  Near-term quantum computers often have connectivity constraints, i.e.
restrictions, on which pairs of qubits in the device can interact. Optimally
mapping a quantum circuit to a hardware topology under these constraints is a
difficult task. While numerous approaches have been proposed to optimize qubit
routing, the resulting gate count and depth overheads of the compiled circuits
remain high due to the short-range coupling of qubits in near-term devices.
Resource states, such as Bell or Einstein-Podolsky-Rosen (EPR) pairs, can be
used to mediate operations that facilitate long-range interactions between
qubits. In this work, we studied some of the practical trade-offs involved in
using resource states for qubit routing. We developed a method that leverages
an existing state-of-the-art compiler to optimize the routing of circuits with
both standard gates and EPR mediated remote controlled-NOT gates. This was then
used to compile different benchmark circuits for a square grid topology, where
a fraction of the qubits are used to store EPR pairs. We demonstrate that
EPR-mediated operations can substantially reduce the total number of gates and
depths of compiled circuits when used with an appropriate optimizing compiler.
This advantage scales differently for different types of circuits, but
nonetheless grows with the size of the architecture. Our results highlight the
relevance of developing efficient compilation tools that can integrate
EPR-mediated operations.
