Two-qubit Unitary Operations Research Articles

Exact two-qubit universal quantum circuit.

We provide an analytic way to implement any arbitrary two-qubit unitary operation, given an entangling two-qubit gate together with local gates. This is shown to provide explicit construction of a universal quantum circuit that exactly simulates arbitrary two-qubit operations in SU(4). Each block in this circuit is given in a closed form solution. We also provide a uniform upper bound of the applications of the given entangling gates, and find that exactly half of all the controlled-unitary gates satisfy the same upper bound as the CNOT gate. These results allow for the efficient implementation of operations in SU(4) required for both quantum computation and quantum simulation.

Optimal entanglement generation from quantum operations

We consider how much entanglement can be produced by a non-local two-qubit unitary operation, $U_{AB}$ - the entangling capacity of $U_{AB}$. For a single application of $U_{AB}$, with no ancillas, we find the entangling capacity and show that it generally helps to act with $U_{AB}$ on an entangled state. Allowing ancillas, we present numerical results from which we can conclude, quite generally, that allowing initial entanglement typically increases the optimal capacity in this case as well. Next, we show that allowing collective processing does not increase the entangling capacity if initial entanglement is allowed.