Akihito Soeda

In this work, we report a deterministic and exact protocol to reverse any unknown qubit-unitary and qubit-encoding isometry operations. We present the semidefinite programming (SDP) to search the Choi matrix representing a quantum circuit reversing any unitary operation. We derive a quantum circuit transforming four calls of any qubit-unitary operation into its inverse operation by imposing the SU(2)×SU(2) symmetry on the Choi matrix. This protocol only applies only for qubit-unitary operations, but we extend this protocol to any qubit-encoding isometry operations. For that, we derive a subroutine to transform a unitary inversion protocol to an isometry inversion protocol by constructing a quantum circuit transforming finite sequential calls of any isometry operation into random unitary operations.