dimensional unitary operation , without any specific description but , and permitted to use times, we present a universal probabilistic heralded quantum circuit that implements the exact inverse , whose failure probability decays exponentially in . The protocol employs an adaptive strategy, proven necessary for the exponential performance. It requires that , proven necessary for the exact implementation of with quantum circuits. Moreover, even when quantum circuits with indefinite causal order are allowed, uses are required. We then present a finite set of linear and positive semidefinite constraints characterizing universal unitary inversion protocols and formulate a convex optimization problem whose solution is the maximum success probability for given and . The optimal values are computed using semidefinite programing solvers for when and for . With this numerical approach we show for the first time that indefinite causal order circuits provide an advantage over causally ordered ones in a task involving multiple uses of the same unitary operation.
- Received 22 October 2018
- Revised 2 September 2019
DOI:https://doi.org/10.1103/PhysRevLett.123.210502
© 2019 American Physical Society