Determining Minimal SWAP Operations for the Qubit-Mapping Problem using Quantum Information Theory

Abstract

This thesis presents a novel formulation to study the qubit-mapping problem (QMP). The presented for- mulation redefines the problem in terms of density matrices which represent the quantum algorithm and the underlying architecture—allowing the implementation of techniques from quantum information theory to es- tablish a bounded metric space for comparing these density matrices. The main contribution of this thesis is implementing this formulation in an algorithm to determine the minimal bound on the required number of SWAP operations for a pairing of a quantum algorithm to an underlying device where the initial mapping has been provided. Benchmarks have shown a clear dependence on the β-value. Emphasising the need for future investigations of this dependence to enhance the algorithm’s effectiveness for more extensive algorithms and architectures. While it is essential to acknowledge that the approach may not currently rival the state of the art.