Abstract
In this work, we report a deterministic and exact algorithm to reverse any unknown qubit-encoding isometry operation. 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 algorithm only applies only for qubit-unitary operations, but we extend this algorithm to any qubit-encoding isometry operations. For that, we derive a subroutine to transform a unitary inversion algorithm to an isometry inversion algorithm by constructing a quantum circuit transforming finite sequential calls of any isometry operation into random unitary operations.
