Geometric Refactoring of Quantum and Reversible Circuits Using Graph Algorithms

With the advent of gated quantum computers and the regular structures for 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 gated quantum computer. The proposed methodology 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 us to additionally reduce the graph according to preferred weights of desired properties. We propose two different methods of reducing the CIG: iterative reduction or the iterative isomorphism search algorithm. The proposed method is verified and tested on a set of standard benchmarks with results showing improvement on certain functions while in average improving the cost of the implementation over the current state of the art methods.