Implementation of multipartite unitary operations with limited resources - Dominic Berry

In quantum information processing it is often necessary to perform operations between qubits (or qudits) which do not directly interact. It is therefore important to know what resources are needed to achieve these operations. In particular, if the interaction is weak it would be desirable to implement it using only a small amount of entanglement and communication. I show that it is possible to implement evolution under multipartite tensor product Hamiltonians using a small amount of entanglement and a small amount of communication in some of the directions. This improves on previous work in three main ways: 1. Previous work only considered simple cases, such as bipartite two-qubit unitaries. This method applies for general multipartite tensor product Hamiltonians. It may also be applied to sums of these Hamiltonians via the Trotter formula. 2. The entanglement required is only 5.6418t|H|. In contrast, the entanglement required for the scheme of Cirac, Dür, Kraus and Lewenstein (which is limited to the two-qubit Ising interaction) requires entanglement of 5.9793t|H|. 3. For many implementations, compression is used to achieve the implementations using average communication in some of the directions as low as the entanglement. The scheme of Cirac, Dür, Kraus and Lewenstein requires a large amount of communication.