Quantum networks for implementing effiently a nonlocal <italic>N</italic>-qubit controlled unitary gate via non-symmetric quantum channels: Designing and optimizing

Abstract

We show how a nonlocal N-qubit controlled unitary gate can be implemented locally and effectively by using non-symmetric quantum channels. We construct respectively two quantum networks for realizing conclusively this nonlocal quantum gate. The first one hires (N-2) symmetric qubit-qubit Bell states and a non-symmetric qubit-qudit Bell state as quantum channels. The basic idea of this scheme is to use (N-2) additional levels of this qudit to "hide" certain computational states of (N-1) nonlocal control states from the conditional dynamics, which results in an effective nonlocal N-qubit controlled unitary gate design. In this scheme, however, either the number of the additional levels or that of 1-qudit gates needs to increase with N. The other one can improve significantly the local implementation of this nonlocal gate if we harness (N-1) non-symmetric qubit-qutrit Bell states as quantum channels. This scheme uses respectively (N-1) qutrits's additional levels to expose one and only one initial computational state of (N-1) nonlocal control states to the conditional dynamics. In comparison with the first one, the procedure is greatly simplified, and the total gate time is reduced. The fact that the quantum network that does the proposed implementation is built entirely of local single-body and two-body gates, and has only (3N-4) two-body gates is notable.