Geometric Refactoring of Quantum and Reversible Circuits: Quantum Layout

With the advent of gated quantum computers and regular structures of the qubit layout, methods for placement, routing, noise estimation and logic to hardware mapping become imminently required. In this paper, we propose a method for quantum circuit layout that is intended to solve such problems when mapping a quantum circuit to a quantum computer. The proposed method starts by building a Circuit Interaction Graph (CIG) that represents the ideal hardware layout minimizing the distance and path length between the individual qubits. The CIG is also used to introduce a qubit noise model. Once constructed, the CIG is iteratively reduced to a given architecture (qubit coupling model) specifying the neighborhood, qubits, priority and qubits noise. The introduced constraints allow to additionally reduce the graph according to preferred weights of desired properties. The proposed method is verified and tested on a set of standard benchmarks.