Using Spectral Graph Theory to Map Qubits onto Connectivity-Limited Devices

TL;DR

This paper introduces a spectral graph theory-based heuristic for efficiently mapping logical qubits to physical qubits in connectivity-limited quantum devices, minimizing additional SWAP gates.

Contribution

It presents a novel spectral graph drawing approach for qubit mapping, extending to various connectivities beyond one-dimensional arrangements.

Findings

Effective qubit placement reduces the number of SWAP gates.

Spectral methods provide a computationally efficient heuristic.

Potential extension to complex connectivity topologies.

Abstract

We propose an efficient heuristic for mapping the logical qubits of quantum algorithms to the physical qubits of connectivity-limited devices, adding a minimal number of connectivity-compliant SWAP gates. In particular, given a quantum circuit, we construct an undirected graph with edge weights a function of the two-qubit gates of the quantum circuit. Taking inspiration from spectral graph drawing, we use an eigenvector of the graph Laplacian to place logical qubits at coordinate locations. These placements are then mapped to physical qubits for a given connectivity. We primarily focus on one-dimensional connectivities, and sketch how the general principles of our heuristic can be extended for use in more general connectivities.