Implementing entangling gates via quantum walks through branching graphs.

Efficient quantum gates are essential to quantum computing. It was found recently that quantum walks can enhance performance of quantum gates. We investigate how the propagation of a complicated, branching system can be solved analytically by first mapping it to linear chain. We found that certain types of systems, including systems of n qubits, can be algorithmically mapped to a system of disjoint linear chains. In particular, we found a solution for the 3 qubit system that performs either a trivial return walk or a return walk with a phase of pi introduced.